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SAVAGE 


L l D K.AK.  I 

OF  THE 

ILN  I V E R.5  ITY 
Of  ILLINOIS 

622.  OS 
C63c9 


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' 


THE 


T.  E,  SAVAGE. 


COAL^METAL  MINERS’ 
POCKETBOOK 

OF 

. PRINCIPLES,  RULES,  FORMULAS, 

AND  TABLES. 


SPECIALLY  COMPILED  AND  PREPARED  FOR  THE  CONVENIENT  USE  OF 
MINE  OFFICIALS,  MINING  ENGINEERS,  AND  STUDENTS  PREPAR- 
ING THEMSELVES  FOR  CERTIFICATES  OF  COMPETENCY 
AS  MINE  INSPECTORS  OR  MINE  FOREMEN. 


NINTH  EDITION:  REVISED  AND  ENLARGED, 

WITH 

ORIGINAL  MATTER. 


“Though  index  learning  turns  no  student  pale, 
It  grasps  the  Eel  ol  Science  by  the  tail.” 

Pope. 


SCRANTON,  PA.: 

INTERNATIONAL  TEXTBOOK  COMPANY. 

1907. 


Copyright,  1890,  1893,  1900, 

BY 

Th,e  Colliery  Engineer  Company. 

Copyright,  1901,  1905, 

BY 

International  Textbook  Company. 
Entered  at  Stationers’  Hall,  London, 
All  Rights  Reserved. 


PRINTED  BY 

International  textbook  Company, 
Scranton,  pa.,  U.  S.  A. 


£2 


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Preface  to  Ninth  Edition. 


In  this  edition,  the  principal  changes  are  in  the  section  on 
wire  rope,  which  has  been  greatly  enlarged  by  the  addition 
of  material  treating  on  cableways,  tramways,  transmission  of 
\ power  by  wire  rope,  and  wire-rope  calculations.  A glossary  of 
~ wire-rope  terms  has  been  added  which  has  been  checked  up 
by  the  leading  wire-rope  makers  of  the  United  States,  and 
therefore  represents  the  latest  practice. 

A number  of  changes  have  been  made  in  this  and  previous 
editions,  based  on  suggestions  of  users  of  the  Pocketbook. 
We  will  appreciate  any  notice  of  errors  or  omissions  so  that 
future  editions  may  be  made  as  complete  and  accurate  as 
possible. 

4 


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Preface  to  Eighth  Edition. 


The  eighth  edition  of  The  Coal  and  Metal  Miners’  Pocket- 
book  is  an  exact  reprint  of  the  seventh  edition,  issued  to 
supply  the  demand  while  the  ninth  edition  was  being  pre~ 
pared,  and  in  which  a number  of  changes  will  be  made. 


Preface  to  Seventh  Edition. 


The  speedy  exhaustion  of  the  sixth  edition  of  The  Coal  and 
Metal  Miners’  Pocketbook,  coupled  with  a steady  and  increas- 
ing demand  for  it,  has  made  necessary  this  seventh  edition. 
In  it  a few  typographical  errors  which  unavoidably  occurred 
(as  is  the  case  in  every  book  of  this  nature  and  size),  have 
been  corrected,  all  departments  have  been  carefully  revised, 
improved,  and  brought  up  to  date,  and  considerable  new 
matter  has  been  added.  Thus,  the  value  of  the  work  has  been 
materially  increased.  The  value  of  suggestions  as  to  improve- 
ments in  this  edition  made  by  users  of  the  sixth  edition  is 
acknowledged  with  thanks,  and  we  request  that  users  of  this 
new,  or  seventh,  edition,  will  kindly  call  our  attention  to  any 
errors  or  omissions  they  may  discover,  so  that  future  editions 
may  be  kept  fully  abreast  with  the  requirements  of  mining 
practice  as  such  practice  continues  to  advance. 


v 


; • 


Preface  to  Sixth  Edition. 


The  fifth  edition  of  The  Coal  and  Metal  Miners’  Pocketbook 
was  very  kindly  received,  and  the  criticisms  of  it  were  most 
friendly  and  flattering. 

The  sixth  edition  has  been  compiled  under  particularly 
favorable  circumstances  and  is  much  more  complete  than  any 
previous  edition. 

Prominent  engineers  and  manufacturers  of  mining  machinery 
throughout  the  world  have  kindly  criticized  the  previous 
edition,  have  suggested  wherein  it  could  be  improved,  and 
have  sent  to  us  information  from  their  private  note  books 
that  has  never  before  been  published. 

The  staff  of  Mines  and  Minerals,  the  large  force  of  Mining, 
Mechanical,  and  Electrical  Engineers  connected  with  The 
International  Correspondence  Schools,  and  many  other  engi- 
neers and  mine  managers  have  contributed  to  it. 

All  this  material  has  been  carefully  sifted,  verified  wherever 
possible,  and  combined  with  the  data  in  the  former  edition. 
By  careful  selection  and  rewriting,  or  by  different  methods  of 
presentation,  it  has  been  possible  to  include  essentially  all  that 
was  in  the  fifth  edition,  and  at  the  same  time  to  add  from  one- 
third  to  one-half  again  as  much  entirely  new  matter,  without 
materially  increasing  the  size  of  the  book. 

Every  portion  of  the  fifth  edition  has  been  either  entirely 
rewritten,  or  revised,  enlarged,  and  brought  up  to  date.  New 
illustrations  have  been  drawn,  and  the  entire  book  has  been 
printed  from  new  plates. 

The  sections  on  Mathematics  and  Surveying  have  been 
amplified  by  the  addition  of  new  tables  and  by  text  treating 
of  the  Solar  Transit  and  Pocky  Mountain  methods  of  sur- 
veying. 

The  sections  on  Hydraulics;  the  Application  of  Electricity  to 
Mining;  Timbering,  Haulage,  Blasting,  Ore  Dressing,  and  Coal 
Washing  are  entirely  new. 


vii 


viii 


PREFACE . 


The  sections  on  Prospecting,  Ventilation,  and  Methods  of 
Working  have  been  entirely  rewritten,  enlarged,  and  greatly 
improved. 

The  tables  of  Logarithms,  Trigonometric  Functions,  etc.  have 
been  reset  from  the  latest  corrected  editions  of  standard  tables. 
The  Traverse  Table  has  been  greatly  reduced  in  length,  but 
without  affecting  its  efficiency,  while  the  table  of  Squares, 
Cubes,  etc.  has  been  added  to  by  the  addition  of  Circumfer- 
ences and  Areas  of  Circles. 

The  Glossary,  which  contains  about  2,500  words,  is  believed 
to  be  the  most  complete  mining  glossary  ever  published,  as  it 
is  a combination  of  all  the  mining  glossaries  extant  of  which 
the  compilers  could  hear. 

Wherever  possible,  credit  has  been  given  the  authorities 
from  whom  data  have  been  taken,  but  in  such  a work  it  is  mani- 
festly impossible  to  give  full  credit  for  everything  that  has 
been  extracted,  quoted,  and  compiled,  and  we  can  only  in  this 
very  general  way  acknowledge  our  indebtedness  to  the  large 
number  of  authors  and  engineers  whom  we  have  failed  to 
mention  by  name  in  the  text. 

No  one  appreciates  as  fully  as  does  the  editor  of  such  a pub- 
lication the  value  of  the  suggestions  and  data  that  have  been 
so  generously  furnished  to  assist  us  in  the  compilation.  We 
shall  be  greatly  obliged  to  all  readers  of  this  volume  who  may 
call  our  attention  to  any  errors  that  they  may  discover,  or  to 
the  omission  of  any  data  that  they  may  feel  the  lack  of,  so 
that  attention  may  be  given  to  these  matters  in  future  editions. 


TABLE  OF  CONTENTS. 


( For  detailed  Index , see  back  of  volume.  See  also  Glossary  of  Minina  Terms, 
•page  565.) 


WEIGHTS  AND  MEASURES. 

The  Metric  System.— l. 

Weights.— Troy,  1;  Apothecaries’,  1;  Avoirdupois,  2;  Metric,  2. 

M easu  res  of  Length.—  American  and  British,  2;  Reduction  of  Inches 
to  Decimals  of  a Foot,  2;  Decimals  of  a Foot  for  Each  ^ of  an  Inch,  3; 
Metric,  3;  Russian,  3;  Prussian,  Danish,  and  Norwegian,  3;  Austrian,  3: 
Swedish,  4;  Chinese,  4. 

Measures  of  Area.— American  and  British,  4;  Table  for  Reducing 
Square  Feet  to  Acres,  4;  Metric,  4. 

Measures  of  Volume.— American  and  British,  5;  Metric,  5;  Liquid 
(U.  S.),  5;  Dry  (U.  S.),  5;  British  Imperial  (Liquid  and  Dry),  5; 
Contents  of  Cylinders  or  Pipes  for  1 Foot  in  Length,  6;  Mexican, 
Central  American,  and  South  American  Weights  and  Measures,  7. 

Conversion  Tables.— Customary  to  Metric,  7;  Metric  to  Customary,  9. 

Money.— United  States,  10;  British,  10;  Standard  U.  S.  Coins,  Weights  and 
Fineness,  Space  Required  to  Store,  10;  Conversion  of  English  and 
American  Money  Values,  11;  Value  of  Foreign  Coins,  U.  S.  Treasury 
Department,  11;  Carat  Measures,  12. 

Timber  and  Board  Measure.— Rule  for  Measuring,  12;  Timber 
Measure,  12;  Round  Timber,  Table  of  £ Girths,  13;  Board  Measure,  13. 

Mathematics.— General  Principles,  14;  Signs  and  Abbreviations,  14. 

Arithm  etic.— To  Cast  the  Nines  Out  of  a Number,  15;  To  Prove  Addition, 
Subtraction,  Multiplication,  and  Division,  15;  Common  Fractions,  15; 
Decimals,  16;  Simple  and  Compound  Proportion,  18;  Involution.  19; 
Evolution,  19;  Percentage,  20;  Arithmetical  Progression,  20;  Geomet- 
rical Progression,  21;  Logarithms,  22. 

Geometry.— Principles,  24;  Practical  Problems  in  Geometrical  Construc- 
tion, 25. 

Mensuration.— Surfaces,  28;  Solids,  33;  Prismoidal  Formula,  34. 

Plane  Trigonometry.— Principles  of  Trigonometry,  34;  Practical 
Examples  in  the  Solution  of  Triangles,  35. 

Surveying.— The  Compass,  38;  Adjustments,  38;  Use  of  Compass,  39; 
Magnetic  Variation,  39;  Isogonic  Chart,  39;  The  Vernier,  39;  The 
Transit,  40;  Adjustments,  41;  The  Chain,  or  Steel  Tape  and  Pins,  42; 
Plumb-Bob,  44;  The  Clinometer  or  Slope  Level,  44;  Field  Notes  for  an 
Outside  Compass  Survey,  44;  Transit  Surveying,  45;  Determination  of 
Meridian  by  Polaris,  46;  Determination  of  Meridian  With  Solar  Attach- 
ment, 47;  Use  of  Solar  Attachment,  47;  General  Remarks,  49;  Plotting 
49;  Coordinates,  51;  Contents  of  Coal  Seam,  52;  Leveling,  53;  Adjust- 
ments, 53;  Use  of  Level,  54;  Field  Work  54;  Notes,  55;  Trigonometric 
Leveling,  56;  Underground  Surveying,  56;  Establishment  and  Marking 
of  Stations,  57;  Centers,  59;  Notes,  60;  Stope  Books,  62;  Mine  Corps,  66; 
Surveying  Methods,  67;  Outside  Surveys,  67;  Inside  Surveys,  67;  Closing 
Surveys,  68;  Connecting  Outside  and  Inside  Works  Through  Shafts 
and  Slopes,  68;  Notes  on  Mapping,  74;  Locating  Errors,  76;  Locating 
Special  Work,  77;  Calculation  of  Areas,  77;  Railroad  Curves,  78;  Hints 
to  Beginners,  80;  Theory  of  Stadia  Measurements,  81;  Tables,  88. 


X 


TABLE  OF  CONTENTS. 


Fi  ruirNTS  OF  M EC han  i CS.— Levers,  91;  Wheel  and  Axle,  92;  Inclined 
E E Plane  S93; Sere w,  93;  ^ Wedge,  93;  Pulleys,  94;  Composition  of  Forces,  95. 

Friction— Coefficients,  95;  Shafting,  96;  Friction  of  Mine  Cars,  96. 
Lubrication— Best  Lubricants  for  Different  Purposes,  102. 

APPLIED  MECHANICS. 

n__ _ . . _TlJ  Aun  WnrwT  OF  Materials. — Wooden  Beams,  102;  Iron 
S and  Ste«£  Beamsf  lo3?  Stractural-Steel  I Beams  104;  Pillars  or  Props, 
105;  Cast-Iron  Columns,  106;  Specific  Gravity,  Weight,  and  Properties 
of  Materials,  107;  Line  Shafting,  110;  Weight  of  Castings,  Sheets,  and 
Plates,  111;  Weight  of  Cast-Iron  Pipe  per  Foot  m Pounds, 113 ’ Wood 
Screws,  113;  Weight  of  Wrought  Iron,  114;  Iron  Required  for  1 Mile  ot 
Track,  117;  Rails,  Splices,  and  Bolts  for  1 Mile  of  Track,  117;  Wire  and 
Sheet-Metal  Gauges,  122d. 

...  « p e»-n pm l Remarks  118-  Flat  Ropes,  119;  Standard  Hoisting 

lUssfep.llES 

127;  Ordinary  Long  Splice,  129;  Chains,  129. 

H fD  P?e!™Is of  ifiqueffisr?n 

WR^ht  A*’  ffi|htVANltch  V138  0t&igink  Wefrt  fssT  CoefficffiSt  gohf 

isit 

SSffi  water,  H3; 

mMMxmm 

mmmm 

Impulse  Wheels,  158;  Turbines,  158. 

PuMPMaCH,^ 

K^ASgTMr ^gt|V  W^and  the  H=wer 
wXrKaised  by' a 

Delivered'^r  ^M^utef^fo^V^rhra^Sized  ^mps,  16^  Mis^llanTO^w 

KSSSS  PAu^KpSpb  for  Acid  Water,  165. 


TABLE  OF  CONTENTS. 


xi 


FORMS  OF  POWER. 

Fuels.— Table  of  Combustibles,  166;  Analyses  and  Heating  Values  of 
American  Coals,  168;  Thermal  Unit,  168;  Composition  of  Fuels,  169; 
Classification,  Composition,  and  Properties  of  Coals,  169;  Weights  and 
Measurements  of  Coal,  170;  Coke,  172;  Analysis  of  Coal,  173. 

Steam.— High-Pressure  Steam,  175;  Expansion  of  Steam,  176:  Condens- 
ers, 176. 

Bo  l leRS.- Lancashire  Boiler,  177;  Horsepower  of  Boilers,  177;  Heating 
Surface,  177;  Choice  of  a Boiler,  179;  Explosions,  179;  Questions  to  Be 
Asked  Concerning  New  Boilers,  180;  Incrustation  and  Scale,  182; 
Covering  for  Boilers,  Steam  Pipes,  Etc.,  183;  Data  for  Proportioning  an 
Economizer,  185;  Care  of  Boilers,  185;  Thickness  of  Boiler  Iron,  187; 
Pressure  of  Steam  at  Different  Temperatures,  188;  Maximum  Economy 
of  Plain  Cylinder  Boilers,  188;  Scheme  for  Boiler  Test,  188;  Chim- 
neys, 189. 

Steam  Engines.— What  Is  a Good  Engine?  190;  Determination  of 
M.  E.  P.,  190;  Buies  for  Engine  Drivers,  191;  Belting  and  Velocity  of 
Pulleys,  193. 

Compressed  Air.— Classification  of  Compressors,  194;  Construction  of 
Compressors,  194;  Theory  of  Air  Compression,  194;  Rating  of  Com- 
pressors, 195;  Cooling,  195;  Dry  Versus  Wet  Compressors,  196;  Trans- 
mission of  Air  in  Pipes,  196;  Losses  in  the  Transmission  of  Compressed 
Air,  198;  Friction  of  Air  in  Pipes,  201;  Loss  of  Pressure  in  Pounds  per 
Square  Inch,  by  Flow  of  Air  in  Pipes,  202;  Loss  by  Friction  in  Elbows, 
203. 

Electricity.— Practical  Units,  203;  Strength  of  Current,  203;  Electric 
Pressure  or  Electromotive  Force,  203;  Resistance,  203;  Power,  204;  Cir- 
cuits, 205;  Series  Circuits,  205;  Parallel  Circuits,  206;  Resistance  in 
Series  and  Multiple,  206;  Shunt,  207;  Electric  Wiring,  207;  Materials, 
207;  Forms  of  Conductors,  207;  Wire  Gauge,  207;  Estimation  of  Cross- 
Section  of  Wires,  207;  Properties  of  Copper  Wire,  208;  Properties  of 
Aluminum  and  Copper,  209;  Estimation  of  Resistance,  209;  Calculation 
of  Wires  for  Electric  Transmission,  210;  Current  Estimates,  212;  Incan- 
descent Lamps,  213;  Arc  Lamps,  214;  Motors,  214;  Conductors  for  Electric- 
Haulage  Plants,  214;  Dynamos  and  Motors,  215;  Direct-Current  Dynamos, 
215;  Factors  Determining  E.  M.  F.  Generated,  218;  Field  Excitation  of 
Dynamos,  218;  Series-Wound  Dynamos,  219,  Shunt- Wound  Dynamos, 
219;  Compound-Wound  Dynamos,  219;  Direct-Current  Motors,  220; 
Principles  of  Operation,  220;  Speed  Regulation  of  Motors,  222;  Connec- 
tions for  Continuous-Current  Motors,  223;  Alternating-Current  Dyna- 
mos, 224;  Single-Phase  Alternators,  225;  Multiphase  Alternators,  225; 
Uses  of  Multiphase  Alternators,  226;  Alternating-Current  Motors,  226; 
Synchronous  Motors,  226;  Induction.  Motors,  227,  Transformers,  228; 
Electric  Signaling,  229;  Batteries,  229;  Bell  Wiring,  230;  Special  Mine 
Applications,  233;  Telephones,  233. 


MINING. 

Prospecting.— Outfit  Necessary,  235;  Plan  of  Operations,  236;  Geological 
Table,  237;  Coal  or  Bedded  Materials,  238;  Formations  Likely  to  Con- 
tain Coal,  238;  Ore  Deposits,  238;  Position  of  Veins  and  Ore  Deposits,  239; 
Underground  Prospecting,  239;  Prospecting  for  Placer  Deposits,  240; 
Value  of  Free  Gold  per  Ton  of  Quartz,  241;  Gems  and  Precious  Stones, 
241;  Exploration  by  Drilling  or  Bore  Holes,  242;  Earth  Augers,  242; 
Percussion  or  Churn  Drills,  242;  The  Diamond  Drill,  243;  Selecting  the 
Machine,  243;  Size  of  Tools,  243;  Drift  of  Diamond-Drill  Holes,  243; 
The  Surveying  of  Diamond-Drill  Holes,  243;  The  Value  of  the  Record 
Furnished  by  the  Diamond  Drill,  244;  The  Arrangement  of  Holes,  244; 
The  Cost  and  Speed  of  Drilling,  244;  Records  of  Cost  per  Foot  in 
Diamond  Drilling,  246;  Cost  of  Operation  per  Month  of  Bed-Rock 
Exploration,  247;  Magnetic  Prospecting,  248;  Prospecting  for  Petro- 
leum, Natural  Gas,  and  Bitumen,  249;  Construction  of  Geological  Maps 
and  Cross-Sections,  249;  To  Obtain  Dip  and  Strike  From  Bore-Hole 
Records,  250;  Sampling  and  Estimating  the  Amount  of  Mineral  Avail- 
able, 251;  Diagram  for  Reporting  on  Mineral  Lands,  252. 


Xll 


TABLE  OF  CONTENTS. 


Opening  a Mine  —Opening  a Gold  Mine,  258;  Form  of  Shafts,  259;  Com- 
partments, 259;  Shaft  Sinking,  259;  Size  of  Shaft,  259;  Forepoling,  260; 
Metal  Linings  Forced  Down,  260;  Pneumatic  Method  of  Shaft  Sinking, 
260;  Freezing  Process,  260;  Table  of  Well-Known  Shafts,  261;  Kind- 
Chaudron  Method,  262;  Long-Hole  Process,  262;  Comparison  of  Methods 
of  Shaft  Sinking,  262;  Sinking  Head-Frames,  262;  Sinking  Engines,  263; 
Tools,  263;  Speed  and  Cost  of  Sinking,  263;  Slope  Sinking,  263;  The 
Sump,  264;  Driving  the  Gangway,  264;  Levels  in  Metal  Mines,  264; 
Mining  Tunnels,  265. 

Mine  Timber  and  Timbering. — Choice  of  Timber,  265,  Preserva- 
tion of  Timber,  265;  Placing  of  Timber,  266;  Size  of  Timber,  267;  Joints 
in  Mine  Timbering,  267;  Undersetting  of  Props,  267;  Forms  of  Mine 
Timbering  and  Underground  Supports,  267;  Gangway  or  Level  Tim- 
bers, 268;  Shaft  Timbering,  270;  Square  Sets,  270;  Landing,  Plats,  or 
Stations,  272;  Special  Forms  of  Supports,  272;  Iron  and  Steel  Supports, 
272;  Trestles,  274;  Timber  Head-Frames  or  Head-Gears,  275;  Steel  Shaft 
Bottoms,  276. 

Methods  of  Working  — Open  Work,  277;  Steam-Shovel  Mines,  278, 
ETMUhng,°278;  ^ Cableways,  278;  Placers,  278;  Hydraulicking,  278;  Dredg- 
ing, 279;  Closed  Work,  279;  Bedded  Deposits,  279;  Coal  Mining,  279; 
Roof  Pressure,  280;  Character  of  Floor,  280;  Systems  of  Working  Coal, 
280;  Room-and-Pillar  System,  280;  Longwall  Method,  281;  Panel  System, 
283;  Control  of  Roof  Pressure,  2S4;  Number  of  Entries,  284;  Direction 
of  Face,  284;  Size  of  Pillars,  285;  Room  Pillars,  286;  Barrier  Pillars,  28/; 
Weight  on  Pillars  in  Pounds  per  Square  Inch,  287;  Drawing  Pillars,  289; 
Compressive  Strength  of  Anthracite,  290;  Gob  Fires,  291;  Spontaneous 
Combustion,  291;  Coal  Storage,  291;  Modifications  of  Room-and-Pillar 
Methods,  291;  Buggy  Breasts,  291;  Chute  Breasts,  292;  Pillar-and-Stall, 
292;  Connellsville  Region,  293;  Pittsburg  Region,  295;  Clearfield  Region, 
295;  Reynoldsville  Region,  295;  West  Virginia,  296;  Alabama  Methods, 
297;  George’s  Creek,  297;  Blossburg  Region,  Pa.,  298;  Indiana  Mining,  298; 
Iowa  Mining,  299;  Tesla,  California,  Method,  300;  New  Castle,  Colorado 
Method,  302;  Modifications  of  Longwall  Methods,  302;  Overhand 
Stoping,  304;  Methods  of  Mining  Anthracite,  305;  Brown’s  Method, 
306;  Battery  Working,  307;  Single-Chute  Battery,  309;  Double-Chute 
Battery,  309;  Rock-Chute  Mining,  310;  Williams’  Method,  312;  Running 
of  Coal,  312;  Hints  for  Working  Thin  Seams,  313;  Flushing  of  Culm,  314; 
Methods  of  Mining  Mineral  Deposits,  316;  Winzes,  316;  Raises,  316; 
Stoping,  316;  Flat  Deposits,  318;  Large  Deposits,  Over  8 Feet  Thick  318; 
Square  Work,  318;  Filling,  319;  Slicing,  319;  Transverse  Rooming  With 
Filling1,  319;  Caving,  320;  Square-Set  System,  321;  Irregular  Deposits, 
321;  Coyoting,  321;  Special  Methods,  322:  Frozen  Ground,  322;  Leaching, 


Wyoming  Region  (Pa. ),  325^  Prices  of  Coal,  326;  Cost  of  Coking  Coal,  328. 

Explosives  — Low  Explosives,  329;  High  Explosives,  329;  Thawing 
Dynamite,  329;  Common  Blasting  Explosives,  330;  Drilling,  330;  Diam- 
eter of  Hole,  330;  Amount  of  Charge,  331;  Tamping,  331;  Firing,  331; 
Detonators;  332;  Electric  Firing,  332;  Power  of  an  Explosive,  334; 
Arrangement  of  Drill  Holes,  335. 

Machine  Mining.— Pick  Machines,  336;  Chain-Cutter  Machines,  337; 
Shearing,  337;  Capacity,  337. 

Ventilation  of  M i n es.—  Atmosphere,  337;  Atmospheric  Pressure,  339; 

N Barometric  Variations,  339;  Barometers,  339;  Water  Column  Corre- 
sponding to  Anv  Mercury  Column,  340;  Barometric  Elevations,  340; 
Chemistry  of  Gases.  341;  Absolute  Temperature,  344; . Absolute  Pressure, 
345;  Diffusion  and  Transpiration,  346;  Gases  Found  in  Mines,  348;  Con- 
stants for  Mine  Gases,  349;  Gas  Feeders,  352;  Pressure  of  Occluded 
Gases,  352;  Amount  of  Gas,  352;  Outbursts  of  Gas,  3o2;  Testing  for  Gas 
by  Lamp  Flame,  354;  Safety  Lamps,  355;  Lamps  tor  Testing,  355;  Detec- 
tion of  Small  Percentages  of  Gas,  356;  Oils  for  Safety  Lamps,  3o6,  Types 
of  Safety  Lamps,  356;  Locking  Lamps,  358;  Cleaning  Safety  Lamps,  3o8* 
Relighting  Stations,  359;  Illuminating  Power  of  Safety  Lamps,  359 
Explosive  Conditions  in  Mines,  359;  Derangement  of  Ventnating  Cu.r 
rent,  359;  Sudden  Increase  of  Gas,  360;  Effect  of  Coal  Dust  in  Mine 


TABLE  OF  CONTENTS. 


xiii 


Workings,  360;  Pressure  as  Affecting  Explosive  Conditions,  361;  Rapid 
Succession  of  Shots  in  Close  Workings,  361;  Mine  Explosions,  361; 
Recoil  of  an  Explosion,  361;  Exploring  Workings  After  a Serious  Explo- 
sion,361;  Quantity  of  Air  Required  for  Ventilation,  362;  Elements  in  Ven- 
tilation, 363;  Power  of  the  Current,  363;  Mine  Resistance,  364;  Velocity 
of  the  Air-Current,  364;  Measurement  of  Ventilating  Currents,  364; 
Water  Gauge,  365;  Thermometer^,  366;  Calculation  of  Mine  Resistance, 
366;  Calculation  of  Power  or  Units  of  Work  per  Minute,  367;  Equivalent 
Orifice,  367;  Potential  Factor  of  a Mine,  367;  Formulas,  370;  Variation 
of  the  Elements,  372;  Practical  Splitting  of  the  Air-Current,  373; 
Primary  Splits,  374;  Secondary  Splits,  374;  Tertiary  Splits,  374;  Equal 
Splits  of  Air,  374;  Unequal  Splits  of  Air,  374;  Natural  Division  of  the 
Air-Current,  374;  Calculation  of  Natural  Splitting,  374;  Proportional 
Division  of  the  Air-Current,  375;  Box  Regulator,  375;  Door  Regulator, 
375;  Splitting  Formulas,  378;  Methods  and  Appliances  in  the  Ventila- 
tion of  Mines,  381;  Ascensional  Ventilation,  381;  General  Arrangement 
of  Mine  Plan,  381;  Natural  Ventilation,  381;  Ventilation  of  Rise  and 
Dip  Workings,  382;  Influence  of  Seasons,  382;  Construction  of  a Mine 
Furnacp,  383;  Air  Columns  in  Furnace  Ventilation,  384;  Inclined  Air 
Columns,  384;  Calculation  of  Ventilating  Pressure  in  Furnace  Ventila- 
tion, 384;  Calculation  of  Motive  Column  or  Air  Column,  384;  Influence 
of  Furnace  Stack,  385;  Mechanical  Ventilators,  385;  Vacuum  System  of 
Ventilation,  386;  Plenum  System  of  Ventilation,  386;  Comparison  of 
Vacuum  and  Plenum  Systems,  386;  Types  of  Centrifugal  Fans,  387; 
Manometrical  Efficiency*,  390;  Mechanical  Efticiency,  390;  Fan  Con- 
struction, 391;  High-Speed  and  Low-Speed  Motors,  392;  Fan  Tests,  392; 
Conducting  Air-Currents,  393;  Doors,  393;  Stoppings,  393;  Bridges,  393; 
Air  Brattice,  394;  Curtains,  394. 

Hoisting.— Double  Cylindrical  Drums,  394;  Single  Cylindrical  Drums,  394; 
Koepe  System,  395;  Whiting  System,  395;  Problems  in  Hoisting,  396; 
Balancing  a Conical  Drum,  396;  Horsepower  of  an  Engine  for  Hoisting, 
396;  Load  That  a Given  Pair  of  Engines  Will  Start,  396;  Approximate 
Period  of  Winding  on  a Cylindrical  Drum,  397;  Head-Frames,  397; 
Head-Sheaves,  397;  Guides  and  Conductors,  398;  Safety  Catches,  398; 
Detaching  Hooks,  398. 

Hau  lag  E.— 1 Gravity  Planes,  398;  Number  of  Cars  in  a Trip  on  a Self-Acting 
Incline,  399;  Engine  Planes,  399;  Size  of  Engines  Required  for  Engine- 
Plane  Haulage,  399;  Horsepower  of  an  Engine  to  Hoist  a Given  Load 
Up  an  Incline,  400;  Rope  Haulage,  400;  Tail-Rope  System,  400;  Tension 
of  Hauling  Rope,  401;  Endless-Rope  System,  401;  Friction  Pull  on  an 
Endless-Rope  Haulage,  402;  Inclined  Roads,  402;  Motor  Haulage,  402; 
Locomotive  Haulage,  402;  Compressed-Air  Haulage,  403;  Tractive 
Efforts  of  Compressed-Air  Locomotives,  404;  Electric  Haulage,  406; 
Speed  of  Haulage,  408;  Cost  of  Haujage,  409;  Mine  Roads  and  Tracks, 
410;  Grade,  410;  Rails,  411;  Gauge,  411;  Curves,  411;  To  Bend  Rails  to 
Proper  Arc  for  Any  Radius,  412;  Rail  Elevation,  412;  Rollers,  412; 
Switches,  413;  Turnouts,  413;  Slope  Bottoms,  413;  Tracks  for  Bottom  of 
Shafts,  416;  Surface  Tracks  for  Slopes  and  Shafts,  417. 

Ore  Dressing  and  the  Preparation  of  Coal.  — Crushing 
Machinery,  418;  Object  of  Crushing,  418;  Selection  of  a Crusher,  418; 
Jaw  Crushers,  419;  Blake  Crusher,  419;  Dodge  Crusher,  419;  Roll-Jaw 
Crushers,  420;  Gyratory  Crushers,  420;  Rolls,  421;  Cracking  Rolls,  421; 
Corrugated  Rolls,  422;  Disintegrating  Rolls  and  Pulverizers,  423;  Ham- 
mers, 423;  Crushing  Rolls,  423;  Amount  Crushed,  424;  Speeds,  424;  Speed 
of  Rolls,  425;  Crushing  Mills, 426;  Roller  Mills,  426;  Ball  Mills,  427;  Gravity 
Stamps,  427;  Order  of  Drop,  428;  Speed  of  Stamps,  429;  Shoes  and  Dies, 
429;  Life  of  the  Shoes  and  Dies,  429;  Cams,  Stamp  Heads,  and  Stems, 
429;  Tappets,  429;  Battery  Water,  430;  Duty  of  Stamps,  430;  Horsepower 
of  Stamps,  430;  Cost  of  Stamping,  430;  Pneumatic  Stamps,  430;  Power 
Stamps,  431;  Steam  Stamp,  431;  Miscellaneous  Forms  of  Crushers,  431. 

Sizing  and  Classifying  Apparatus.— Stationary,  Screens,  Griz- 
zlies, Head-Bars,  or  Platform  Bars,  431;  Adjustable  Bars.  432;  Shaking 
Screens,  432;  Revolving  Screens,  or  Trommels,  433;  Speed,  434;  Duty  of 
Anthracite  Screens,  434;  Revolving  Screen  Mesh  for  Anthracite,  434; 
Hydraulic  Classifiers,  434;  Spitzkasten,  435;  Spitzlutten,  4$?;  Cftluni^t 


xjy  TABLE  OF  CONTENTS. 

Classifier,  435;  Settling  Boxes,  435;  Jeffrey-Robinron 
t op-  Washer  436;  Scaife  Trough  Washer,  437;  Jig&,  437,  fetationary 
Screen  Jigs  437'  Theory  of  Jigging,  439;  Equal  Settling  Particles,  439, 
In Acclferation,  440;  Suction 440;  Removal  of 
Sulphur  From  Coal,  441;  Preparation  of  Anthracite,  442. 

M a Kin  i i mo  op  Material  — Anthracite  Coal,  413;  Bituminous  Coal,  443; 
H Ore  R^ck  Etc  44^ Flumes  and  Launders,  443;  Horizontal  Pressure 
Exerted  Against  Vertical  Retaining, Walls 

roovpvers  445'  Weights  and  Capacities  of  Standard  Steel  BucKets,  wo, 
Malleable  Iron  Buckets  446;C<»nve^ngCapaci- 

Wounds,  451;  Treatment  of  Persons  Overcome  by  Gas,  451. 

Tables— Goal  Dealers’  Table,  Giving  Cost  of  Any .N^ber ^ 
i ABLEb.  p -ce  p r rpon  452-  Natural  Sines  and  Cosines,  453,  Natural  lan 

gents  and  Cotangents,  464;  Logarithms  of  Numbers,  473;  L° eanthi ms  of 
Trigonometric  Functions,  Slims,  Cosines,  Tangents,  Cotangents^!, 
Latitudes  and  Departures  (Traverse  Table), J >3 7,  SquMes^  OuDes, 
Square  and  Cube  Roots,  Circumferences,  Areas,  and  Reciprocal^ 
Horn  1 to  1,000,  545;  Diameters,  Circumferences,  and  Areas,  **  w 
100,  561. 


Glossary  of  Mining  Terms.—565* 


COAL  AND  METAL  MINERS’ 


POCKETBOOK. 


WEIGHTS  AND  MEASURES. 


THE  METRIC  SYSTEM. 


Since  the  metric  system  is  the  adopted  system  in  many  countries,  and  as 
it  is  almost  universally  used  in  connection  with  scientific  work,  a brief 
description  of  it  is  here  given  as  preliminary  to  the  following  tables  of  weights 
and  measures. 


The  metric  system  has  three  principal  units: 

1.  The  meter , or  unit  of  length , supposed  to  be  the  one  ten-millionth  part 
of  the  distance  from  the  equator  to  the  pole  on  the  meridian  of  longitude 
passing  through  the  city  of  Paris.  Its  actual  value  is  39.370432  in.,  the  stand- 
ard authorized  by  the  United  States  Government  being  39.37  in.  According 

to  this  standard,  1 yd.  = meter. 

OjUOl 

2.  The  gram , or  unit  of  weight , is  the  weight  of  a cubic  centimeter  of  dis- 
tilled water  at  4°  centigrade  and  776  millimeters  of  atmospheric  measure. 
The  kilogram  (Kg.)  = 1,000  grams  = 2.2046  lb.,  is  the  ordinary  unit  of  weight 
corresponding  to  the  English  pound.  According  to  the  United  States  Gov- 


ernment regulations,  1 lb.  avoirdupois  = 


1 

2.2046 


kilogram. 


3.  The  liter , or  unit  of  liquid  volume , is  the  volume  of  1,000  cubic  centi- 
meters of  distilled  water  at  4°  centigrade  and  776  millimeters  pressure. 

Multiples  of  these  units  are  obtained  by  prefixing  to  the  names  of  the 
printed  units  the  Greek  words  deka  (10),  hekto  (100),  kilo  (1,000).  The  sub- 
multiples or  divisions  are  obtained  by  prefixing  the  Latin  words  deci  (TV), 
centi  (Tfo),  and  milli  (^W)-  The  abbreviations  of  these  several  units  as  given 
in  the  following  tables  are  those  commonly  used.  The  kilogram-meter  is  the 
work  done  in  raising  1 kg.  through  a height  of  1 m.,  and  equals  7.233  ft.-lb. 
One  metric  horsepower  (force  de  cheval  or  cheval  vapeur)  equals  .98633  English 
horsepower. 


TROY  WEIGHT. 

24  grains  = 1 pennyweight. 

20  pennyweights  = 1 ounce  = 480  grains. 

12  ounces  = 1 pound  = 5,760  grains  = 240  pennyweights. 

In  troy,  apothecaries’,  and  avoirdupois  weights,  the  grains  are  the  same. 


APOTHECARIES’  WEIGHT. 

20  grains  = 1 scruple. 

3 scruples  = 1 dram  = 60  grains. 

8 drams  = 1 ounce  = 480  grains  = 24  scruples. 

12  ounces  = 1 pound  = 5,760  grains  =,288  scruples  = 96  drams. 


2 


WEIGHTS  AND  MEASURES. 


AVOIRDUPOIS  WEIGHT. 


27.34375  grains 
16  drams 
16  ounces 
28  pounds 
4 quarters 


= 1 dram. 

= 1 ounce 
= 1 pound 
= 1 quarter 
= 1 hundredweight 


20  hundredweight  = 1 ton 
1 stone 
1 quintal 
1 “ short  ton  ” 

1 “long  ton ” 

1 ounce  troy  or  apothecaries’  = 1.09714 
1 pound  troy  or  apothecaries’  = .82286 
1 ounce  avoirdupois  = .911458 

1 pound  avoirdupois  = 1.21528 


= 437i  grains. 

= 7,000  grains  = 256  drams. 
= 448  ounces. 

= 112  pounds. 

= 2,240  pounds. 

= 14  pounds. 

= 100  pounds. 

= 2,000  pounds. 

= 2,240  pounds, 
avoirdupois  ounces, 
avoirdupois  pound, 
troy  or  apothecaries’  ounce, 
troy  or  apothecaries’  pounds. 


10  milligrams  (mg.) 
10  centigrams 
10  decigrams 
10  grams 
10  decagrams 
10  hectograms 
10  kilograms 
10  myriagrams 
10  quintals 


METRIC  WEIGHT. 

= 1 centigram  (eg.) 

= 1 decigram  (dg.) 

= 1 gram  (g.) 

= 1 decagram  (Dg.) 

= 1 hectogram  (Hg.) 

= 1 kilogram  (Kg.) 

= 1 myriagram  (Mg.) 

= 1 quintal  (Q.) 

= 1 tonneau,  millier,  or  tc 


= .15432  grain. 

= 1.5432  grains. 

= 15.432  grains. 

= .0220461b.  avoir. 

= .22046  lb.  avoir. 

==  2.2046  lb.  avoir. 

= 22.046  lb.  avoir. 

= 220.46  lb.  avoir. 

= 2,204  lb.  avoir. 


MEASURES  OF  LENGTH. 


AMERICAN  AND  BRITISH. 

12  inches  = 1 foot. 

3 feet  = 1 yard  = 36  in. 

6 feet  = 1 fathom  = 2 yd.  = 72  in. 

66  feet  = 1 chain  *=  11  fath.  = 22  yd.  = 792  in. 

10  chains  = 1 furlong  = 110  fath.  = 220  yd.  = 660  ft.  = 7,620  in. 

8 furlongs  = 1 mile  = 80  chains  = 880  fath.  = 1,760  yd.  = 5,280  ft.  = 

A nautical  mile,  or  knot  = 1.15136  statute  miles.  [63,360  in. 
A league  = 3 nautical  miles. 

*The  chain  of  66  ft.  is  practically  obsolete.  Chains  of  50  or  100  ft.  are  now  used  exclusively  by 
American  surveyors. 

To  Reduce  Inches  to  Decimals  of  a Foot.— Divide  the  number  of  inches  by 
12.  Thus,  7 in.  = 7 -f- 12,  or  .58333  ft.  To  reduce  fractions  of  inches  to  deci- 
mals of  a foot,  divide  the  fraction  hv  12,  and  then  divide  the  numerator  of 
the  quotient  by  the  denominator.  Thus,  f in.  = | -s- 12  = g3g.  g3g  — .0313  ft. 

The  annexed  scale  shows  on  one  side,  proportionately  reduced,  a scale  of 
tenths.  On  the  other,  a scale  of  twelfths,  corresponding  to  inches.  To 
reduce  inches  to  decimal  parts  of  a foot,  find  the  number  of  inches  and 


TENTHS  OF  A FOOT 


O 1 



3 

I 

4 

5 6 7 

8 9 10 

1.1.1-U  yi,  i.i.i .i. i,i.i  ,1  ,i  ,i  ,i  ,i  J J uJ 

rnr 

5 t 

j ,'iijr r i f f r ' ! 1 ‘ 1 [ 

7 S S 

H 1 l • i ' ' » I | 1 i • | ' • ■ i ■ ' 1 | 

) 10  11  12 

LSTCHUS 


fractional  parts  thereof  on  the  side  marked  “inches.”  Opposite,  on  the 
scale  of  tenths,  will  be  found  the  decimal  part  of  a foot.  Thus,  if  we  want 
to  find  the  decimal  part  of  a foot  represented  by  7£  inches,  we  find  the  mark 
corresponding  to  7£  inches  on  the  side  marked  “inches.”  Opposite  this 
mark  we  read  6 tenths,  2 hundredths,  and  5 thousandths;  or,  expressed 
decimally,  .625.  ♦ 


MEASURES  OF  LENGTH. 


3 


DECIMALS  OF  A FOOT  FOR  EACH  1-32  OF  AN  INCH. 


Inch. 

0" 

1" 

2" 

3" 

4" 

5" 

6" 

7" 

8" 

9" 

10" 

11" 

0 

0 

.0833 

.1667 

.2500 

.3333 

.4167 

.5000 

.5833 

.6667 

.7500 

.8333 

.9167 

32 

.0026 

.0859 

.1693 

.2526 

.3359 

.4193 

.5026 

.5859 

.6693 

.7526 

.8359 

.9193 

1^5 

.0052 

.0885 

.1719 

.2552 

.3385 

.4219 

.5052 

.5885 

.6719 

.7552 

.8385 

.9219 

3% 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

.5078 

.5911 

.6745 

.7578 

.8411 

.9245 

i 

.0104 

.0937 

.1771 

.2604 

.3437 

.4271 

.5104 

.5937 

.6771 

.7604 

.8437 

.9271 

3*2 

.0130 

.0964 

.1797 

.2630 

.3464 

.4297 

.5130 

.5964 

.6797 

.7630 

.8464 

.9297 

t3s 

.0156 

.0990 

.1823 

.2656 

.3490 

.4323 

.5156 

.5990 

.6823 

.7656 

.8490 

.9323 

32 

.0182 

.1016 

.1849 

.2682 

.3516 

.4349 

.5182 

.6016 

.6849 

.7682 

.8516 

.9349 

5 

.0208 

.1042 

.1875 

.2708 

.3542 

.4375 

.5208 

.6042 

.6875 

.7708 

.8542 

.9375 

35 

.0234 

.1068 

.1901 

.2734 

.3568 

.4401 

.5234 

.6068 

.6901 

.7734 

.8568 

.9401 

t6s 

.0260 

.1094 

.1927 

.2760 

.3594 

.4427 

.5260 

.6094 

.6927 

.7760 

.8594 

.9427 

33 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

.5286 

.6120 

.6953 

.7786 

.8620 

.9453 

i 

.0312 

.1146 

.1979 

.2812 

.3646 

.4479 

.5312 

.6146 

.6979 

.7812 

.8646 

.9479 

M 

.0339 

.1172 

.2005 

.2839 

.3672 

.4505 

.5339 

.6172 

.7005 

.7839 

.8672 

.9505 

I 

.0365 

.1198 

.2031 

.2865 

.3698 

.4531 

.5365 

.6198 

.7031 

.7865 

.8698 

.9531 

33 

.0391 

.1224 

.2057 

.2891 

.3724 

.4557 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

h 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

e. 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.5443 

.6276 

.7109 

.7943 

.8776 

.9609 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

.5469 

.6302 

.7135 

.7969 

.8802 

.9635 

if 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.5495 

.6328 

.7161 

.7995 

.8828 

.9661 

| 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.5521 

.6354 

.7188 

.8021 

.8854 

.9688 

flf 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.5547 

.6380 

.7214 

.8047 

-.8880 

.9714 

tt 

.0573 

.1406 

.2240 

.3073 

.3906 

.4740 

.5573 

.6406 

.7240 

.8073 

.8906 

.9740 

if 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

.5599 

.6432 

.7266 

.8099 

.8932 

.9766 

£ 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

.5625 

.6458 

.7292 

.8125 

.8958 

.9792 

If 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.5651 

.6484 

.7318 

.8151 

.8984 

.9818 

if 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

.5677 

.6510 

.7344 

.8177 

.9010 

.9844 

if 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

.5703 

.6536 

.7370 

.8203 

.9036 

.9870 

7 

.0729 

.1562 

.2396 

.3229 

.4062 

.4896 

.5729 

.6562 

.7396 

.8229 

.9062 

.9896 

If 

.0755 

.1589 

.2422 

.3255 

.4089 

.4922 

.5755 

.6589 

.7422 

.8255 

.9089 

.9922 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

.5781 

.6615 

.7448 

.8281 

.9115 

.9948 

33 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.5807 

.6641 

.7474 

.8307 

.9141 

.9974 

METRIC  SYSTEM. 


10  millimeters  (mm.) 
10  centimeters 
10  decimeters 
10  meters 
10  decameters 
10  hectometers 
10  kilometers 


= 1 centimeter  (cm.)  = 

= 1 decimeter  (dm.)  = 

= 1 meter  (m.)  = 

= 1 decameter  (Dm.)  = 
= 1 hectometer  (flm.)  = 
= 1 kilometer  (Km.)  = 

— 1 myriameter(Mm.)  = 


.3937079  inch. 
3.937079  inches. 
3.2808992  feet. 
10.9363  yards. 

109.363  yards. 

.6213824  mile. 
6.213824  miles. 


RUSSIAN. 

12  inches  = 1 foot  = 1 American  foot. 
7 feet  = 1 sachine,  or  sagene. 

500  sachine  = 1 verst  = 3, 500 'feet. 


PRUSSIAN,  DANISH,  AND  NORWEGIAN. 

12  inches  = 1 foot  = 1.02972  American  feet. 
12  feet  = 1 ruth  = 12.35664  American  feet. 
2,000  ruths  = 1 mile  — 4.68+  American  miles. 


AUSTRIAN. 

12  inches  = 1 foot  = 1.03713  American  feet. 

6 feet  = 1 klafter. 

4,000  klafters  = 1 mile  = 4.71+  American  miles, 


4 


WEIGHTS  AND  MEASURES. 


SWEDISH. 

12  inches  = 1 foot  = .97410  American  foot. 

6 feet  = 1 fathom. 

6,000  fathoms  = 1 mile  = 6.64+  American  miles. 


CHINESE. 

1 chih  = 1-054  American  feet. 

10  chih  = 1 chang  = 10.54  American  feet. 

180  chang  = 1 li  = 1,897  American  feet. 


MEASURES  OF  AREA. 


144  sq.  inches 
9 sq.  feet 
30i  sq.  yards 
40  perches 
4 roods 
640  acres 


AMERICAN  AND  BRITISH. 


3 square  foot. 

1 square  yard  = 
1 perch  = 

1 rood  = 

1 acre  = 

1 square  mile. 


1,296  sq.  in. 

272i  sq.  ft. 

1,210  sq.  vd.  = 10,890  sq.  ft. 

160  perches  = 4,640  sq.  yd.  = 43,560  sq.  ft. 


TABLE  FOR  REDUCING  SQUARE  FEET  TO  ACRES. 


Square 

Feet. 

Acres. 

Square 

Feet. 

Acres.  1 

Square 
Feet.  1 

Acres. 

Square 

Feet. 

Acres. 

100,000,000 

90.000. 000 

80.000. 000 

70.000. 000 

60.000. 000 

50.000. 000 

40.000. 000 

30.000. 000 

20.000. 000 
10,000,000 

2,295.684 

2,066.116 

1,836.547 

1,606.979 

1,377.410 

1,147.842 

918.274 

688.705 

459.137 

229.568 

900,000 

800,000 

700.000 

600.000 
500,000 

400.000 

300.000 
200.000 
100,000 

20.661 

18.365 

16.070 

13.774 

11.478 

9.183 

6.887 

4.591 

2.296 

9.000 

8.000 

7.000 

6.000 

5.000 

4.000 

3.000 
2,000 
1,000 

.207 

.184 

.161 

.138 

.115 

.092 

.069 

.046 

.023 

90 

80 

70 

60 

50 

40 

30 

20 

10 

.0021 

.0018 

.0016 

.0014 

.0011 

.0009 

.0007 

.0005 

.0002 

9.000. 000 

8.000. 000 

7.000. 000 

6.000. 000 
5.000,000 

4.000. 000 

3.000. 000 
2,000,000 
1,000,000 

206.612 

183.655 

160.698 

137.741 

114.784 

91.827 

68.870 

45.914 

22.957 

90.000 

80.000 
70.000 
60,000 
50.000 

40.000 

30.000 
20.000 
10,000 

2.066 

1.836 

1.607 

1.377 

1.148 

.918 

.689 

.459 

.230 

900 

800 

700 

600 

500 

400 

300 

200 

100 

.021 

.018 

.016 

.014 

.011 

.009 

.007 

.005 

.0023 

9 

8 

7 

6 , 

5 

4 

3 

2 

1 

.00021 

.00018 

.00016 

.00014 

.00011 

.00009 

.00007 

.00005 

.00002 

METRIC  SYSTEM. 

1 square  millimeter  (sq.  mm.)  = 

1 square  centimeter  (sq.  cm.) 

1 square  decimeter  (sq.  dm.)  -~ 

1 square  meter,  or  centare  (m.1 2  or  sq.  m.)  — 
1 square  decameter,  or  are  (sq.  Dm.) 

1 hectare  (ha. ) 

1 square  kilometer  (sq.  Km.) 

1 square  myriameter  (sq.  Mm.) 


.001550  sq.  in. 
.155003  sq.  in. 
15.5003  sq.  in. 
10.764101  sq.  ft. 

.024711  acre. 
2.47110  acres. 
247.110  acres. 
38.61090  sq.  mi. 


MEASURES  OF  VOLUME. 


5 


MEASURES  OF  VOLUME. 


AMERICAN  AND  BRITISH. 

1,728  cubic  inches  = 1 cubic  foot. 

27  cubic  feet  = 1 cubic  yard. 

A cord  of  wood  = 128  cu.  ft.,  or  a pile  of  wood  8 ft.  long,  4 ft.  wide,  and 
4 ft.  high  = 1 cord.  A perch  of  masonry  contains  24f  cu.  ft.;  but  in  practice 
it  is  taken  as  25  cu.  ft. 

A ton  (2,240  lb.)  of  Pennsylvania  anthracite,  when  broken  for  domestic 
use,  occupies  about  42  cu.  ft.  of  space;  bituminous  coal,  about  46  cu.  ft.;  and 
coke,  about  88  cu.  ft.  A bushel  of  coal  is  80  lb.  in  Kentucky,  Illinois,  and 
Missouri,  76  lb.  in  Pennsylvania,  70  fb.  in  Indiana,  and  76  lb.  in  Montana. 


METRIC  SYSTEM. 

1 milliliter,  or  cu.  centimeter  (cc.  or  cm.3) 

1 centiliter  (cl.) 

1 deciliter  (dl.  or  dl.3) 

1 liter,  or  cu.  decimeter  (1.) 

1 decaliter,  or  centistere  (Dl.  or  dal.) 

1 hectoliter,  or  decistere  (HI.) 

1 kiloliter,  or  cu.  meter,  or  stere  (Kl.  or  cm.3) 
1 myrialiter,  or  decastere  (Ml.) 


.0610254  cu.  in. 
.610254  cu.  in. 
6.10254  cu.  in. 
61.0254  cu.  in. 
.353156  cu.  ft. 
3.53156  cu.  ft. 
35.3156  cu.  ft. 
353.156  cu.  ft. 


4 gills 
2 pints 
4 quarts 
3H  gallons 
63  gallons 
2 hogsheads 
2 pipes 


LIQUID  MEASURE  (u.  S.). 


1 pint 
1 quart 
1 gallon 
1.  barrel 
1 hogshead. 
1 pipe. 

1 tun. 


16  liquid  oz. 
8 gills 


= 28.876  cu.  in. 
= 57.75  cu.  in. 


32  gills  = 8 pints  = 231 
7,276i  cu.  in.  = 4.21 


cu.  in. 
cu.  ft. 


A box  19f  in.  on  each  side  contains  1 barrel. 
1 cu.  ft.  — 7.48  gallons. 


DRY  MEASURE  (u.  S.). 

2 pints  = 1 quart  = 67.2006  cu.  in.  = 1.16365  liquid  qt. 

4 quarts  = 1 gallon  = 268.8025  cu.  in.  = 1.16365  liquid  gal. 

2 gallons  = 1 peck  = 8 quarts  * = 537.6050  cu.  in. 

4 pecks  = 1 bushel  = 64  pints  = 32  quarts  = 8 gal.  = 2,150.42  cu.  in. 


BRITISH  IMPERIAL  MEASURE,  BOTH  LIQUID  AND  DRY. 

4 gills  = 1 pint  = 34.6592  cu.  in. 

2 pints  = 1 quart  = 69.3185  cu.  in. 

4 quarts  = 1 gallon  = 277.274  cu.  in. 

8 quarts  = 1 peck  = 554.548  cu.  in. 

4 pecks  = 1 bushel  — 2,218.192  cu.  in. 


The  standard  U.  S.  bushel  is  the  Winchester  bushel,  which  is  in  cylinder 
form,  18£  inches  diameter  and  8 inches  deep,  and  contains  2,150.42  cubic 
inches. 

The  British  Imperial  bushel  is  based  on  the  Imperial  gallon  and  con- 
tains 8 such  gallons,  or  2,218.192  cubic  inches  = 1.2837  cubic  feet. 

Capacity  of  a cylinder  in  U.  S.  gallons  = square  of  diameter  in  inches 
X height  in  inches  X .0034  (accurate  within  1 part  in  100,000). 

Capacity  of  a cylinder  in  U.  S.  bushels  = square  of  diameter  in  inches 
><  height  in  inches  X .0003652. 


6 


WEIGHTS  AND  MEASURES. 


CONTENTS  OF  CYLINDERS  OR  PIPES  FOR  1 FOOT  IN  LENGTH, 

The  contents  of  pipes  or  cylinders  in  gallons  or  pounds  are  to  each  other 
as  the  squares  of  their  diameters.  Thus,  a pipe  9 ft.  in  diameter  will  contain 
9 times  as  much  as  a 3'  pipe,  or  4 times  as  much  as  a 4k'  pipe. 


Diameters  in  Inches. 


1 

Diam. 

in 

Inches. 

Diameter 
in  Decimals 
of  a Foot. 

Gallons  of 
231  Cu.In. 
(U.  S.  Stand- 
ard.) 

Weight  of 
Water  in  Lb. 
in  1 Ft.  of 
Length. 

Diam.  j 
in  | 
Inches.  1 

Diameter 
in  Decimals  ' 
of  a Foot.  | 

1 

- ! 

Gallons  of 
231  Cu.  In. 
(U.  S.  Stand- 
ard.) 

Weight  of 
Water  in  Lb. 
in  1 Ft.  of 
Length. 

•1_ 

.0208 

.0025 

.02122 

5 

.4167 

1.020 

8.488 

l 

.0417 

.0102 

.08488 

5i 

.4583 

1.234 

10.270 

| 

.0625 

.0230 

.19098 

6 

.5000 

1.469 

12.223 

1 

.0833 

.0408 

.33952 

6£ 

.5417 

1.724 

14.345 

li 

.1042 

.0638 

.53050 

7 

.5833 

1.999 

16.636 

H 

.1250 

.0918 

.76392 

n 

.6250 

2.295 

19.098 

H 

.1458 

.1249 

1.0398 

8 

.6667 

2.611 

21.729 

2 

.1667 

.1632 

1.3581 

8i 

.7083 

2.948 

24.530 

2i 

.1875 

.2066 

1.7188 

9 

.7500 

3.305 

27.501 

2i 

.2083 

.2550 

2.1220 

9i 

.7917 

3.682 

30.641 

2f 

.2292 

.3085 

2.5676 

10 

.8333 

4.080 

33.952 

3 

.2500 

.3672 

3.0557 

10i 

.8750 

4.498 

37.432 

3i 

.2917 

.4998 

4.1591 

11 

.9167 

4.937 

41.082 

4 

.3333 

.6528 

5.4323 

1H 

.9583 

5.396 

44.901 

4i 

.3750 

.8263 

6.8750 

12 

1.0000 

5.875 

48.891 

Diameters  in  Feet. 


li 

1.25 

9.18 

76.392 

10 

10.00 

587.6 

4,889.12 

li 

1.50 

13.22 

110.00 

10i 

10.50 

647.7 

5,404.24 

If 

1.75 

17.99 

149.73 

11 

11.00 

710.9 

5,915.84 

2 

2.00 

23.50 

195.56 

1H 

11.50 

777.0 

6,485.72 

2t 

2.25 

29.74 

247.51 

12 

846.1 

7,040.00 

2k 

2.50 

36.72 

305.57 

13 

992.8 

8,710.00 

2f 

2.75 

44.43 

369.74 

14 

1,152.0 

10,096.00 

3 

3.00 

52.88 

440.00 

15 

1,322.0 

11,000.50 

31 

3.25 

65.28 

544.37 

16 

1,504.0 

12,516.00 

°4 

3k 

3.50 

71.97 

631.00 

17 

1,698.0 

14,166.00 

St 

3.75 

82.62 

687.53 

18 

1,904.0 

15,841.00 

4 

4.00 

94.0 

782.24 

19 

2,121.0 

17,691.00 

4i 

4.25 

106.1 

885.40 

20 

2,350.0 

19,556.50 

4 i 

4.50 

119.0 

990.04 

21 

2,591.0 

21,617.00 

4f 

4.75 

132.5 

1,105.71 

22 

2,844.0 

23,663.00 

5 

5.00 

146.9 

1,222.28 

23 

3,108.0 

25,943.00 

5£ 

5.25 

161.9 

1,351.06 

24 

3,384.0 

28,160.00 

5k 

5.50 

177.7 

1,478.96 

25 

3.672.0 

30.557.00 

5£ 

5.75 

194.3 

1.621.43 

26 

3,971.0 

34,840.00 

6 

6.00 

211.5 

1,760.00 

27 

t 

4,283.0 

35,641.00 

6i 

6.25 

229.5 

1,915.18 

28 

4,606.0 

40,384.00 

6| 

6.50 

248.2 

2,177.48 

29 

4,941.0 

41,117.00 

6| 

6.75 

267.7 

2,233.96 

30 

5,288.0 

44.002.00 

7 

7.00 

287.9 

2,524.00 

31 

5,646.0 

46,984.00 

7k 

7.50 

330.5 

2,750.12 

32 

6,017.0 

50,064.00 

8 

8.00 

376.0 

3,128.96 

33 

6,398.0 

53,242.00 

8£ 

8.50 

424.5 

3,541.60 

34 

6,792.0 

56,664.00 

9 

9.00 

475.9 

3,960.16 

35 

7.197.0 

59.891.50 

9i 

9.50 

530.2 

1 

1,122.84 

36 

| 7.61  1.0 

1 

63.36^.00 

WEIGHTS  AND  MEASURES. 


7 


MEXICAN,  CENTRAL  AMERICAN,  AND  SOUTH  AMERICAN 
WEIGHTS  AND  MEASURES. 


The  following  table  gives  weights  and  measures  in  commercial  use  in  Mex- 
ico and  the  republics  of  Central  and  South  America,  and  their  equivalents 
in  the  United  States.  Published  by  the  Bureau  of  the  American  Republics. 


Denomination. 

Where  Used. 

U.  S.  Equivalents. 

Arobe  ..." 

Paraguay 

25  pounds. 

Arroba  (dry)  

Argentine  Republic  

25.3175  pounds. 

Arroba  (dry)  

Brazil 

32.38  pounds. 

Arroba  (dry)  

Cuba  

25.3664  pounds. 

Arroba  (dry)  

Venezuela  

25.4024  pounds. 

Arroba  (liquid) ... 

Cuba  and  Venezuela 

4.263  gallons. 

Barril > 

Argentine  Republic  and  Mexico 

20.0787  gallons. 

Carga 

Mexico  and  Salvador  

300  pounds. 

Centavo  

Central  America  

4.2631  gallons. 

Cuadra  

Argentine  Republic  

4.2  acres. 

Cuadra  

Paraguay 

78.9  yards. 

Cuadra  (square)... 

Paraguav 

8.077  square  feet. 

Cuadra  

Uruguay  

*2  6A  OTPS  ( 71  PS 

Fanega  (dry)  

Cen tral" America  

Clvi.  v/O  \ IlvCli  1 V J « 

1.5745  bushels. 

Fanega  (dry)  

Chile 

2.575  bushels. 

Fanega  (dry)  

Cuba  

1.599  bushels. 

Fanega  (dry)  

Mexico 

1.54728  bushels. 

Fanega  (dry)  

Uruguay  (double)  

7.776  bushels. 

Fanega  (dry)  

Uruguay  (single) 

3.888  bushels. 

Fanega  (dry)  

Venezuela  

1.599  bushels. 

Frasco 

Argentine  Republic  

2.5096  quarts. 

Frasco  

Mexico 

2.5  quarts. 

League  (land)...'.... 

Paraguay 

4,633  acres. 

Libra  

Argentine  Republic  

1.0127  pounds. 

Libra  

Central  America 

1.043  pounds. 

Libra  

Chile 

1.014  pounds. 

Libra  

Cuba 

1.0161  pounds. 

Libra  

Mexico 

1.01465  pounds. 

Libra  

Peru  

1.0143  pounds. 

Libra  

Uruguay  

1.0143  pounds. 

Libra  

Venezuela  

1.0161  pounds. 

Livre  

Guiana 

1.0791  pounds. 

Manzana  

Costa  Rica 

If  acres. 

Marc 

Bolivia „ 

.507  pound. 

Pie  

Argentine  Republic  

.9478  foot. 

Quintal  

Argentine  Republic  

101.42  pounds. 

Quintal  

Brazil  

130.06  pounds. 

Quintal  

Chile,  Mexico,  and  Peru 

101.61  pounds. 

Quintal  

Paraguay 

100  pounds. 

Vara 

Argentine  Republic 

34.1208  inches. 

Vara 

Central  America 

38.874  inches. 

Vara 

Chile  and  Peru  

33.367  inches. 

Vara  

Cuba 

33.384  inches. 

Vara 

Mexico 

33  inches. 

Vara 

Paraguay  

34  inches. 

Vara  

Venezuela  

33.384  inches. 

CONVERSION  TABLES. 

( United  States  Coast  and  Geodetic  Survey. ) 

The  method  of  using  the  following  tables  for  converting  United  States 
weights  and  measures  into  metric  weights  and  measures  will  be  understood 
by  the  following  example: 

Find  the  number  of  kilometers  in  125  miles. 

From  column  “ Miles  to  Kilometers,”  1 mile  = 1.60935  kilometers,  or  100 
miles  = 160.935  kilometers;  2 miles  = 3.21869  kilometers,  or  20  miles  — 32.1869 
kilometers;  and  5 miles  •=  8.04674  kilometers.  Hence,  125  miles  = 160.935  -+• 
32.1869  + 8.04674  = 201.16864  kilometers, 


8 WEIGHTS  AND  MEASURES. 

CUSTOMARY  TO  METRIC. 


Linear. 

Capacity. 

i 

to  © 
© a 

to 

© 

© 

S 

3 

© 

© 

l 

1 

to 
Vh  © 

to 

s © 

03  © 

SB 

aa 

W 

is  . « 

03  tO 

a s 

csj  © 

Ss  S3  S 

fee 
2 o 

. l 
sg 
3 8a 

3 © r* 

sga 

OS 

3 . 
“ 8 
15  © 
5.-S 

O’ 

o 

•M  . 

to  to 

*3  ^ 
o 

1 

2 

3 

4 

5 

6 

7 

8 
9 

25.4 

50.8 

76.2 

101.6 

127.0 

152.4 

177.8 

203.2 

228.6 

0.304801 

0.609601 

0.914402 

1.219202 

1.524003 

1.828804 

2.133604 

2.438405 

2.743205 

).914402 
L. 828804 
>.743205 
3.657607 
4.572009 
3.486411 
5.400813 
7.315215 
8.229616 

1.60935  1 
3.21869  2 
4.82804  3 
6.43739  4 
8.04674  5 
9.65608  6 
11.26543  7 
12.87478  8 
14.48412  9 

3.70 
7.39 
11.09 
14.79 
18.48 
22.18  • 
25.88 
29.57 
33.27 

29.57 

59.15 

88.72 

118.29 

147.87 

177.44 

207.02 

236.59 

266.16 

0.94636 

1.89272 

2.83908 

3.78543 

4.73179 

5.67815 

6.62451 

7.57087 

8.51723 

3.78543 
. 7.57087 
vll. 35630 
15.14174 
18.92717 
22.71261 
26.49804 
30.28348 
34.06891 

\ 

1 

2 

3 

4 

5 

6 

7 

8 
9 

Square. 

Weight. 

to 

© to 

« £<2 
C®5) 
I— I P m 

© O’.S 
s-  CO  +3 

=3  Q s 

C O 
cc 

g © B ' 

sfs 

Cj  CC-rH 

co  H 

to 

rrt 

1 £ • 
^ H 05 

t-  S S3 

So® 

00 

si 

Sg  08 

Sg 

SB 

to  g3 

II 

to 

*2  OB  S 

B4©  d 
£ © § 
c S 

co« 

5 2 

to 

a~i 

S3  “ c3 

|ga 

to 

© . 
© cc 

s s 
SS 

ss 

6.452 
12.903 
1 9.355 
25.807 
32.258 
38.710 
45.161 
51.613 
58.065 

9.290 

18.581 

27.871 

37.161 

46.452 

55.742 

65.032 

74.323 

83.613 

0.836 

1.672 

2.508 

3.344 

4.181 

5.017 

5.853 

6.689 

7.525 

0.4047  : 

0.8094  : 

1.2141  : 

1.6187  - 

2.0234 
2.4281 
2.8328 
3.2375 
3.6422 

1 64.7989 

2 129.5978 

3 194.3968 

4 259.1957 

5 323.9946 

6 388.7935 

7 453.5924 

8 518.3914 

9 583.1903 

28.3495 

56.6991 

85.0486 

113.3981 

141.7476 

170.0972 

198.4467 

226.7962 

255.1457 

0.45359 

0.90719 

1.36078 

1.81437 

2.26796 

2.72156 

3.17515 

3.62874 

4.08233 

31.10348 

62.20696 

93.31044 

124.41392 

155.51740 

186.62088 

217.72437 

248.82785 

279.93133 

Cubic. 

Miscellaneous. 

1 

1 © to 

§*•§1 
t-1  S d 

n O (3 

5 o 

©3  to 
2o% 

P* 

to 

?o  . 
© 

©o  © 
o 

o£ 
**  © 
OQ 

l's 

CC  © 

PJ  © 

WW 

1 Gunter’s  chain  = 20.1168  meters. 

1 sq.  statute  mile  = 259.000  hectares. 

1 fathom  = 1-829  meters. 

1 nautical  mile  = 1,853.25  meters. 

1 ft.  = .304801  meter  9.4840158  log. 

1 avoir,  pound  = 453.5924277  gram . 

15,432.35639  grains  = 1 kilogram. 

1 

2 

1 

( 

i 

ij 

. 16.387 

5 32.774 

i 49.161 
[ 65.54< 

j 81.93( 
5 98.321 

1 114.711 
3 131.09' 
d 147.48 

1 .02832 

t .05663 
L .08495 
) .11327 

3 .14158 

3 .16990 

3 .19822 

7 .22654 

4 .25485 

0.765 

1.529 

2.294 

3.058 

3.823 

4.587 

5.352 

6.116 

6.881 

0.35239 

0.70479 

1.05718 

1.40957 

1.76196 

2.11436 

2.46675 

2.81914 

3.17154 

CONVERSION  TABLES. 


9 


The  method  of  using  the  following  tables  for  converting  metric  weights 
and  measures  into  United  States  weights  and  measures  may  he  understood 
by  the  following  example:  . 

Find  the  number  of  yards  in  86  meters. 

From  column  “ Meters  to  Yards,”  8 meters  = 8.748889  yards,  or  80  meters 
_ 87.48889  yards;  and  6 meters  — 6.561667  yards.  Hence,  86  meters 
87.48889  + 6.561667  = 94.050557  yards. 

METRIC  TO  CUSTOMARY. 


Capacity. 


fj 

-iS  O 
<D  rj 

o 

OS  -M 

as  as 
a>£ 

eters  to 
Yards. 

Kilometers 
to  Miles.  | 

£ 

1 

39.37 

3.28083 

1.093611 

0.62137 

2 

78.74 

6.56167 

2.187222 

1.24274 

3 

118.11 

9.84250 

3.280833 

1.86411 

4 

157.48 

13.12333 

4.374444 

2.48548 

5 

196.85 

16.40417 

5.468056 

3.10685 

6 

236.22 

19.68500 

6.561667 

3.72822 

7 

275.59 

22.96583 

7.655278 

4.34959 

8 

314.96 

26.24667 

8.748889 

4.97096 

9 

354.33 

29.52750 

9.842500 

5.59233 

Square. 

i »s 

•iH  <D 

OS’S 

■A 
O ® 

os 

oS 

b ass., 

2 

^ f-i  l— I 

as 

H OS^ 
o3  fi 

li 

rs  i— i 

S|-g 

c3  g 3 
a* 

CO  OQ 

rj  0^  ^ 

§ 

m 

2 £ a> 
a<as  b 

“si 

GO 

c3  as 

■4—*  ~ 

m 

1 

0.155 

10.764 

1.196 

2.471 

2 

0.310 

21.528 

2.392 

4.942 

3 

0.465 

32.292 

3.588 

7.413 

4 

0.620 

43.055 

4.784 

9.884 

5 

0.775 

53.819 

5.980 

12.355 

6 

0.930 

64.583 

7.176 

14.826 

7 

1.085 

75.347 

8.372 

17.297 

8 

1.240 

86.111 

9.568 

19.768 

9 

1.395 

96.875 

10.764 

22.239 

Cubic 


Cubic  Centi- 
meters to 
Cubic  Inches. 

Cubic  Deci- 
meters to 
Cubic  Inches. 

Cubic 
Meters  to 
Cubic  Feet. 

Cubic  Meters 
to 

Cubic  Yards. 

.0610 

61.023 

35.314 

1.308 

1 

.1220 

122.047 

70.629 

2.616 

2 

.1831 

183.070 

105.943 

3.924 

3 

.2441 

244.094 

141.258 

5.232 

4 

.3051 

305.117 

176.572 

6.540 

5 

.3661 

366.140 

211.887 

7.848 

6 

.4272 

427.164 

247.201 

9.156 

7 

.4882 

488.187 

282.516 

10.464 

8 

.5492 

549.210 

317.830  I 11.771 

9 

Milliliters,  or 
Cubic  Centi- 
liters to 
Fluid  Drams. 

Centiliters  to 
Fluid  Ounces. 

Liters  to 
Quarts. 

Decaliters 

to 

Gallons. 

Hectoliters 

to 

Bushels. 

0.27 

0.338 

1.0567 

2.6417 

2.8377 

0.54 

0.676 

2.1134 

5.2834 

5.6755 

0.81 

1.014 

3.1700 

7.9251 

8.5132 

1.08 

1.353 

4.2267 

10.5668 

11.3510 

1.35 

1.691 

5.2834 

13.2085 

14.1887 

1.62 

2.029 

6.3401 

15.8502 

17.0265 

1.89 

2.367 

7.3968 

18.4919 

19.8642 

2.16 

2.705 

8.4535 

21.1336 

22.7019 

2.43 

3.043 

9.5101 

23.7753 

25.5397 

Weight. 


Milligrams  to 
Grains. 

Kilograms  to 
Grains. 

Hectograms 
to  Ounces 
Avoir. 

Kilograms 
to  Pounds 
Avoir. 

.01543 

15,432.36 

3.5274 

2.20462 

.03086 

30,864.71 

7.0548 

4.40924 

.01630 

46,297.07 

10.5822 

6.61387 

.06173 

. 61,729.43 

14.1096 

8.81849 

.07716 

77,161.78 

17.6370 

11.02311 

.09259 

92,594.14 

21.1644 

13.22773 

.10803 

108,026.49 

24.6918 

15.43236 

.12346 

123,458.85 

28.2192 

17.63698 

.13889 

138,891.21  | 31.7466 

19.84160 

Weight— ( Continued). 


® 02  . 

'S  'g.ft 

I an 
§ 


220.46 

440.92 

661.39 

881.85 

1,102.31 

1,322.77 

1,543.24 

1,763.70 

1,984.16 


os  OS 

Sggf 

$ 


2.204.6 
4,409.2 
6,613.9 
8,818.5 

11,023.1 

13,227.7 

15,432.4 

17,637.0 

19.841.6 


32.1507 

64.3015 

96.4522 

128.6030 

160.7537 

192.9044 

225.0552 

257.2059 

289.3567 


10 


WEIGHTS  AND  MEASURES. 


METRIC  CONVERSION  TABLE. 

( Arranged  by  C.  W.  Hunt,  New  York. ) 


Millimeters  X .03937  = in. 

Millimeters  -4-  25.4  = in. 

Centimeters  X .3937  = in. 

Centimeters  -4-  2.54  = in. 

Meters  X 39.37  = in.  (Act  Congress). 
Meters  X 3.281  = ft. 

Meters  X 1.094  = yd. 

Kilometers  X .621  = miles. 
Kilometers  -4-  1.6093  = miles. 
Kilometers  X 3,280.7  = ft. 

Square  millimeters  X .0155  = sq.  in. 
Square  millimeters  -4-  645.1  = sq.  in. 
Square  centimeters  X .155  = sq.  in. 
Square  centimeters  -4-  6.451  = sq.  in. 
Square  meters  X 10.764  = sq.  ft. 
Square  kilometers  X 247.1  = acres. 
Hectare  X 2.471  = acres.  ' ! 
Cubic  centimeters  -4-  16.383  - cu.  in. 
Cubic  centimeters  -4-  3.69  = fluid 
drams  (U.  S.  P.). 

Cubic  centimeters  -4-  29.57  = fluid  oz. 
(U.  S.  P.). 

Cubic  meters  X 35.315  = cu.  ft. 

Cubic  meters  X 1.308  = cu.  yd. 

Cubic  meters  X 264.2  = gal.  (231 
cu.  in.). 

Liters  X 61.022  = cu.  in.  (Act  Con- 
gress). 

Liters  X 33.84  = fluid  oz.  (U.  S.  Phar.). 
Liters  X .2612  = gal.  (231  cu.  in.). 
Liters  -4-  3.78  = gal.  (231  cu.  in.). 
Liters  -4-  28.316  = cu.  ft. 

Tonnes  X 1.102  = short  tons. 

Tonnes  “X  .9839  = long  tons. 


Hectoliter^  X 3.531  = cu.  ft. 

Hectoliters  X 2.84  = bu.  (2,150.42 
cu.  in.). 

Hectoliters  X .131  = cu.  yd. 

Hectoliters  -4-  26.42  = gal.  (231 
cu.  in.). 

Grams  X 15.432  = gr.  (Act  Con- 
gress) . 

Grams  -4-  981  = dynes. 

Grams  (water)  -4-  29.57  = fluid  oz. 

Grams  -4-  28.35  = oz.  avoir. 

Grams  per  cu.  cent,  -4-  27.7  = lb.  per 
cu.  in. 

Joule  X .7373  = ft. -lb. 

Kilograms  X 2.2046  = lb. 

Kilograms  X 35.3  = oz.  avoir. 

Kilograms  -4- 1,102.3  = ton  (2,000 lb.). 

Kilogr.  per  sq.  cent.  X 14.223  = lb. 
per  sq.  in. 

Kilogram-meters  X 7.233  = ft.-lb. 

Kilo  per  meter  X .672  = lb.  per  ft. 

Kilo  per  cu.  meter  X .026  = lb.  per 
cu.  ft. 

Kilo  per  cheval  X 2.235  = lb.  per 
H.  P. 

Kilowatts  X 1.34  = H.  P. 

Watts  -4-  746  = H.  P. 

Watts  -4-  .7373  = ft.-lb.  per  sec. 

Calorie  X 3.968  = B.  T.  U. 

Cheval  vapeur  X .9863  = H.  P. 

(Centigrade  X 1.8)  +32  = degree  F. 

Franc  X .193  = dollars. 

Gravity  Paris  = 980.94  centimeters 
per  sec. 


United  States  Currency. 
10  mills  = 1 cent. 

10  cents  = 1 dime. 

10  dimes  = 1 dollar. 

10  dollars  = 1 eagle. 


MONEY. 

British  Money. 

4farthings  = 1 penny. 

12  pence  1 = 1 shilling. 

20  shillings  = 1 pound  sterling. 

21  shillings  = 1 guinea. 


Standard  United  States  Coins. 


Gold. 

Silver. 

Denomination. 

Value. 

Weight. 

Denomination. 

Value. 

Weight. 

* Dollar  

Quarter  eagle 

* Three-doll ar  piece 

Half  eagle 

Eagle  

Double  eagle  

$1.00 

2.50 

3.00 

5.00 
10.00 
20.00 

25.8  gr. 
64.5  gr. 
77.4  gr. 

129.0  gr. 

258.0  gr. 

516.0  gr. 

* Trade  dollar... 
Standard  silver 

dollar 

Half  dollar  

Quarter  dollar... 
Dime  

$1.00 

1.00 

.50 

.25 

.10 

420.0  gr. 

412.5  gr. 
192.9  gr. 
96.45  gr. 
38.58  gr. 

“Fineness”  expresses  the  proportion  of  pure  metal  in  1,000  parts;  thus, 
“ 900  fine  ” means  that  900  of  every  1,000  parts  are  pure  metal.  Fineness  of 


* No  longer  coined. 


MONETARY  VALUES. 


11 


U.  S.  coins  = 900  pure  metal,  100  alloy;  alloy  of  gold  coin  is  copper  or  copper 
and  silver,  but  in  no  case  shall  silver  exceed  & of  total  alloy.  Alloy  of  silver 
coin  is  copper. 

Piece.  Weight.  Contents. 

5-cent( nickel) 77.16  grains 75$  copper,  25$  nickel. 

*3-cent  .... 30  grains 75$  copper,  25$  nickel. 

*2-cent 66  grains 95$  copper,  5$tin  and  zinc. 

1-cent  (copper)  48  grains 95$  copper,  5$  tin  and  zinc. 

*No  longer  coined. 

Space  Required  to  Store  U.  S.  Coins. 


Description. 

Amount. 

How  Put  Up. 

Space. 

Gold  coins 

$1,000,000 

$5,000  in  8-oz.  duck  bags 

Nearly  17  cu.  ft. 

Silver  dollars  

1,000,000 

1,000  in  8-oz.  duck  bags 

250  cu.  ft. 

Subsidiary  silver 

1,000,000 

1,000  in  8-oz.  duck  bags 

150  cu.  ft. 

A bag  of  standard  silver  dollars  occupies  a space  12  in.  X 9 in.  X 4 in. 


To  Convert  Value  of  U.  S.  Coins  Into  English  Values  and  Vice  Versa. 
Rule. — Cents  ( U.  S.)  2.02771,  or  X -179312  = English  pence. 

Example.—  100  cents  X .49312  = 49.312  pence  — 4s.  1.312d. 

Rule. — English  pence  X 2.02771  — cents  (U.  S.). 

Example.—  lOOd.  X 2.02771  = 202.771  cents  = $2.0277. 

„ , Dollars  , ... 

Rule.—  -jgjjQfi  = Rounds  sterling. 

Example.—  = £20.548.  £.548  X 240  = 131.5d.  = 10s.  11.5d. 

4.ooo5 

Rule. — Pounds  X 7.8665  = dollars  ( U.  S.).  Shillings  X 2U.332+  = cents  ( U.S.). 


VALUES  OF  FOREIGN  COINS,  U.  S.  TREASURY  DEPT.,  JAN.  1,  1899. 


Argentine,  Argentine  Re- 
public   $ 4.824 

Bolivar,  Venezuela .193 

Boliviano,  Bolivia 439 

Centen,  Cuba 5.017 

Colon,  Costa  Rica  465 

Condor,  Chile  7.300 

Condor,  U.  S.  of  Colombia  and 

Ecuador  9.647 

Copeck,  Russia  .0075 

Crown,  Austria-Hungary .203 

Crown,  Denmark,  Norway, 

and  Sweden  268 

Crown,  Germany 1.06 

Crown,  Great  Britain 1.13 

Crown,  Sicily 96 

Crown,  Spain  (half  pistole)  1.95 

Dollar,  Bolivia .96 

f Dollar,  British  Honduras, 

British  Possessions,  N.  A. 

( except  N e wfoundland ) , 

and  Liberia 1.000 

Dollar,  Chile,  Peru,  and 

Ecuador  93 

Dollar,  Mexican  (gold)  983 

Dollar,  Mexican  (silver) 477 

Dollar,  Newfoundland 1.014 

Dollar,  U.  S.  of  Colombia 935 


Doubloon,  Central  America  $14.50 

Doubloon,  Chile  , 3.650 

Doubloon,  New  Granada 15.34 

Doubloon,  Spain  and  Mexico  15.65 

Drachma,  Greece  193 

Ducat,  Austria,  Bohemia, 

Hamburg,  Hanover  2.28 

Ducat,  Denmark 1.11 

Ducat,  Sweden 2.20 

Escudo,  Chile 1.825 

Florin,  Austria-Hungary 1.929 

Florin,  Hanover  (gold)  1.66 

Florin,  Hanover  (silver) 56 

Florin,  Holland,  South  Ger-  . 

many .38 

Florin,  Netherlands  402 

Florin,  Prussia 55 

Florin,  Silesia  48 

Franc,  Belgium,  Bulgaria, 

France,  Italy,  Roumania, 

Switzerland  193 

Gourde,  Hayti  965 

Groschen,  Prussian  Poland  .024 

Guinea,  Great  Britain  5.11 

Gulden,  Baden 40 

Imperial.  Russia 7.92 

Kran,  Persia 081 

Kreutzer,  Bavaria  .0067 


tThe  British  dollar  has  the  same  legal  value  as  the  Mexican  dollar  in  Hongkong,  the  Straits 
Settlements,  and  Labuan. 


12 


WEIGHTS  AND  MEASURES. 


VALUES  OF  FOREIGN  co  I ns.  {Continued.) 


Lira,  Italy  - $ -193 

Mark,  Finland 193 

Mark,  German  Empire 238 

Maximilian,  Bavaria 3.30 

Milreis,  Brazil  546 

Milreis,  Portugal 1.080 

Mohur,  India 7.105 

Napoleon,  France  3.84 

Peseta,  Spain 193 

Peso,  Argentine  Republic ...  .965 

Peso,  Chile 365 

Peso,  U.  S.  of  Colombia 439 

Peso,  Cuba 926 

Peso,  Guatemala,  Honduras, 

Nicaragua,  Salvador 365 

Peso,  Uruguay 1.034 

Piaster,  Egypt  049 

Piaster,  Turkey .044 

Piastre,  Spain  .1.04 

Pistole,  Rome  '. 3.37 

Pistole,  Spain 3.90 

Pound,  Egypt  4.943 

Pound  Sterling,  Great  Britain  4.8665 
Ruble,  Russia  .515 


Rupee,  India S .208 

Shilling,  Great  Britain 243 

Sol,  Peru 439 

Sou,  France  01 

Sovereign,  Great  Britain 4.8665 

Sucre,  Ecuador .439 

' Amoy  .710 

Canton 708 

Chefoo 679 

Chin  Kiang .693 

Fuehau 656 

Haikwan  (Cus- 
toms)   .722 

Tael,  China  i Hankow 664 

' Hongkong f 

Niuchwang  .665 

Ningpo  682 

Shanghai 648 

Swatow  655 

Takau  714 

L Tientsin 688 

Toman,  Persia 3.409 

Yen,  Japan - 498 


t The  British  dollar  has  the  same  legal  value  as  the  Mexican  dollar  in  Hongkong,  the  Straits 
Settlements,  and  Labuan. 

The  carat  (a  24th  part)  is  used  to  express  the  proportion  of  gold  in  an 
alloy;  thus,  gold  18  carats  tine  is  pure.  The  carat  is  also  a unit  of  weight 
for  precious  stones.  Its  value  vanes  according  to  different  authorities,  but 
the  international  carat  is  3.168  grains,  or  206  milligrams. 


Diamond  Weight  (Nystrom). 

Carats.  Grains.  Parts, 

1 = 4 = 64  = 3.2  (3.168) 

.25  =1  = 16  = .8 

.015625  = .0625  = 1 = .05 
.3125  = 1.25  — 20  —1 

151.5  = 1 ounce 


TIMBER  AND  BOARD  MEASURE. 


TIMBER  MEASURE. 

Volume  of  Round  Timber.— The  volume  in  cubic  feet  equals  the  length 
multiplied  by  one-fourth  the  product  of  mean  girth  and  diameter,  all  dimen- 
sions being  in  feet.  If  length  is  given  in  feet  and  girth  and  diameter  in 
inches,  divide  by  144;  if  all  dimensions  are  in  inches,  divide  by  1,728. 

Volume  of  Square  Timber.— When  all  dimensions  are  in  feet; 

Ru|e<—  Multiply  the  breadth  by  the  depth  and  that  product  by  the  length , and  the 
product  will  give  the  volume  in  cubic  feet. 

When  either  of  the  dimensions  is  in  inches: 

Rule. — Multiply  as  above  and  divide  by  12. 

When  any  two  of  the  dimensions  are  in  inches: 

Rule. — Multiply  as  before  and  divide  by  144. 


TIMBER  AND  BOARD  MEASURE. 
Round  Timber —Table  of  4 Girths. 


13 


4 Girths. 
Inches. 

Area  in 
Feet. 

1 Girths. 
Inches. 

Area  in 
Feet. 

£ Girths. 
Inches. 

Area  in 
Feet. 

6 

.250 

121 

1.04 

19 

2.50 

6f 

.272 

121 

1.08 

194 

2.64 

.294 

124 

1.12 

20 

2.77 

.317 

13 

1.17 

204 

2.91 

7 

.340 

131 

1.21 

21 

3.06 

7r 

.364 

131 

1.26 

214 

3.20 

7£ 

.390 

13f 

1.31 

22 

3.36 

7| 

.417 

14 

1.36 

224 

3.51 

8 

.444 

141 

1.41 

23 

3.67 

81 

.472 

141 

1.46  1 

234 

3.83 

w4 

.501 

14f 

1.51 

24 

4.00 

si 

.531 

15 

1.56 

m 

4.16 

9 

.562 

151 

1.61 

25 

4.34 

.594 

151 

1.66 

254 

4.51 

94 

.626 

151 

1.72 

26 

4.69. 

9| 

.659 

16 

1.77 

26| 

4.87 

10 

.694 

161 

1.83 

27 

5.06 

10r 

.730 

161 

1.89 

274 

5.25 

xv4 

104 

.766 

161 

1.94 

28 

5.44 

104 

.803 

17 

2.00 

284 

5.64 

11 

.840 

171 

2.09 

29 

5.84 

1H 

.878 

171 

2.12 

294 

6.04 

x-1-4 

111 

.918 

171 

2.18 

30 

6.25 

Ilf 

. .959 

18 

2.25 

12 

1.000 

181 

2.37 

Area  corresponding  to  4 girth  (mean)  in  inches  multiplied  by  length 
in  feet  equal  solidity  in  feet  and  decimal  parts. 


BOARD  MEASURE. 

In  measuring  boards,  they  are  assumed  to  be  1 inch  in  thickness.  The 
number  of  feet,  board  measure  (B.  M.),in  a given  board  or  stick  of  timber, 
equals  the  length  in  feet  multiplied  by  the  breadth  m feet  multiplied  by  the 
thickness  in  inches. 


Breadth. 

Inches. 

Area  of  a 
Lineal  Foot. 

Breadth. 

Inches. 

Area  of  a 
Lineal  Foot. 

Breadth. 

Inches. 

Area  of  a 
Lineal  Foot. 

A 

.021 

44 

.354 

84 

.688 

A 

A 

.042 

44 

.375 

84 

.708 

a 

i 

.063 

44 

.396 

84 

.729 

* 

1 

.083 

5 

.417 

9 

.750 

14 

.104 

54 

.438 

94 

.771 

14 

.125 

54 

.458 

94 

.792 

■*-3 

If 

.146 

54 

.479 

94 

.813 

-*-4 

2 

.167 

6 

.500 

10 

.833 

24 

.188 

64 

.521 

104 

.854 

"4 

24 

.208 

64 

.542 

104 

.875 

4ia 

24 

.229 

64 

.563 

104 

.896 

3 

250 

7 

.583 

11 

.917 

34 

.271 

74 

.604 

114 

.938 

'-’A 

34 

.292 

74 

.625 

Hi 

.958 

3f 

.313 

74 

.646 

114 

.979 

4 

.333 

8 

.667 

12 

1.000 

Area  oi  a lineai  i 
tents  in  square  feet. 


14 


MATHEMATICS. 


MATHEMATICS. 


By  Edward  H.  Williams,  Jr.,  E.  M. 

Professor  of  Mining  Engineering  and  Geology  at  the  Lehigh  University. 


GENERAL  PRINCIPLES. 

Quantity  or  magnitude  is  anything  that  can  he  increased  or  decreased,  or 
that  is  capable  of  any  sort  of  measurement  or  calculation,  such  as  numbers, 
lines,  space,  time,  motion,  weight,  force,  power,  heat,  light,  electricity,  etc. 
We  can  measure  a quantity  by  applying  to  it  a portion  of  the  same  quantity, 
called  a unit.  If  the  quantities  are  of  different  kinds,  we  cannot  measure 
them  by  one  another,  but  we  can  compare  them  or  institute  a calculation 
between  them. 

Mathematics  treats  of  all  kinds  of  quantity  that  can  be  numbered  or  meas- 
ured. Arithmetic  is  that  part  that  treats  of  numbering,  and  is  called  the 
science  of  numbers.  Geometry  is  the  science  of  measuring.  These  two  are 
the  foundation  of  all  other  parts  of  mathematics,  and  are  called  pure  mathe- 
matics. We  can  also  reason  about  numbers  by  substituting  letters  for  num- 
bers, and  represent  their  relations  by  signs.  This  is  called  algebra , and  it 
may  be  likened  to  a shorthand  arithmetic.  An  extension  of  arithmetic  to 
geometry,  by  which  angles  and  triangles  are  subjected  to  numerical  compu- 
tation, is  called  trigonometry,  and  plane  trigonometry  treats  of  methods  of 
computing  plane  angles  and  triangles,  and  embraces  the  investigations  of  the 
relations  of  angles  in  general,  which  is  called  angular  analysis.  Another 
extension  of  arithmetic  to  geometry,  by  which  lines,  areas,  and  volumes  are 
computed,  is  called  mensuration.  Mensuration  of  large  portions  of  the  earth’s 
surface,  where  the  curvature  of  the  same  is  taken  into  calculation,  is  called 
geodesy.  If  the  portions  are  smaller  and  curvature  is  neglected,  the  science 
is  called  surveying,  and  mine  surveying  if  confined  to  underground  work. 


COMMONLY  USED  MATHEMATICAL  SIGNS  AND  ABBREVIATIONS. 


-f  means  plus,  or  addition. 

— means  minus,  or  subtraction. 

X means  multiplication. 

± means  plus  or  minus. 

+ means  minus  or  plus. 

-r-  means  division. 

means  ratio. 

: ::  : means  proportion. 

2 : 3 : : 4 : 6 shows  that  2 is  to  3 
as  h is  to  6. 

= means  equality. 

means  equivalency, 
y means  square  root, 

f'  means  cube  root , etc. 

l/3  square  root  of  3. 

^ 5 cube  root  of  5. 

T1  7 squared. 

83  8 cubed. 

5 = a/b,  a + b.  15  -h  16  = 

0 Id 

. * . therefore. 

> greater  than. 

< less  than. 

□ square. 

□'  square  feet. 


□"  square  inches. 

O round. 

( ) [ 1 | | , vincula , denoting  that 

the  numbers  enclosed  are 
to  be  taken  together;  as, 

(a  + 6)c  = 4 + 3X5  = 35. 
degrees,  arc  or  thermometer, 
minutes  or  feet, 
seconds  or  inches. 

30°  40'  4"  is  30  degrees  40 
minutes  4 seconds. 
is  4 feet  6 inches, 
accents  to  distinguish  letters , 
as  a',  a",  a'", 
ai,  «2,  ab,  ac,  read  a sub  1,  a sub  b,  etc. 
a2,  a3  a squared,  a cubed. 

as  = i Yofi,  at  = >/a3. 

sin  a = the  sine  of  a. 

log  = logarithm, 

angle. 

L right  angle. 

_|_  perpendicular  to. 

sin  sine. 

cos  cosine. 


4'  6" 

/ //  nt 


ARITHMETIC. 


15 


MATHEMATICAL  SIGNS  AND  ABBREVIATIONS—  {Continued). 


tan,  or  tang,  tangent. 
sec  secant. 

versin  versed  sine. 

cot  cotangent. 

cosec  cosecant. 

covers  coversed  sine. 

tt'  pi,  ratio  of  circumference  of 

circle  to  diameter  3.14159. 
g acceleration  due  to  gravity 

= (32.16  ft.  per  sec.). 

R,  r radius. 

W,  w weight. 

H.  P.  horsepower. 


I.  H.  P.  indicated  horsepower. 

B.  H.  P.  brake  horsepower. 

A.  W.  G.  American  wire  gauge 

(Brown  & Sharpe). 

B.  W.  G.  Birmingham  wire  gauge. 

r.  p.  m.,  or  rev.’  per  min.,  revolutions 
per  minute. 

A decimal  point  is  a period  (.)  pre- 
fixed to  a number  to  show 
that  the  number  is  less  than 
unity  (1);  thus,  .2  = •&; 
.35  = y3(fo>  5.75  = 5yo%>  or  5|. 


ARITHMETIC. 


To  Cast  the  Nines  Out  of  a Number.— Add  together  the  digits,  and  find  how 
many  nines  are  contained  in  their  sum.  Reject  these  nines  and  set  down  the 
remainder  to  the  right  of  the  number. 

Example —Cast  the  nines  out  of  18.304.  18,304.  /.  Ans. 

To  Prove  Addition.— Cast  the  nines  out  of  each  row  of  figures  added,  and 
out  of  their  sum.  Add  together  the  remainder  and  cast  the  nines  from  its 
sum  If  the  remainder  from  this  last  process  is  equal  to  the  remainder 
obtained  from  the  sum  of  the  numbers,  the  addition  is  correct. 

Example— Prove  this  addition:  2,1 4 3,5  6 8 2 

8,560,391  5 

1 0,7  0 3,9  5 9 7.  Ans. 

To  Prove  Subtraction.— Add  the  remainder  to  the  lesser  number;  their  sum 
should  equal  the  larger  number.  ..  , , ... 

To  Prove  Multiplication. —Cast  the  nines  out  of  multiplicand  and  multi- 
plier and  multiplv  the  remainders  together.  Cast  the  nines  out  of  the 
product,  and  the  remainder  should  equal  the  remainder  obtained  by  cast- 
ing the  nines  from  the  original  product. 

Example.— Prove  this  multiplication:  3,542  X 6,196  = 21,946,232. 

3,5  4 2 5 

6,1  9 6 4 

2 1,9  4 6,2  3 2 2.  Ans. 

To  Prove  Division.— Subtract  the  remainder,  if  there  be  any,  from  the 
dividend,  and  divide  what  remains  by  the  quotient.  If  the  new  quotient 
equals  the  old  divisor,  the  work  is  right. 

Example.— Divide  31,046,835  by  56.  554,407p.  Ans.  . 

Proof.— Take  43  from  31,046,835,  and  divide  the  remainder,  31,046, /92,  by 

Rule.— To  square  any  number  containing  the  fraction  multiply  the  whole 
number  by  the  next  higher  whole  number , and  add  |. 

Example.—  (8£)*2  — 8 X 9 + i = 72£. 


COMMON  FRACTIONS. 

A fraction  is  a part  of  a whole,  as  f,  etc.  „ 

The  numerator  of  a fraction  is  the  number  that  tells  how  many  parts  of  a 
whole  are  taken.  Thus,  2 is  the  numerator  of  § , as  it  shows  that  two  of  the 
three  parts  into  which  the  whole  is  divided  are  taken. 

The  denominator  of  a fraction  is  the  number  that  shows  into  how. many 
parts  the  whole  is  divided.  Thus,  in  the  fraction  §,  the  3 is  the  denominator. 

A common  denominator  is  a denominator  common  to  two  or  more  fractions. 
Thus  4 and  f have  common  denominators;  and  again,  12  is  a common  de- 
nominator for  I-,  and  £,  as  they  each  are  respectively  equal  to  T25,  T5, 

T<T  Add^Common  Fractions.— If  of  the  same  denominator,  add  together  the 
numerators  only.  Thus  & + ts  + ts  = iV 


16 


FRACTIONS. 


If  they  have  different  denominators,  change  them  to  fractions  with  com- 
mon denominators,  and  proceed  as  before. 

Example.— What  is  the  sum  of  § + i + i ? 

I = hi  i = ift,  and  i = ||. 

If  + If  + if  — If*  Ans. 

To  Multiply  Common  Fractions.— Multiply  the  numerators  together  for  the 
numerator,  and  the  denominators  for  the  denominator.  Thus,  £ X & X I 
==  9%>  or  tV 

To  Divide  Common  Fractions.— Invert  the  divisor,  and  multiply. 

Example. — Divide  & by  §. 

AXf  = T25*  Ans. 

To  Reduce  Compound  Fractions  to  Simple  Fractions.— Multiply  the  integer 
by  the  denominator  of  the  fraction,  add  the  numerator  for  the  new  numera- 
tor, and  place  it  over  the  denominator. 

Example.— Reduce  5§  to  a simple  fraction. 

5X3  + 2 = 17,  or  the  numerator,  and  the  fraction  is  therefore 

To  Reduce  Simple  Fractions  to  Compound  Fractions.— Divide  the  numerator 
by  the  denominator,  and  use  the  remainder  as  the  numerator  of  the  remain- 
ing fraction. 

Example.— Reduce  -6#  to  a compound  fraction. 

9)64(7 

6 3 Compound  fraction  = 7+  Ans. 

“I 

To  Reduce  Common  Fractions  to  Decimal  Fractions.— Annex  ciphers  to  the 
numerator,  and  divide  by  the  denominator,  and  point  off  as  many  decimal 
places  in  the  quotient  as  there  are  ciphers  annexed. 

Example.— Reduce  A to  a decimal  fraction. 

16  ) 9.0  000  (.5  6 25  Ans. 

Note.— Ciphers  annexed  to  a deci- 
mal do  not  increase  its  value.  1.13  is 
the  same  as  1.1300.  Every  cipher 
placed  between  the  first  figure  of  a 
decimal  and  the  decimal  point  divides 
the  decimal  by  10.  Thus, 

.13  -r- 10  = .013, 


80 
100 
96 
40 
32 
80 
80 


Table  of  Fractions  Reduced  to  Decimals. 


Si 

.015625 

If 

.265625 

if 

.515625 

11 

l 

.765625 

3*2 

.03125 

52 

.28125 

If 

.53125 

hi 

.78125 

.046875 

19 

64 

.296875 

if 

.546875 

6] 

63 

.796875 

T 5 

.0625 

T6 

.3125 

is 

.5625 

1 c 

Tt 

.8125 

Si 

.078125 

n 

.328125 

ii 

.578125 

6 1 
63 

.828125 

.09375 

ii 

.34375 

if 

.59375  ! 

hi 

f 

.84375 

£ 

.109375 

if 

.359375 

if 

.609375 

11 

.859375 

.125 

f 

.375 

i 

.625 

i 

.875 

Si 

.140625 

if 

.390625 

u 

.640625 

64 

.890625 

S2 

.15625 

if 

.40625 

hi 

.65625 

If 

.90625 

ii 

.171875 

if 

.421875 

If 

.671875 

IS 

.921875 

T6 

.1875 

TS 

.4375 

ii 

.6875 

ft 

.9375 

£f 

.203125 

if 

.453125 

If 

.703125 

fc 

.953125 

"52 

.21875 

it 

.46875 

it 

.71875 

hi 

.96875 

if 

.234375 

if 

.484375 

if 

.734375 

ii 

.984375 

i 

.25 

1 

.5 

f 

.75 

l 

1.0000 

DECIMALS. 

Decimal  fractions  have  for  their  denominators  10  or  a power  of  10, 
but  the  denominator  is  usually  omitted.  Thus,  .1  = .01  = T|^;  .001 

= Tt ha}  e^c. 

To  Add  Decimals.— Place  whole  numbers  under 
whole  numbers,  tenths  under  tenths,  hundredths 
under  hundredths,  etc.,  and  add,  placing  the  deci- 
mal point  in  the  sum  directly  under  the  points 
above.  Thus,  1 9.6  3 1 7 


.00  7 5 
.6  3 
1.0  6 

1 7.9  3 4 2 


DECIMALS. 


17 


To  Subtract  Decimals.— Arrange  the  figures  as  in  5.9  69  7 8 

addition,  and  proceed  as  in  simple  subtraction.  3.2  8 6 9 4 

Thus  2.6  8 2 8 4 


To  Multiply  Decimals.— Proceed  as  in  ' £ ££ 

simple  multiplication,  pointing  oft*  as  

many  decimal  places  in  the  result  as  14  0 2 5 9 3 

there  are  decimal  places  in  both  mul-  2 3 3 7 6 5 5 
tiplicand  and  multiplier.  Thus  0.2  4 7 7 9 1 4 3 

To  Divide  Decimals.— Proceed  as  in  simple  division,  and 
decimal  places  in  the  quotient  as  the  number  of  decimal 
dend  exceeds  those  in  the  divisor. 


(5  decimal  places) 
(3  decimal  places) 


(8  decimal  places) 
point  off  as  many 
places  in  the  divi- 


Example  1.— Divide  4.756  by  3.3. 

. 3.3  ) 4.7  5 6 0 0 ( 1.4  4 1 2 Ans. 

33 

145 

1 ^ Example  2.— Divide  .006  by  20 

Too  2 0 ).0  0 60  (.0  0 0 3.  Ans. 

—40  — $-° 

33 

70 

66 

4 


U0TE it  has  been  said  before  that  algebra  is  a shorthand  arithmetic. 

Before  proceeding  further  with  the  various  methods  of  arithmetic,  the 
principles  of  algebra  will  be  stated,  and,  after  the  subsequent  examples  are 
worked  out  by  arithmetical  rules,  an  example  will  be  given  of  the  algebraic 
method  of  doing  the  same.  In  every  example,  we  have  known  quantities 
from  which  we  seek  to  find  certain  unknown  ones.  While  there  is  no  way  of 
indicating  these  in  arithmetic , we  can  readily  do  so  in  algebra , by  placing  the 
first  letters  of  the  alphabet  as  representatives  of  the  known  quantities 
(as  a,  b,  c),  and  the  last  letters  ( x , y,  z)  of  the  unknown  ones.  The  signs  m 
algebra  are  those  just  given  for  arithmetic.  In  addition  to  them,  we  can 
indicate  multiplication  by  placing  a period  (.)  between  the  quantities,  as  a.b 
(read  a multiplied  by  b),  or  simply  by  placing  the  two  letters  together,  as  ab. 

We  can  indicate  division  as  in  common  fractions,  ^ being  read  a divided  by  b. 

To  illustrate  algebraic  symbols,  let  l denote  the  length,  b the  breadth,  and 
h the  height  of  a mine  car.  If  it  be  desired  to  divide  the  height  into  the 
product  of  the  length  and  breadth,  it  is  expressed  as  follows: 

lb 

h‘ 

When  two  or  more  letters  are  placed  together,  without  anything  between 
them,  it  is  understood  that  the  quantities  represented  by  those  letters  should 
be  multiplied  together.  If  l represents  8 and  b represents  4,  then  4 and  8 are 
multiplied  together;  thus,  4 X 8 = 32.  , ,,  , ,,, 

If  it  be  desired  to  divide  the  height  into  the  sum  of  the  length  and  breadth, 
it  is  expressed  thus: 

l -}-  b 
h '' 


The  square  of  the  length  multiplied  by  the  cube  of  the  breadth,  thus: 

l*b\ 

The  square  root  of  the  length  divided  by  the  cube  root  of  the  breadth,  thus: 

VT 


The  square  root  of  the  difference  of  the  length  and  breadth  divided  by  the 
height,  thus: 


V l — b 


18 


PROPORTION. 


SIMPLE  PROPORTION,  OR  SINGLE  RULE  OF  THREE. 

.A  PJ0P°rti?n  is,  expression  of  equality  between  equal  ratios;  thus,  the 
ratio  of  10  to  5 = the  ratio  of  4 to  2,  and  is  expressed  thus: 

10  : 5 : : 4 : 2. 

There  are  four  terms  in  proportion.  The  first  and  last  are  the  extremes 
and  the  second  and  third  are  the  means. 

Quantities  are  in  proportion  by  alternation  when  antecedent  is  compared 
with  antecedent  and  consequent  with  consequent.  Thus,  if  10  : 5 : : 4 : 2, 
then  10  ! 4 i ! 5 * 2. 

Quantities  are  in  proportion  by  inversion  when  the  antecedents  are  made 
consequents  and  the  consequents  antecedents.  Thus,  if  10  : 5 • • 4 • 2 then 
5 : 10  : : 2 : 4.  ’ 

In  any  proportion,  the  product  of  the  means  will  equal  the  product  of  the 
extremes.  Thus,  if  10  : 5 : : 4 : 2,  then  5X4-10X2. 

A mean  proportional  between  two  quantities  equals  the  square  root  of  their 
product.  Thus,  a mean  proportional  between  12  and  3 = the  square  root  of 
12  x 3,  or  o. 

If  the  two  means  and  one  extreme  of  a proportion  are  given,  we  find  the 
other  extreme  by  dividing  the  product  of  the  means  by  the  given  extreme. 

1°  : : : 4 : ( )•  then  (4  X 5)  -4-  10  = 2,  and  the  proportion  is  10  : 5 : : 4 : 2 

,.  tt  the  two  extremes  and  one  mean  are  given,  we  find  the  other  mean  bv 
dividing  the  product  of  the  extremes  bv  the  given  mean.  Thus.  10  * M • • 4 • 2 
then  (10  X 2)  4-  4 = 5,  and  the  proportion  is  10  : 5 : : 4 : 2.  ’ ' " ’ 

.Example.— If6  men  load  30  wagons  of  coal  in  a day,  how  many  wagons 
will  10  men  load?  (They  will  evidently  load  more,  so  the  second  term  of  the 


proportion  must  be  greater  than  the  first.) 

6 : 10  : : 30  : ( );  then,  (10  X 30)  4-  6 = 50. 


Ans. 


COMPOUND  PROPORTION,  OR  DOUBLE  RULE  OF  THREE. 

Principles. 

1.  The  product  of  the  simple  ratios  of  the  first  couplet  equals  the  product 
of  the  simple  ratios  of  the  second  couplet.  T-hus, 

/4  : 12)  . (5  : 10)  = ± 7_  _ _5  6 

(7  : 14 J (6  : 18/  12  X 14  10  X 18‘ 

2.  The  product  of  all  the  terms  in  the  extremes  equals  the  product  of  all 
the  terms  m the  means.  Thus,  in 


J 4 : 121 

(5  : 10) 

17  : 14/ 

* ' 

16  : 18/ 

we  have  4 X 7 X 10  X 18  - 12  X 14  X 5 X 6. 

3.  Any  term  in  either  extreme  equals  the  product  of  the  means  divided 
by  the  product  of  the  other  terms  in  the  extremes.  Thus,  in  the  same 
proportion,  we  have 

4 = 5 X 6 X 12  X 14 
7X10X18  * 

4.  Any  term  in  either  mean  equals  the  product  of  the  extremes  divided 
by  the  product  of  the  other  terms  in  the  means.  Thus,  in 


J4  : 12)  . 

. (5  : 101 

17  : 14/  ‘ 

* 16:18/ 

we  have  5 = (4  X 7 X 10  X 18)  4-  (6  X 12  X 14). 

RuJ?-— >•  Put the  required  quantity  for  the  first  term  and  the  similar  known 
quantity  for  the  second  term , and  form  ratios  with  each  pair  of  similar  quantities 
for  the  second  couplet , as  if  the  result  depended  on  each  pair  and  the  second  term. 

II.  the  required  term  by  dividing  the  product  of  the  means  by  the  product 

oj  inejourtn  terms. 

. SX/MP^E  1*— If  4 men  can  earn  $24  in  7 days,  how  much  can  14  men  earn 
in  12  days? 


= $144.  Ans. 


The  sum  : $24  : : : 4 j . or>  the  sum  = 

Example  2.— If  12  men  in  35  days  build  a wall  140  rd.  long,  6 ft.  high,  how 


24  X 14  X 12 
4X7 


EVOLUTION. 


19 


many  men  can,  in  40  days,  build  a wall  of  the  same  thickness  144  rd.  long, 
5 ft.  high? 

12:()=??4^^  = 9.  Ans. 


f 40  : 35  ) 

4 140  : 144  y : : 

l 6:5  J 


40  X 140  X 6 


INVOLUTION. 


To  Square  a Number.-— Multiply  the  number  by  itself.  Thus,  the  square  of 
4 = 4 X 4,  or  16. 

To  Cube  a Number.— Multiply  the  square  of  the  humber  by  the  number. 
Thus,  the  cube  of  4 = 16  X 4 = 64. 

To  Find  the. Fourth  Power  of  a Number.— Multiply  the  cube  by  the  number. 
Thus,,  the  fourth  power  of  4 = 64  X 4 = 256. 

To  Raise  a Number  to  the  Sixth  Power. — Square  its  cube. 

To  Raise  a Number  to  the  Twelfth  Power.— Square  its  sixth  power. 

(See  logarithms  for  shorter  method.) 


EVOLUTION. 


To  Find  the  Square  Root  of  a Number: 

Rule. — I.  Separate  the  given  number  into  periods  of  two  figures  each , beginning 
at  the  units  place. 

II.  Find  the  greatest  number  whose  square  is"  contained  in  the  period  on  the 
left;  this  will  be  the  first  figure  in  the  root.  Subtract  the  square  of  this  figure  from 
the  period  on  the  left , and  to  the  remainder  annex  the  next  period  to  form  a 
dividend. 

III.  Divide  this  dividend , omitting  the  figure  on  the  right , by  double  the  part  of 
the  root  already  found,  and  annex  the  quotient  to  that  part , and  also  to  the  divisor; 
then , multiply  the  divisor  thus  completed ' by  the  figure  of  the  root  last  obtained , 
and  subtract  the  product  from  the  dividend. 

IV.  If  there  are  more  periods  to  be  brought  down , continue  the  operation  as 
before. 

Example.— Find  the  square  root  of  8 7'4  2'2  5 ( 9 3 5 Ans. 

874,225.  8 1 


18  31 


TT41T 

549 


186  5 | 9325 
9 3 25 


OPERATION. 

9 X 2 = 18.  18  into  64  goes  3 times,  hence 
new  divisor  = 183.  93  X 2 = 186.  186  into 
932  goes  5 times,  hence  new  divisor  = 1,865. 

(See  logarithms  for  shorter  method.) 

The  square  root  of  a fraction  is  found  by  extracting  the  square  root  of  the 
numerator  and  denominator  separately.  Thus,  the  square  root  of  ^ f . 

When  decimals  occur,  the  number  is  pointed  off  into  periods  both  right 
and  left  from  the  decimal  point,  and  there  will  be  as  many  decimal  places  in 
the  root  as  there  are  periods  to  the  right  of  the  decimal  point  in  the  number. 
Example  1.— Find  the  square 


root  of  874.225. 

8'7  4.2  2'5  ( 2 9.5  6+ 


4 9i  4 7 4 
441 


Example  2.— Find  the  square 
root  of  .00874225. 

.0  0'8  7'4  2'2  5 (.0  9 3 5 
81 


18  3|" 


590 


29  25 

7]  39  75W 

35442 


642 

549 


18  6 5|  93  25 
9325 


4 3 08+ 


To  Find  the  Cube  Root  of  a Number: 

Rule. — I.  Separate  the  given  number  into  periods  of  three  figures  each , beginning 
at  the  units  place. 

II.  Find  the  greatest  number  whose  cube  is  contained  in  the  period,  on  the  left; 
this  will  be  the  first  figure  in  the  root.  Subtract  the  cube  of  this  figure  from  the 
period  on  the  left , and  to  the  remainder  annex  the  next  period  to  form  a dividend • 


20 


PERCENTAGE. 


Ill  Divide  this  dividend  by  the  partial  divisor , which  is  3 times  the  square  of 
the  root  aS found?  considered  as  tens;  the  quotient  is  the  second  figure  of  the 

r°°\\l  To  the  vartial  divisor  add  3 times  the  product  of  the  second  figure  of  the 
root  by  the  firsf  considered  as  tens , also  the  square  of  the  second  figure,  the  result 

willbe  compiete  divisor  by  the  second  figure  of  the  root , and  subtract 

the^oduct^J^dMdend.  dolOTl,  proceed™  before,  using  the 

part  of  the  root  already  found,  the  same  as the  JM. figure  t»  thepremous  process. 
Example.— Find  the  cube  root  of  12,812,904. 

operation.  • j ^ . . 

1 2,8  1 2,9  0 4 ( 2 3 4 Ans. 


2}  = 

= 8 

1st  partial  divisor,  3 X 202  = 
3 X 20  X 3 = 

1,2  0 0 
180 

4,812 

32  = 

9 

4,1  6 7 

1st  complete  divisor, 

1,3  8 9 

6 4 5,9  0 4 

2d  partial  divisor,  3 X 2302  == 
3 X 230  X 4 = 

1 5 8,7  0 0 
2,7  6 0 

6 4 5,9  0 4 

42  = 

16 

2d  complete  divisor,  1 6 1,4  7 6 , 

The  cube  root  of  a fraction  is  found  by  extracting  the  cube  root  of  the 
numerator  and  denominator  separately.  Thus,  the  cube  root  of  64 
(See  logarithms  for  shorter  method.) 

PERCENTAGE. 

Percentage  means  by  or  on  the  hundred.  Thus,  1 J>  = xh  = -01> 

plue“theratle  SSjS  ft  SSZSTgSSXZXA 

agebythe  rate68' Thus?!" ' 'the' rateVt^and  thepwclnkg^sll^!  thebase 

™ ^dtbeD^S« 
equals  115.80  -e- 1,930  = .06,  or  6£  

ARITHMETICAL  PROGRESSION. 

sum  of  the  terms  49. 

In  any  arithmetical  progression, 

Tpt  f = first  term; 

l = last,  or  nth  term; 
d = common  difference; 
n = number  of  terms;  and 

s = their  sum.  , fA  ^ 

The  second  term  =/  + ( S-D*  =/+  *.  the  fourth  term  -/+(4-l)d. 
and  the  nth  term  = /+(„_1)d.  (1) 

From  equation  (1)  we  obtain  , 

f=l±{n-l)d.  (2)  d==^ITi 


„ ^ f 4-1 


(3) 


(4) 

(5) 


GEOMETRICAL  PROGRESSION, 


21 


Substituting  the  value  of  l from  (1), 


«=  2[2/+(w“"1)<q* 


(6) 


Example  1.— A company  contracts  to  put  down  a bore  hole  at  one  dollar 
if1)  Per  foot  tor  the  first  100  ft.;  three  dollars  ($3)  per  foot  for  the  second  100 
ft.;  and  two  dollars  ($2)  per  foot  additional  for  each  successive  100  ft.  The 
hole  was  800  ft.  deep.  What  was  the  cost  ? 

n = 8;  / = 100;  and  d = 2.  Substitute  these  values  in  formula  (6). 

„ „ s = f [2  X 100  + (8  - 1)  200]  = $6,400.  Ans. 

Example  2.— If  water  flowing  10.12  gal.  per  min.  be  struck  in  a shaft  30  ft 
SSjow  the^rface’  and  the  increase  in  flow  be  .02  gal.  per  ft.  till  the  depth  be 
200  ft.,  and  thence  the  flow  decreases  .02  gal.  per  ft.  till  the  rock  be  dry  how 
deep  was  the  shaft  at  the  last  point,  and  what  was  the  total  amount  of  water 
flowing  into  it  per  minute  ? 

During  the  increase  of  flow,  n = 170;  / = 10.12;  and  d = .02.  I Tbv 
formula  (1)]  — 10.12 -f  (170  — 1).02  = 13150,  or  13.50  gal.  flow  at  a depth  of  200 
20*6  ft^in^de  tli  ^2X10'12  (170  — 1). 02]  = 2,007.7  gal.  flowing  in  along  the  first 

During  the  decrease  in  flow/  = 13.50;  d = .02,  and  l = .02. 

n [formula  (3)]  = — + 1,  for  a decreasing  progression 

n = 1. 


Then. 


13.50 -.02 

.02 


d 


+ 1 


675, 


the  depth  at  which  the  rock  will  run  dry, 

ai?£  a = t2  X -02  + (675  — 1)  .02],  or  4,563  gal.,  the  amount  of  water  that 
will  flow  in  per  minute  along  the  last  675  ft.  The  total  amount  of  water 
flowing  in  along  the  total  depth  of  875  ft.  is  2,007.7  + 4,563,  or  6,570,7  gal.  Ans. 


GEOMETRICAL  PROGRESSION. 

A series  of  quantities,  in  which  each  is  derived  from  that  which  precedes 
W by  multiplication  by  a constant  quantity,  is  called  a geometrical  progression. 
It  the  multiplier  be  a whole  number,  the  progression  is  styled  increasing;  if 
it  be  a fraction,  the  progression  is  styled  decreasing.  The  series 
, 1,  2,  4,  8,  16,  32 

has  2 for  a multiplier,  and  is  an  increasing  progression.  The  series 

32,^16,  8,  4,  2,  1, 

have  \ for  a multiplier,  and  are  decreasing  progressions. 

The  common  multiplier  in  a geometrical  progression  is  called  the  common 
ratio;  or,  briefly,  the  ratio. 

Let  / = first  term; 

l = last  term,  whose  number  from  /is  n\ 
n = number  of  terms; 
r = ratio; 
s = sum  of  terms. 


1 = 

J rpn — 1^ 

(1) 

J rpn — 1 

(4) 

s = 

/(»•»  - 1) 
r — 1 

(2) 

/ = s — r (s  — l). 

(5) 

s = 

lr  -/ 
r — 1 * 

(3) 

r = s — f ' 
s — l 

(6) 

Example.— -If  a man  should  contract  to  sink  a shaft  to  the  base  of  the  coal 
measures  at  the  rate  of  cent  for  the  first  50  ft.;  | cent  for  the  second  50  ft ; 
i cent  lor  the  third  50  ft.;  and  so  on  at  the  same  rate,  how  much  would  be 
due  if  the  shaft  were  1,500  ft.  deep  ? 

0 . ...  „ / = tsI  n = 30;  and  r = 2. 

Substituting  m formula  (1), 

1 = A X (229)  33,554,432,  and  s [formula  (3)]  = 3.3>554>432j<  2 — Ty 

= $671,088.63i|.  Ans. 


22 


LOGARITHMS. 


LOGARITHMS. 

USE  OF  LOGARITHMS. 

I nparithms  are  designed  to  diminish  the  labor  of  multiplication  and  divi- 
sion bv  substituting  in  their  stead  addition  and  subtraction.  A logarithm us 
the  exponent  of  the  power  to  which  a fixed  number,  called  the  base,  must  be 
raised  to  produce  a given  number.  The  base  of  the  common  systein  is  10, 
and  as  a logarithm  is  the  exponent  of  the  power  to  which  the  base  must  be 
raised  in  order  to  be  equal  to  a given  number,  all  numbers  are  to  be  regarded 
as  powers  of  10;  hence, 

100  = 1,  we  have  logarithm  of  1 = 0. 

101  = io,  we  have  logarithm  of  10  = 1. 

102  = ioo,  we  have  logarithm  of  100  = 2. 

103  = i ooo,  we  have  logarithm  of  1,000  = 3. 

104  = 10,000,  we  have  logarithm  of  10,000  = 4. 

The  logarithms  of  numbers  between  1 and  10  are  less  than  unity,  and  are 
pxnressed  as  decimals.  The  logarithm  of  any  number  between  10  and  100  is 
moreXn  1 anTless  than  2,  hence  it  is  equal  to  X plus  a decimal.  Between 

^Thf^  in^ral'parfof  a* logarithmls'tts ^clwraoteristio,  the  decimal  part  is 

ltS  Example.— The  log  of  67.7  is  1.83059,  the  characteristic  of  this  logarithm 

lS  1 Th^  charter  illic  of  a logarithm  is  always  1 less  than  the  number  of  whole 
^es  expressing  that  lumber  and  may  ^ fher  neg^i veorposvUve 
y <rv.fi  nhflTpeteristic  of  the  logarithm  of  7 is  0;  of  1/  is  1,  oi  tu  is  z,  cio. 

Tte  mantissa  is  the  decimal  portion  of  a logarithm,  and  is  always  considered 

opposite  it  will  be  found  the  logarithm  with  its  ch^a£^”stcf ' -proceed 

of  327  is  2 51455  *As  the  first  two  figures  of  the  decimal  are  the  same  lo 

lillsSisiiss 

number  into  an  integer  and  a decimal..  If  the  decimal  part  contains  i 

ssswsss  iffijssst « »«<. 

for  the  first  four  figures  of  the  given  number 

Example.— What  is  the  logarithm  of '234,56/?  we  have 

and  in  the  column  headed  19,  under  “ P.  P.,”  oppos, ite  t » e fl nd  l^whmh 
added  to  the  portion  of  the  mantissa  already  found,  .3/014,  gnes  .3/U2,. 
characteristic  is  5,  hence  the  iogBntto  is  5.3 according  to  previous 


LOGARITHMS. 


23 


of  a whole  number  and  a decimal,  the  characteristic  is  1 less  than  the  whole 
number.  Where  it  is  a simple  decimal,  or  when  there  are  no  ciphers  between 
the  decimal  point  and  the  first  numerator,  the  characteristic  is  negative, 
and  is  expressed  by  1,  with  a minus  sign  over  it.  Where  there  is  one  cipher 
between  the  decimal  point  and  first  numerator,  the  characteristic  is  2,  with 
a minus  sign  over  it.  Where  there  are  2 ciphers,  the  characteristic  is  3,  with 
a minus  sign  over  it.  Thus: 

The  logarithm  of  67.7  is  1.83059. 

The  logarithm  of  6.77  is  0.83059. 

The  logarithm  of  .677  is  1.83059. 

The  logarithm  of  .0677  is  2.83059. 

The  logarithm  of  .00677  is  3.83059. 

The  characteristic  only  is  negative.  The  decimal  part  is  positive. 

To  Find  the  Logarithm  of  a Vulgar  Fraction.— Subtract  the  logarithm  of  the 
denominator  from  the  logarithm  of  the  numerator.  The  difference  is  the 
logarithm  of  the  fraction. 

Example.— Find  logarithm  of 

Log  4 = 0.60206 
Log  10  = L 

1.60206 

1.60206  is  the  logarithm  of  .4. 

To  Find  the  Natural  Number  Corresponding  to  Any  Logarithm.— Look  in  the 
column  headed  “ 0 ” for  the  first  two  figures  of  the  decimal  part;  the  other  four 
figures  are  to  be  looked  for  in  the  same  or  in  one  of  the  nine  following  col- 
umns.  If  they  are  exactly  found,  the  number  must  be  made  to  correspond 
with  the  characteristic  by  pointing  off  decimals  or  annexing  ciphers. 

If  the  decimal  portion  cannot  be  found  exactly,  find  the  next  lower  loga 
rifhm,  subtract  it  from  the  given  logarithm,  divide  the  difference  by  the 
difference  between  the  next  lower  and  the  next  higher  logarithm,  and  annex 
the  quotient  to  the  natural  number  found  opposite  the  lower  logarithm. 

To  Multiply  by  the  Use  of  Logarithms. — Add  the  logarithms  of  the  factors 
together;  the  sum  will  be  the  logarithm  of  their  product. 

Example.—  67.7  X .677. 

Log  67.7  = 1.83059 

Log  .677  = 1.83059 

1.66118 

1.66118  is  the  logarithm  of  45.833. 

To  Divide  by  the  Use  of  Logarithms.— Subtract  the  logarithm  of  the  divisor 
from  the  logarithm  of  the  dividend;  the  difference  will  be  the  logarithm  of 
the  quotient. 

Example.— Divide  67.7  by  .0677. 

Log  67.7  = 1.83059 
Log  .0677  = 2.83059 
3.00000 

3 is  the  logarithm  of  1,000. 

To  Square  a Number  by  the  Use  of  Logarithms.— Multiply  the  logarithm  of 
the  number  by  2.  The  product  will  be  the  logarithm  of  the  square  of  the 
number. 

Example.— Square  .677. 

Log  .677  = L 83059 
2 

1.66118 

1.66118  is  the  logarithm  of  .45833. 

To  Cube  a Number.— Multiply  the  logarithm  of  the  number  by  3.  The 
product  will  be  the  logarithm  of  the  cube  of  the  number. 

To  Raise  a Number  to  Any  Power,  as  4th,  5th,  6th,  or  7th,  multiply  the  loga- 
rithm of  the  number  by  4,  5,  6,  or  7,  and  the  results  will  be  the  logarithms  of 
the  4th,  5th,  6th,  or  7th  powers,  respectively.  Thus,  a number  can  readily  be 
raised  to  any  power  required. 


24 


GEOMETRY. 


7 


To  Extract  the  Square,  Cube,  Fourth,  Fifth,  or  Any  Root  of  a Number. — Divide 

the  logarithm  of  the  number  by  the  index  of  the  root  required,  and  the 
quotient  will  be  the  logarithm  of  the  required  root. 

Thus,  to  find  the  square  root  of  625: 

Logarithm  of  625  = 2.79588. 

2.79588  -T-  2 = 1.39794 

1.39794  = logarithm  of  25. 

Therefore,  the  square  root  of  625  is  25. 

To  Find  the  Cube,  Fourth,  or  Any  Root.— Proceed  in  the  same  way,  using 
the  index  of  the  required  root  as  a divisor. 

To  Divide  a Logarithm  Having  a Negative  Characteristic.— If  the  characteristic 
is  evenly  divisible  by  the  divisor,  divide  in  the  usual  manner  and  retain  the 
negative  sign  for  the  characteristic  in  the  quotient.  But  if  the  negative 
characteristic  is  less  than,  or  not  evenly  divisible  by,  the  divisor,  add  such  a 
negative  number  to  it  as  will  make  it  evenly  divisible,  and  prefix  an  equal 
positive  number  to  the  decimal  part  of  the  logarithm;  then  divide  the 
increased  negative  characteristic  by  the  divisor,  to  obtain  the  characteristic 
of  the  quotient  desired.  To  obtain  the  decimal  part  of  the  quotient,  divide 
the  decimal  part  of  the  logarithm,  with  the  positive  number  prefixed,  in  the 
usual  manner.  To  this  quotient  prefix  the  negative  characteristic  already 
found,  and  this  will  be  the  quotient  desired. 


Example  1.— 


6.3246846 

3 


2.1082282. 


Example  2.—  _ 

14.3268472  = (]q+4  = i8)  + (4  + .3268472)18  +>32GM72  J 2.4807608. 

9 y 

Example  3.— 


5/--  log  .677  1.830589  5 4.830589 

v -677  = 5 = 5 ' 5 + 5 


1.9661178  m .9249+. 


GEOMETRY. 


PRINCIPLES  OF  GEOMETRY. 

1.  The  sum  of  all  the  angles  formed  on  one  side  of  a straight  line  equals 
two  right  angles,  or  180°. 

2.  The  sum  of  all  the  angles  formed  around  a point  equals  four  right 

angies,  or  360°.  ,,  .,  ..  . 

3.  When  two  straight  lines  intersect  each  other,  the  opposite  or  vertical 

angies  are  equal.  . „ „ _ , 

4.  If  two  angles  have  their  sides  parallel,  they  are  equal. 

5.  If  two  triangles  have  two  sides,  and  the  included  angle  of  the  one 
equal  to  two  sides  and  the  included  angle  of  the  other,  they  are  equal  in  all 

their  parts^  ^rjang^es  have  two  angles,  and  the  included  side  of  the  one  equal 
to  two  angles  and  the  included  side  of  the  other,  they  are  equal  in  all  their 
Darts 

7.  ’ In  any  triangle,  the  greater  side  is  opposite  the  greater  angle,  and  the 
greater  angle  is  opposite  the  greater  side.  . . , 

» 8.  The  sum  of  the  lengths  of  any  two  sides  of  a triangle  is  greater  than 

the  length  of  the  third  side.  . 

9 In  an  isosceles  triangle,  the  angles  opposite  the  equal  sides  are  equal 
10.  In  any  triangle,  the  sum  of  the  three  angles  is  equal  to  two  right 
sniffles  or  180^ 

ll/’lf  two  angles  of  a triangle  are  given,  the  third  may  be  found  by 
subtracting  their  sum  from  two  right  angles,  or  180°. 

12.  A triangle  must  have  at  least  two  acute  angles,  and  can  have  but  one 

obtuse  triangle!  a perpendicular  let  fall  from  the  apex  to  the  base  is 

shorter  than  either  of  the  two  other  sides. 


GEOMETRY. 


25 


14.  In  any  parallelogram,  the  opposite  sides  and  angles  are  equal  each  to 
each. 

15.  The  diagonals  divide  any  paralellogram  into  two  equal  triangles. 

16.  The  diagonals  of  a parallelogram  bisect  each  other;  that  is,  they 
divide  each  other  into  equal  parts. 

17.  If  the  sides  of  a polygon  be  produced  in  the  same  direction,  the  sum 
of  the  exterior  angles  will  equal  four  right  angles. 

18.  The  sum  of  the  interior  angles  of  a polygon  is  equal  to  twice  as  many 
right  angles  as  the  polygon  has  sides,  less  four  right  angles. 

Example.— The  sum  of  the  interior  angles  of  a quadrilateral  = (2X4) 
— 4 = 4 right  angles.  The  sum  of  the  interior  angles  of  a pentagon  = 
(2  X 5)  — 4 = 6 right  angles.  The  sum  of  the  interior  angles  of  a hexagon 
= (2  X 6)  — 4 = 8 right  angles. 

19.  In  equiangular  polygons,  each  interior  angle  equals  the  sum  divided 
by  the  number  of  sides. 

20.  The  square  described  on  the  hypotenuse  of  a right-angled  triangle  is 
equal  to  the  sum  of  the  squares  described  on  the  other  two  sides.  Thus,  in  a 
right-angled  triangle  whose  base  is  20  ft.  and  altitude  10  ft.,  the  square  of 
the  hypotenuse  equals  the  square  of  20  + the  square  of  10  , or  500.  Then  the 
hypotenuse  equals  the  square  root  of  500,  or  22.3607  ft. 

21.  Having  the  hypotenuse  and  one  side  of  a right-angled  triangle,  the 
other  side  may  be  found  by  subtracting  from  the  square  of  the  hypotenuse 
the  square  of  the  other  known  side.  The  remainder  will  be  the  square  of 
the  required  side. 

22.  Triangles  that  have  an  angle  in  each  equal,  are  to  each  other  as  the 
product  of  the  sides  including  those  equal  angles. 

23.  Similar  triangles  are  to  each  other  as  the  squares  of  their  correspond- 
ing sides. 

24.  The  perimeters  of  similar  polygons  are  to  each  other  as  any  two 
corresponding  sides,  and  their  areas  are  to  each  other  as  the  squares  of 
those  sides. 

25.  The  diameter  of  a circle  is  greater  than  any  chord. 

26.  Any  radius  that  is  perpendicular  to  a chord,  bisects  the  chord  and  the 
arc  subtended  by  the  chord. 

27.  Through  three  points  not  in  the  same  line,  a circumference  may  be 
made  to  pass. 

Directions— Draw  two  lines  connecting  the  three  points.  Erect  perpen- 
diculars from  the  centers  of  each  of  these  two  lines,  and  the  point  of  inter- 
section of  the  perpendiculars  will  be  the  center  of  the  circle. 

28.  The  circumferences  of  circles  are  to  each  other  as  their  radii,  and 
their  areas  are  to  each  other  as  the  squares  of  their  radii. 

Example  1.— If  the  circumference  of  a circle  is  62.83  in.  and  its  radius  is 
10  in.,  what  is  the  circumference  of  a circle  whose  radius  is  15  in.  ? 

10  : 15  : : 62.83  : 94.245  in.  Ans. 

Example  2— If  a circle  6 in.  in  diameter  has  an  area  of  28.274  sq.  in.,  what 
is  the  area  of  a circle  12  in.  in  diameter  ? 

32  : 62  : : 28.274  : 113.096  sq.  in.  Ans. 


PRACTICAL  PROBLEMS  IN  GEOMETRICAL  CONSTRUCTION. 

\E  To  Bisect  a Given  Straight  Line  AB. — From 

A and  B as  centers,  with  a radius  greater  than 
l one-half  of  A B,  describe  arcs  intersecting  at  E 

A k B and  F.  Draw  E F.  It  will  bisect  A B.  C will 

1°  be  the  middle  point,  and  ^Fwill  be  perpendic- 

ular to  AB.  The  points  ^and  i^will  be  equi- 
distant  from  A,  B,  or  C. 


From  a Given  Point  C,  Without  a Straight  Line  AB, 
to  Draw  a Perpendicular  to  the  Line.— From  C as  a 
center,  with  a radius  sufficiently  great,  describe 
an  arc  cutting  AB  in  points  A and  B;  then  from 
A and  B as  centers,  with  a radius  greater  than 
one-half  of  A B , describe  two  arcs  cutting  each 
other  at  Z>,  and  draw  CD. 


C 

_E 


26 


GEOMETRY. 


A 


XD 


A+ 


4 B 


At  a Given  Point  C in  a Straight  Line  AB,  to 
Erect  a Perpendicular  to  That  Line.— Take  the  points 
A and  B equally  distant  from  C,  and,  with  A and 
B as  centers,  and  a radius  greater  than  one-half 
of  A B , describe  two  arcs  cutting  each  other  at 
D,  and  draw  the  line  D C. 


At  a Point  i on  a Given  Straight  Line  A B, 
to  Make  an  Angle  Equal  to  a Given  Angle  Ei  G. 

From  F as  a center,  with  any  radius  ± G, 
describe  the  arc  EG.  From  A as  a center, 
with  the  same  radius,  describe  the  arc  CB\ 
then  with  a radius  equal  to  the  chord  EG, 
describe  an  arc  from  £ as  a center,  cutting 
Oil  at  D,  and  draw  A D 


To  Bisect  a Given  Arc  ACB.-With  the  same 
radii  and  the  extremities  A B as  centers,  descnbe 
arcs  intersecting  at  D and  E.  The  line  D E 
bisects  the  arc  at  C. 


To  Bisect  an  Angle  A B C.-With  any  radius  and 
R as  a center,  describe  an  arc  cutting  the  sides  at 
A and  C With  these  points  as  centers,  describe 
arcs  of  equal  radius  intersecting  at  D.  The  line 
B D is  the  bisector,  and  the  LAB  D = LB  B C.  & 


R 


Through  a Given  Point  A to  Draw  a Straight 
Line  Parallel  to  a Given  Straight  L|ne  CD.— From 
A as  a center,  with  a radius  greater  than 
the  shortest  distance  from  A to  CD,  describe 
an  indefinite  arc  D E.  From  D as  a center, 
with  the  same  radius,  describe  the  arc  A 
Take  D E equal  to  A F,  and  draw  A B. 


To  Bisect  an  Open  Angle  ( Method  by  L.  L. 
Logan).— Let  AB  and  CD  be  the  sides  of 
an  open  angle.  With  any  point  0 as  a cen- 
ter, describe  a circle  cutting  the  sides  at 
e f a and  h,  and  with  e and/,  and  g and  h 
as  centers  and  any  radius,  describe  arcs 
intersecting  at  k and  l,  respectively.  Draw 
Ok  and  01  and  mn.  With  p and  gas  cen- 
ters, and  any  radius,  describe  arcs  intersect- 
ing at  R and  S.  The  line  drawn  through 
is  the  required  bisector. 


C ft1 


/' 


\ 


\ B 


To  Find  the  Center  of  a Given  Circumference  or  Arc. 

Take  any  three  i>oints  ,4,  B.and  C on  the  circumfer 
ence,  and  unite  them  by  the  lines  A 5andJ  C.  Bisect 
these  chords  by  the  perpendiculars  D 0 and  E 0,  their 
intersection  is  the  center  of  the  circle. 


GEOMETRY. 


27 


Through  a Given  Point  P,  to  Draw  a Tangent  to  a Given 
Circle.— 1.  If  P be  in  the  circumference:  Find  C the 
center  of  the  circle,  draw  the  radius  CP , and  draw 
D E perpendicular  to  C P. 


2.  If  P be  without  the  circle:  Join  P and 
the  center  of  the  circle.  Bisect  P C in  D;  with 
D as  a center,  and  a radius  D 0 , describe  the  cir- 
cumference intersecting  the  given  circumference 
at  A and  B.  From  the  intersections  A and  B, 
draw  B P and  A P. 


An  acute  angle  having  its  vertex  in  the  circumference  and 

subtended  by  an  arc  is  equal  to  one-half  the  central 
angle  subtended  by  the  same  arc.  Thus,  the  L A B C 
— w L.  A O C. 


An  acute  angle  included  between  a chord  and  a tangent  is 

equal  to  one-half  the  central  angle  subtended  by  the 
chord.  Thus,  [_  ABC  = £ l_  COB. 


If,  from  a point,  two  tangents  be  drawn  to  a circle,  they 
will  be  equal,  and  their  angle  of  intersection  will  be 
equal  to  the  central  angle  subtended  by  the  chord 
joining  the  two  points  of  tangency.  Thus,  A B = AC. 
and  c DAC  = L BOC. 


To  Divide  a Straight  Line  Into  Any  Number 
of  Equal  Parts.— To  divide  the  line  AB 
into,  say,  6 parts,  draw  the  line  A C from 
A,  making  any  angle  with  A B;  measure 
off  6 equal  spaces  on  A C;  draw  6 B , and 
from  1,  2,  3,  U,  5 on  A Cdraw  parallels  to 
6 B.  These  divide  A B as  required  into 
6 equal  parts. 

By  a similar  process  a line  may  be 
divided  into  a number  of  unequal  parts. 
Set  off  on  A C divisions  proportional  to 
the  required  divisions,  and  draw  the 
parallel  lines  as  explained  above. 


23 


MENSURATION. 


MENSURATION. 


MENSURATION  OF  SURFACES. 


PARALLELOGRAMS. 

A parallelogram  is  a four-sided  figure  whose  opposite  sides  are  parallel. 


'sJtZista* 

and  four  right  an-  and  opposite  sides  and  oblique  angles.)  opposite  sides  equal.) 
gtes.)  equal.) 

Tn  Find  the  Area  of  Anv  Parallelogram.— Multiply  the  length  of  any  side 
by  the  length  of  a perpendicular  line  from  that  side  to  the  oppositeone. 
Thus,6  in  ^he  foregoing^  figures,  the  areas  of  the square  are 

the  length^B  by  the 

«o« 

To  Find  the  Area  of  the  Largest  Square  That  May  be  Inscribed  in  a Circle. 

Snuare  the  radius  of  the  circle,  and  multiply  by  2.  , . «■  «_. 

^Tn  Find  the  Side  of  the  Largest  Square  That  May  be  Inscribed  in  a Circle. 

Dhdde  the  Lmeter  of  the  circle  4 1.41421,  or  multiply  it  by  .707107. 


TRIANGLES. 

A triangle  is  a figure  having  three  straight  sides. 


Equilateral. 

( Three  equal 
sides.) 


Isosceles. 

( Two  equal 
sides.) 


Scalene. 

( Three  un- 
equal sides.) 


To  Find  the  Area  of.  a Triangle.-Multiply  its  base  by  one-half  the  perpen- 

^Tonndf^er^ndfcu^Height  of  an  Equilateral  Triangle.-Multiply  the  length 

*Nr&s 

tipiy  the  length  of  one  of  its  sides  by  .658037. 


TRIANGLES. 


29 


To  Find  the  Diameter  of  a Circle  of  Same  Area  as  an  Equilateral  Triangle. 

Divide  the  length  of  one  of  its  sides  by  1.34677. 

The  following  rules  apply  to  any  triangle: 

Having  Two  Sides  and  the  Included  Angle,  to  Find  the  Area. — Multiply  together 
the  two  sides  and  the  natural  sine  of  the  included  angle,  and  divide  the 
product  by  2.  Or,  by  logarithms,  add  together  the  logarithms  of  the  two 


sides  and  the  logarithmic  sine  of  the  included  angle,  and  from  the  sum 
subtract  the  logarithm  of  2,  and  the  result  will  be  the  logarithm  of  the  area. 

Having  Three  Sides  of  a Triangle,  to  Find  the  Area.— Add  the  three  sides 
together,  divide  the  sum  by  2;  from  the  half  sum,  subtract  each  side  sep- 
arately; multiply  the  half  sum  and  the  three  remainders  continuously 
together,  and  extract  the  square  root  of  the  product.  Thus,  if  the  triangle 

has  three  sides  whose  lengths  are  30,  40,  and  50  ft.,  then  = 60. 

Then,  subtracting  from  this  60  each  side  separately,  we  have:  60  — 30  = 30; 
60  — 40  - 20;  60  - 50  = 10.  Then,  60  X 30  X 20  X 10  = 360,000.  The  square 
root  of  360,000  = 600  sq.  ft.,  or  area. 

Having  the  Three  Sides  of  a Triangle,  to  Find  Its  Angles.— In  the  triangle 
A B C,  let  A B = 21  ft.,  B C = 17.25  ft.,  and  A C = 32  ft.  Draw  B D per- 
pendicular to  AC’,  then, 

32  : 21  + 17.25  = 21  — 17.25  AD  - DC’, 


But 

Adding, 

Subtracting, 


AD  — DC  = 4.48 
AD  + DC  = 32 
2 AD  — 36.48 
AD  = 18.24 
2 DC  = 27.52 
DC  = 13.76 


cos  A = = .86857,  or  A = 29°  42'  25.7". 

13  76 

cos  0 = Wm  = *79768’ or  c = 370  5' 26.7". 

B = 180°  — (A  + C)  = 1.80  — (29°  42'  25.7"+  37°  5'  26.7")  = 113°  12'  7.6". 
Having  Two  Sides  and  Included  Angle,  to  Find  Third  Side  and  the  Other  Angles. 

In  the  triangle  ABC,  let  A B = 19  ft.,  A C = 2P  ft.,  and  A = 36°  3'  29". 

Draw  B D perpendicular  to  AC.  BD  = 19  X sin  A = 19  X .58861  = 11.18  ft. 

A D = 19  X cos  A = 19  X .80842  = 15.36  ft.  D C = 23  — 15.36  = 7.64  ft. 

11 18 

Tan  C = = 1.46335,  or  C = 55°  39'  10".  B = 180  — (A  + C)  = 180 

- (36°  3'  29"  + 55°  39'  10")  = 88°  17'  21".  B C = B?  = -11’18  = 13  54  ft 
„ . , - sin  C .82562 

^naving  One  Side  and  the  Two  Adjacent  Angles,  to  Find  the  Other  Two  Sides. 

The  third  angle  equals  180°  minus  the  sum  of  the  other  two  angles.  This 
third  angle  will  be  the  one  opposite  the  given  side.  Then  the  sine  of  the 

angle  opposite  the  given  side  is  to  the  given  side  as  the  sine  of  either  of  the 

other  angles  is  to  its  opposite  side.  Thus,  in  the  triangle  ABC,  let  A = 60°, 

B 50°700’  and  the  Side  A B = 200  ft*  Then  the  angle  C = 180°”  (60°  + 70°) 
Then,  sin  50°  : 200  : : sin  60°  : B C, 

and  sin  50°  : 200  : : sin  70°  : A C. 

To  Find  the  Area.— Either  find  the  three  sides  as  above,  and  follow  rule 
already  given,  or  multiply  the  natural  sines  of  the  two  given  $pgles  togethgj  •. 


30 


MENSURATION. 


Thpn  ns  the  natural  sine  of  the  single  angle  is  to  the  product  of  the  sines  of 
to  riven ;ang  “is  the°squar^0ffhe  given  side  to  twice  the  reqmred  area, 
rrvmc  «in  r • sin  A y sin  B •:  A B1 : to  twice  the  area  of  the  triangle. 

The  area  of  tny  triangle  is  equal  to  half  the  area  of  a parallelogram 
having  the  same  base  and  perpendicular  height. 


trapezoids. 

A trapezoid  has  four  straight  sides,  only  two  of  which  are  parallel. 

F — ,Z> 


To  Find  the  Area  of  a Trapezoid.-Add  together  the  two  parallel  sides,  and 
dl vider by  2.  Multiply  the  quotient  by  the  perpendicular  height. 


Thus, 


ABA  CD 


X E F = area. 


TRAPEZIUMS. 

A trapezium  has  four  sides,  no  two  of  which  are  parallel. 

To  Find  the  Area  of  a Trapezium.— Divide  the  trape- 
zium into  two  triangles,  and  find  the  area  ol  each 
according  to  the  rules  given  under  the  head  ot 
“ Triangles.”  Add  together  the  areas  of  the  two 
triangles,  and  the  sum  will  equal  the  area  of  the 
trapezium.  The  sides  and  angles  can  be  found  m 

th  mhemagoneais  a'nd  the  perpendiculars  from  them  to  the  opposite  angles 
are  given,  add  together  the  two  perpendiculars,  multiply  the  sum  by  the 

^The^m o^^^four2 angles  included  in  a trapezium  always  equals  four 
right  angles.  


POLYGONS. 

All  figures  bounded  by  more  than  four  straight  lines  are  called  polygons. 


If  all  the  sides  and  angles  are  equal,  it  is  a regular  polygon.  If  not,  it  is 
an  The^sum  o?  the  interior  angles  of  any  polyg<m  is  equal  to  twice  as  many 

right  angles  as  the  polygon  has  sides  less  four  right  angles.  • 

To  Find  thp  Arpa  of  Anv  Regular  Polygon. — Square  one  ot  its  siaes  anu 
multiply  by  the  number  given  in  the  column  of  areas  in 
table  Or  multiply  the  length  of  one  of  the  sides  by  one-half  the  length 
of  a perpendicular  drawn  to  the  center  of  the  figure,  and  this  product  by 

Side  of  a Regular  Polygon,  to  Find  the  Radius  of  a Circumscribing 

CirG|e —Multiply  the  side  by  the  corresponding  number  m following 
column  of  outer  radii.  If  the  radius  of  the  circumscribing  circle  be  given 


CIRCLES. 


31 


divide  it  by  the  number  in  column  of  outer  radii,  and  the  quotient  will  be 
the  side  of  the  polygon.  A A „ , ,, 

To  Find  the  Area  of  an  Irregular  Polygon. — Divide  it  into  triangles,  find  the 

Table  of  Regular  Polygons  Whose  Sides  Are  Unity. 


Number 

of 

Sides. 

Name  of  Polygon. 

Areas. 

Outer 

Radii. 

Angles  Contained 
Between 
Two  Sides. 

Angle  at  Center 
of 

Circle. 

3 

Equilateral  triangle 

.4330 

.5774 

60° 

120° 

4 

Square  

1.0000 

.7071 

90° 

90° 

5 

Pentagon 

1.7205 

.8507 

108° 

72° 

6 

Hexagon 

2.5981 

1.0000 

120° 

60° 

7 

Heptagon  

3.6339 

1.1524 

128°  34'  17"+ 

51°  25'  43"— 

8 

Octagon  

4.8284 

1.3066 

135° 

45° 

9 

Nonagon  

6.1818 

1.4619 

140° 

40° 

10 

Decagon  

7.6942 

1.6180 

144° 

36° 

11 

Undecagon 

9.3656 

1.7747 

147°  16'  22"— 

32°  43'  38"  + 

12 

Dodecagon  

11.1962 

1.9319 

150° 

30° 

The  sum  will  be  the  area 


area  of  each  triangle,  and  add  them  together, 
of  the  polygon.  ...  , ^ 

To  Find  the  Area  of  a Figure  Whose  Outlines  Are  Very  Irregular.— Draw  straight 
lines  around  it  that  will  enclose  within  them  (as  nearly  as  can  be  judged) 
as  much  space  not  belonging  to  the  figure  as  they  exclude  space  belong- 
ing to  it.  The  area  of  the  figure  thus  formed  may  be  easily  found  by 
dividing  into  triangles. 


CIRCLES. 

{See  Table  of  Areas  of  Circles , Etc.) 

A circle  is  a figure  bounded  by  a curved  line,  every  point  of  which  is  equi- 
distant from  the  center.  Or,  a circle  is  a regular  poly- 
gon of  an  infinite  number  of  sides. 

The  circumference  of  a circle  equals  the  diameter 
multiplied  by  3.1416,  or  the  square  root  of  the  product 
of  the  area  multiplied  by  12.566. 

To  Find  the  Diameter.— Divide  the  circumference  by 
3.1416,  or  multiply  it  by  .31831. 

To  Find  the  Area  of  a Circle.— Multiply  the  circumfer- 
ence by  one-fourth  of  the  diameter,  or  the  square  of  the 
radius  by  3.1416.  Multiply  the  square  of  the  diameter 
by  .7854,  or  the  square  of  the  circumference  by  .07958.  lx.  . 

To  Find  the  Diameter  of  a Circle  Equal  in  Area  to  a Given  Square.— Multiply 
one  side  of  the  square  by  1.12838. 

To  Find  the  Radius  of  a Circle  to  Circumscribe  a Given  Square.— Multiply 
one  side  by  .7071;  or  take  one-half  the  diagonal. 

To  Find  the  Side  of  a Square  Equal  in  Area  to  a Given  Circle. — Multiply  the 
diameter  by  .88623.  _ . 

To  Find  the  Side  of  the  Greatest  Square  in  a Given  Circle.— Multiply  the 
diameter  by  .7071.  ^ ^ . , . 

To  Find  the  Area  of  the  Greatest  Square  in  a Given  Circle.— Square  the  radius 
and  multiply  by  2.  . . . _.  . 

To  Find  the  Side  of  an  Equilateral  Triangle  Equal  in  Area  to  a Given  Circle. 
Multiply  the  diameter  by  1.3468.  _ . . 

Having  the  Chord  and  Rise  of  an  Arc,  to  Find  the  Radius. — Square  half  the 
chord,  and  divide  by  the  rise.  To  the  quotient  add  the  rise,  and  divide  by  2. 
Or,  radius  = the  square  of  the  chord  of  half  the  arc  divided  by  twice  the 
rise  of  the  whole  arc.  , 

Having  the  Chord  and  Radius,  to  Find  the  Rise.— Square  the  radius,  also 
square  half  the  chord.  Take  the  last  square  from  the  first.  Extract  square 
root  of  the  remainder,  and  subtract  it  from  the  radius  if  the  radius  is  greater; 
if  not,  add  it  to  the  radius. 

Having  the  Radius  and  Rise,’ to  Find  the  Chord.— From  the  radius  subtract 
the  rise  (or  from  the  rise  subtract  the  radius,  if  rise  is  the  greater),  square 


32 


MENSURATION, 


the  remainder,  and  subtract  it  from  the  square  of  the  radius.  Extract  the 
square  root  of  the  remainder.,  and  multiply  by  2. 

Having  the  Rise  of  the  Arc  and  Diameter  of  Circle,  to  Find  the- Chord.— Sub- 
tract the  rise  from  the  diameter,  and  multiply  the  remainder  by  the  rise. 
Extract  the  square  root  of  the  product,  and  multiply  by  2. 

To  Find  the  Breadth  of  a Circular  Ring,  Having  Its  Area  and  the  Diameter  of 
the  Outer  Circle. — Find  the  area  of  the  whole  circle,  and  from 
it  take  the  area  of  the  ring.  Multiply  the  remainder  by 
1.2732,  and  the  square  root  of  the  product  will  be  the  diam- 
eter of  the  inner  circle.  Take  it  from  the  diameter  of  the 
outer  one,  and  the  remainder  will  be  twice  the  breadth. 

To  Find  the  Area  of  a Circular  Ring.— Take  the  difference  of 
the  squares  of  the  radii,  and  multiply  it  by  3.1416. 

To  Find  the  Length  of  an  Arc  When  Its  Degrees  and  Radius  Are 
Given.  —Multiply  the  number  of  degrees  by  .01745,  and  the  product  by  the 
radius.  ...  , , ,,  ,. 

To  Find  the  Area  of  a Sector.— Multiply  the  arc  by  one-half  the  radius. 
The  area  of  the  sector  is  to  the  area  of  the  circle  as  the  number  of  degrees 
in  the  sector  is  to  360°.  . x . . . . 

To  Find  the  Area  of  a Segment.— Find  the  area  of  the  sector  having  the 
same  arc,  and  also  the  area  of  the  triangie  formed  by  the  chord  of  the  segment 
and  the  radii  of  the  sector.  If  the  segment  is  greater  than  a semicircle,  add 
the  two  areas;  if  less,  subtract  them. 


THE  ELLJPSE. 

To  Find  the  Area  of  an  Ellipse.— Multiply  one-half  of  the  two  axes  AB  and 

CD  together,  and  multiply  the  product  by  3.1416. 

To  Find  the  Perimeter  of  an  Ellipse.— Multiply  one-half 

the  sum  of  the  two  axes  by  3.1416. 

To  Draw  an  Approximate  Ellipse  {Method,  by  Three  Squares). 
Let  a be  the  center,  b c the  major,  and  a e half  the  minor 
axis  of  an  ellipse.  Draw  the  rectangle  bfgc,  and  the 
diagonal  line  be;  at  a right  angle  to  b e,  draw  line/ h cut- 
ting B B at  i . With  radius  a e,  and  from  a as  a center, 
draw  the  dotted  arc  ej,  giving  the  point  j on  the  line  B B.  From  k,  which  is 
central  between  b and  j,  draw  the  semicircle  b mj,  cutting  A A at  l.  Draw 
the  radius  of  the  semicircle  b mj , cutting  fg  at  n.  With  radius  m n,  mark 
on  A A,  at  and  from  a as  a center,  the  point  o.  With  radius  ho,  and  from 
center  h,  draw  the  arc  p o q.  With  radius  a l, 
and  from  b and  c as  centers,  draw  arcs  cut- 
ting p o q at  the  points  p and  q.  Draw  the 
lines  hpr  and  hqs,  and  also  the  lines  pit 
and  qvw.  From  h as  a center,  draw  that 
part  of  the  ellipse  lying  between  r and  s 
with  radius  h r.  From  p as  a center  draw 
that  part  of  the  ellipse  lying  between  r and 
t with  the  radius  p r.  From  q,  draw  the 
ellipse  from  s to  w.  With  radius  i t,  from  i as 
a center,  draw  the  ellipse  from  t to  5 with 
radius  i t,  and  from  v as  a center,  draw  the 
ellipse  from  w to  c,  and  one-half  the  ellipse 
will  be  drawn.  It  will  be  seen  that  the  whole 
construction  has  been  performed  to  find  the 
centers  h,  p,  q,  i,  and  v,  and  that  while  v and  i 
may  be  used  to  carry  the  curve  around  the  other  side  or  half  of  the  ellipse, 
new  centers  must  be  provided  for  h,  p,  and  q ; these  new  centers  correspond 
in  position  to  h,p,  q. 


Straightedge  Method.— On  a straightedge,  lay  off  A B 
equal  to  one-half  the  short  diameter  and  A C equal  to 
one-half  the  long  diameter.  Determine  points  on  the 
circumference  of  the  ellipse  by  marking  positions  of 
A,  as  the  point  B is  moved  along  the  major  axis  and,  at 
the  same  time,  the  point  C along  the  minor  axis. 


MENSURATION  OF  SOLIDS. 


33 


MENSURATION  OF  SOLIDS 


THE  CUBE  AND  THE  PAR  ALLE  LO  PI  PE  D 

To  Find  the  Surface  of  a Cube.— Multiply  the  area  of  one  side  by  6. 

To  Find  the  Surface  of  a Parallelopiped.— Add  together  twice  the  area  of 
the  base,  twice  the  area  of  the  side,  and  twice  the  area  of  the  end. 

To  Find  the  Cubical  Contents  of  a Cube  or  Parallelopiped.— Multiply  the  area 
of  the  base  by  the  perpendicular  height. 


THE  PRISM. 

To  Find  the  Convex  Surface  of  a Right  Prism.— Multiply  the 
perimeter  of  the  base  by  the  altitude. 

To  find  the  entire  surface,  add  the  areas  of  the  bases. 

To  Find  the  Contents  of  a Prism.— Multiply  the  area  of  the 
base  by  the  altitude  of  the  prism. 


THE  CYLINDER. 

To  Find  the  Convex  Surface  of  a Cylinder. — Multiply  the  circum- 
ference of  the  base  by  the  altitude. 

To  find  the  entire  surface,  add  the  areas  of  the  ends. 

To  Find  the  Contents  of  a Cylinder. — Multiply  the  area  of  the 
base  by  the  altitude. 


THE  SPHERE. 

To  Find  the  Surface  of  a Sphere. — Multiply  the  diameter  by  the  circum- 
ference; or,  square  the  radius  and  multiply  it  by  4 and  3.1416. 

To  Find  the  Contents  of  a Sphere.— Multiply  the  surface  by 
one-third  of  the  radius;  or,  multiply  the  cube  of  the  diam- 
eter by  .5236. 

To  Find  the  Surface  of  a Zone. — Multiply  the  height  of  the 
zone  by  the  circumference  of  a great  circle  of  the  sphere. 
To  Find  the  Contents  of  a Spherical  Segment  of  One  Base. 

Add  the  square  of  the  height  to  three  times  the  square  of 
the  radius  of  the  base;  multiply  this  sum  by  the  height, 
and  the  product  by  .5236. 

The  curved  surface  on  a hemisphere  is  equal  to  twice  its  plane  surface,  and 
the  curved  surface  on  a quarter  of  a sphere  is  equal  to  its  plane  surface. 


THE  PYRAMID. 

To  Find  the  Convex  Surface  of  a Pyramid. — Multiply  the  per- 
imeter of  the  base  by  one-half  the  slant  height. 

To  find  the  entire  surface,  add  the  area  of  the  base. 

To  Find  the  Contents  of  a Pyramid. — Multiply  the  area  of  the 
base  by  one-third  of  the  altitude. 


THE  CONE. 

To  Find  the  Convex  Surface  of  a Cone.— Multiply 
the  circumference  of  the  base  by  one-half  the 
slant  height. 

To  find  the  entire  surface,  add  the  area  of  the 
base. 

To  Find  the  Contents  of  a Cone. — Multiply  the  area 
of  the  base  by  one-third  of  the  altitude. 


34 


MENSURATION. 


THE  FRUSTUM  OF  A PYRAMID  OR  CONE. 

To  Find  the  Convex  Surface— Multiply  one-half  of  the  sum  of  the  perim- 
eters or  circumferences  of  the  two  bases 
by  the  slant  height 

’ The  entire  surface  is  found  by  adding 
the  areas  of  the  two  bases. 

To  Find  the  Contents  of  a Frustum. — Add 
together  the  sum  of  the  two  bases  and 
the  square  root  of  their  product,  and  mul- 
tiply the  sum  by  one-third  of  the  altitude  of  the  frustum. 


CYLINDRICAL  RINGS. 

A cylindrical  ring  is  formed  by  bending  a cylinder  or  pipe  until  its  two 
ends  meet.  , , . , 

To  Find  the  Surface  of  a Cylindrical  Ring— To  the  thickness 
of  the  ring,  add  the  inner  diameter,  multiply  this  sum  by  the 
thickness  of  the  ring,  and  the  product  by  9.8696. 

To  Find  the  Contents  of  a Cylindrical  Ring.— To  the  thickness 
of  the  ring  add  the  inner  diameter,  multiply  this  sum  by 
the  square  of  one-half  the  thickness. 

To  Find  the  Volume  of  an  Irregular  Body.— Fill  a vessel  of 
known  dimensions  with  water,  and  immerse  the  body.  The  contents  will 
equal  the  volume  of  water  displaced. 


THE  PRISMOI  DAL  FORMULA. 

This  formula  is  the  invention  of  Mr.  Elwood  Morris,  C.  E.,  of  Philadelphia, 
and  is  extensively  used  in  calculating  the  cubical  contents  of  cuttings, 
embankments,  etc.  . . _ , 

It  embraces  all  parallelopipeds,  pnsms,  pyramids,  cones,  wedges,  etc., 
whether  regular  or  irregular,  right  or  oblique,  with  their  frustums  when  cut 
parallel  to  their  bases.  In  fact,  it  embraces  all  solids  having  two  parallel 
faces  or  sides,  provided  these  two  faces  are  united  by  surfaces,  whether  plane 
or  curved,  on  which,  and  through  every  point  of  which,  a straight  line  may 
be  drawn  from  one  of  the  parallel  faces  to  the  other. 

To  Find  the  Contents  of  Any  Prismoid— Add  together  the  areas  of  the  two 
parallel  surfaces,  and  four  times  the  area  of  the  section  taken  half  way 
between  them,  and  parallel  to  them:  multiply  the  sum  by  the  perpendicular 
distance  between  the  two  parallel  sides,  and  divide  the  product  by  6. 


PLANE  TRIGONOMETRY. 


Plane  trigonometry  treats  of  the  solution  of  plane  triangles. 

In  everv  triangle,  there  are  six  parts— three  sides  and  three  angles.  These 
parts  are  so  related  that  when  three  of  the  parts  are  given,  one  being  a side, 
the  other  parts  may  be  found.  ._  , . . 

An  angle  is  measured  by  the  arc  included  between  its  sides,  the  center  of 
the  circumference  being  at  the  vertex  of  the  angle. 

For  measuring  angles,  the  circumference  is  divided  into  360  equal  parts. 

called  degrees;  each  degree  into  60  equal  parts  called 


minutes. 

A quadrant  is  one-fourth  the  circumference  of  a cir- 
cle, or  90°.  _ _ _ 

The  complement  of  an  arc  is  90°  minus  the  arc;  D C 
is  the  complement  of  B C,  and  the  angle  D O C is  the 
complement  of  BO  C. 

The  supolement  of  an  arc  is  180°  minus  the  arc:  A E 
is  the  supplement  of  the  arc  B D E.  and  the  angle  BO  E. 

In  trigonometrv.  instead  of  comparing  the  angles  of 
triangles  or  the  arcs  that  measure  them,  we  compare 
the  trigonometric  functions  known  as  the  sine,  cosine , tangent,  cotangent, 
secant , and  cosecant.  . ... 

The  sine  of  an  arc  is  the  perpendicular  let  fall  from  one  extremity  of  the 


PLANE  TRIGONOMETRY. 


35 


arc  on  the  diameter  that  passes  through  the  other  extremity.  Thus,  CD  is 
the  sine  of  the  arc  A C. 

The  cosine  of  an  arc  is  the  sine  of  its  complement;  or  it  is  the  distance 
from  the  foot  of  the  sine  to 
the  center  of  the  circle. 

Thus,  C E or  0 D equals  the 
cosine  of  arc  A C. 

The  tangent  of  an  arc  is  a 
line  that  is  perpendicular  to 
the  radius  at  one  extremity 
of  an  arc  and  limited  by  a 
line  passing  through  the  cen- 
ter of  the  circle  and  the  other 
extremity.  Thus,  A T is  the 
tangent  of  A C. 

The  cotangent  of  an  arc  is 
equal  to  the  tangent  of  the 
complement  of  the  arc. 

Thus,  B T'  is  the  cotangent 
of  AC. 

The  secant  of  an  arc  is  a 
line  drawn  from  the  center 
of  the  circle  through  one  extremity  of  the  arc,  and  limited  by  a tangent  at 
the  other  extremity.  Thus,  O T is  the  secant  of  AC. 

The  cosecant  of  an  arc  is  the  secant  of  the  complement  of  the  arc.  Thus. 
O T'  is  the  cosecant  of  A C. 

The  versed  sine  of  an  arc  is  that  part  of  the  diameter  included  between  the 
extremity  of  the  arc  and  the  foot  of  the  sine.  D A is  the  versed  sine  of  A C. 

The  coversed  sine  is  the  versed  sine  of  the  complement  of  the  arc.  Thus, 
B E is  the  coversed  sine  of  A C. 

From  the  above  definitions,  we  derive  the  following  simple  principles: 

1.  The  sine  of  an  arc  equals  the  sine  of  its  supplement , and  the  cosine  of  an 
arc  equals  the  cosine  of  its  supplement. 

2.  The  tangent  of  an  arc  equals  the  tangent  of  its  supplement , and  the  cotan - 
gent  of  an  arc  equals  the  cotangent  of  its  supplement. 

3.  The  secant  of  an  arc  equals  the  secant  of  its  supplement,  and  the  cosecant 
equals  the  cosecant  of  its  supplement. 

Thus, 

sine  of  70°  = sine  of  110°.  cosine  of  70°  = cosine  of  110°. 

tangent  of  70°  = tangent  of  110°.  cotangent  of  70°  = cotangent  of  110°. 

secant  of  70°  = secant  of  110°.  cosecant  of  70°  = cosecant  of  110°. 

Thus,  if  you  want  to  find  the  sine  of  an  angle  of  120°  30',  look  for  the  sine 
of  180  — 120°  30',  or  59°  30',  etc. 

In  the  rt.  [\xyz,  the  following  relations  hold: 


Functions  of  the  sum  and  difference  of  two  angles: 

sin  {A  + B)  = sin  A cos  B + cos  A sin  B. 

cos  (A  4-  B)  = cos  A cos  B — sin  A sin  B. 

sin  (A  — B)  = sin  A cos  B — cos  A sin  B. 

cos  ( A — B)  -=■  cos  A cos  B 4-  sin  A sin  B. 

Natural  sines,  tangents,  etc.  are  calculated  for  a circle  whose  radius  is 
unity,  and  logarithmic  sines,  tangents,  etc.  are  calculated  for  a circle  whose 
radius  is  10,000,000,000.  


PRACTICAL  EXAMPLES  IN  THE  SOLUTION  OF  TRIANGLES. 

CaseI.  To  Determine  the  Height  of  a Vertical  Object  Standing  on  a Horizon- 
tal Plane. — Measure  from  the  foot  of  the  object  any  convenient  horizontal 


86 


PLANE  TRIGONOMETRY. 


distance  A B;  at  the  point  A,  take  the  angle  of  elevation  B A C.  Then,  as  ^ 
is  known  to  be  a right  angle,  we  have  two  angles  and  the  included  side  of  a 

naming  that  the  line  AB  is_30«  ft  and theangle  BAC^  40°,  the  angle 

C sin  C : A B : : sin  A : B C, 


or  .766044  : 300  : 
Or,  by  logarithms: 
Log  300  == 
Log  sin  40°  = 


.642788  : ( ),  or  251.73+  ft. 


2.477121 

9.808067 


12.285188 
Log  sin  50°  = 9.884254 

2.400934  or  log  of  251.73+  ft. 
ft. 


Hence,  B C = 251.73 


Tase  2 To  Find  the  Distance  of  a Vertical  Object  Whose  Height  is  Known.-Ata 

noint  A take  the  angle  of  elevation  to  the  top  of  the  object.  Knowing  that 
the^ngie  B is  Vrigttt  angle,  we  have  the  angles  B and  A and  the  side  B C. 
burning  that  the  side  BC=  .200  ft.  and  the  angle 


'i!0°,  we  have  a triangle  as  follows:  Angle  A - 
B =’  900^  c = 60°,  and  the  side  B C = 200  ft. 


A 

° ^ Then  * sin  A:  B C::  sin  C : A B, 

or  ’ .5  : 200  : : .866025  : ( ),  or  346.41  ft. 


By  logarithms: 

Log  200  = 
Log  sin  60°  = 


2.301030 

9.937531 


Log  sin  30°  — 


12.238561 
9.698970 

2.539591  or  log  of  346.41  ft.  . 

Case  3 To  Find  the  Distance  of  an  Inaccessible  Object.— ^Ie.a^ur®  a 
7ontal  base  line  A B , and  take  the  angles  formed  by  the  lines  B AC  and  ARC. 
zontai  ease  n e , ^ye  then  have  two  angles  and  the  included 

side.  Assuming  the  angle  A to  be  60°,  the 
angle  B 50°,  and  the  side  A B = 500  ft.,  we 
have  the  angle  C = 180°  - (60°  + 50°)  = 70°. 
Then, 

sin  70°  : A B : : sin  A : B C, 
and  sin  70°  : AB  : : sin  B : A C; 
or,  .939693  : 500  : : .866025  : B C,  or  460.8 +, 
and  .939693  : 500  : : .766044  : A C,  or  407.6 +. 
By  logarithms: 

Log  500  = 2.698970 
Log  sin 60°  = 9.937531 


Log 500  = 

Log  sin  50°  = 

12.583224 
Logsin70°=  9.972986 


12.636501 
Log  sin 70°=  9.972986 

2.663515  = log  of  460.8+, 

2.698970 

9.884254 


2.610238  = log  of  407.6+. 


Zi.u ±\JAjOO  7 • 

Case  4 To  Find  the  Distance  Between  Two  Objects  Separated  by  an  impassa- 
ble Barrier— Select  any  convenient  station,  as 
C,  measure  the  linesCA  aoAC  i^and  l*e  angle 


included  between  these  sides, 
two  sides  and  the  included  angle.  . , n . 

Assuming  the  angle  C to  be  60  , the  side  C A, 
600  ft.,  and  the  side  CB,  500  ft.,  we  have  the 
following  formula:  A A B B — A 

CA  + CB:  CA-  CB::  tan — : tan — . 


+ B 180° -60° 


2 2 
1,100 : 100  : : tan  60°  : tan 


or  60°. 
B-A 


(*) 


Then, 

Then, 


PLANE  TRIGONOMETRY. 


29 


or, 


1,100 : 100  : : 1.732050  : .157459,  or  tangent  of 


B-A 
2 ’ 


or  8°  57'. 


Then,  60°  + 8°  57'  = 68°  57',  or  angle  B , 

and  60°  — 8°  57'  = 51°  03',  or  angle  A. 

Having  found  the  angles,  find  the  third  side  by  the  same  method  as  Case  1. 
The  above  formula,  worked  out  by  logarithms,  is  as  follows: 

' Log  100  = 2.000000 
Log  tan  60°  = 10.238561 


Log  1,100  = 


12.238561 

3.041393 

9.197168  = log  tari  of 


B 


-,  or  8°  57'. 


Then, 

and 


M 


60°  + 8°  57'  = 68°  57',  or  angle  B, 

60°  _ 8o  br  = 51o  03',  or  angle  A. 

Note.— The  greater  angle  is  always  oppo- 
site the  greater  side. 

Case  5.  To  Find  the  Height  of  a Vertical 
Object  Standing  Upon  an  Inclined  Plane.— Meas- 
ure any  convenient  distance  D C on  a line 
from  the  foot  of  the  object,  and,  at  the  point 
D,  measure  the  angles  of  elevation  EDA 
and  ED  B to  foot  and  top  of  tower.  We 
then  have  two  triangles,  both  of  which  may 
be  solved  by  Case  1,  and  the  height  above 
D of  both  the  foot  and  top  will  be  known. 

The  difference  between  them  is  the  height 
of  the  tower. 

Case 6.  To  Find  the  Height  of  an  Inaccessible  Object  Above  a Horizontal  Plane. 

Measure  any  convenient  horizontal  line  A B directly  toward  the  object,  and 
take  the  angles  of  elevation  at  A and  B.  We  will  then  have  sufficient  data 

to  work  .with.  Assuming  the  line  A B to  be 
1,200  ft.  long,  the  angle  A , 25°,  and  the  angle 
D B C,  40°,  we  have  the  following:  As  the 
angle  D B C is  40°,  the  angle  A B C — 90°  — 
40°,  or  50°. 

Then,  having  the  side  B C , and  the  angle 
D B C = 40°,  and  the  angle  B D C — 90°,  we 
find  the  side  CD  by  the  same  method  as  in 
Case  1. 

Second  Method. — If  it  is  not  convenient  to 
measure  a horizontal  base  line  toward  the 
object,  measure  any  line  A B,  Fig.  (6a),  and 
also  measure  the  horizontal  angles  BAD , 
ABD , and  the  angle  of  elevation  DBG 
Then,  by  means  of  the  two  triangles  ABD 
and  CBD,  the  height  CD  can  be  found. 

Then,  with  the  line  A B and  the  angles 
BAD  and  ABD  known,  we  have  two 
angles  and  the  included  side  known.  The 
third  angle  is  readily  found,  and  the  side 
BD  can  be  found.  Then,  in  the  triangle 
B DC,  we  have  the  angle  B;  by  measure- 
ment, D = 90°,  and  we  have  the  side  B D. 

Then,  the  side  CD,  or  the  vertical  height, 
can  be  found  by  Case  1. 

Case  7.  To  Find  the  Distance  Between  Two 
Inaccessible  Objects  When  Points  Can  Be  Found 
From  Which  Both  Objects  Can  Be  Seen. — Wish- 
ing to  know  the  horizontal  distance  between 
a tree  and  a house  on  the  opposite  side  of  a river,  measure  the  line  A B,  and, 
at  point  A,  take  the  angles  D AC,  and  DAB,  and, 
at  the  point  B,  take  the  angles  CB  A and  CBD . 
Assume  the  length  of  A B — 400  ft. 

Angle  DAC=  56° 30'. 

Angle  DAB  = 42° 24'. 

Angle  C B A — 44°  36'. 

Angle  CBD  = 68° 50'. 


__.JP 


■0  jjjS, 


03 


38 


SURVEYING. 


th  111  riple  U°3ff+  GPfiO'f  = U3P2S'?SiSCth?S«le 

+ 113°  V ) = °4°  HX.  Then,  according  to  Case  1.  hnd  the  side  Z>  B. 
W^hen  havtT  ttaL  angli  and  two  sides  of  the  triangle  A DB.  * e find 

the  third  side  r we  haye  the  angles  iBC  and  B A C.  and  the 

side  C2>  by  Case  4.  . 

SURVEYING. 

employ^  iXth  are  the 

S aAd  me^ring  pins,  and  Sometimes  eert^n  aeces- 
^ Smenis.  as  clinometers  or  slope  levels,  dipping  needles,  etc.,  as  » dl 

deviations  from  the  practice  of  the  former. 

THE  COMPASS. 

e=^SsSESS 

gs^^safiasssss 

should  never  be  relied  on.  

TO  ADJUST  THE  COMPASS. 

_,  , . Fir^r  \yYins  the  bubbles  into  the  center  by  the  pressure  of  the 

The  Levels.— First  and  theri  turn  the  compass  halfway 

hand  on  ddfarent JK^lPrunto'  the  ends  of  the  tubes,  it  would  Indicate 
around:  should  the  ouDOies  lower  them,  bv  tightening  the  screws 

that^o^  en^  we^he^h^  *hose  linder  t‘he  lower  ends  until  by 
immediately  tinder.  i Tel  ttie  Piate  again,  and  repeat  the 

&^mtionetSmthe^nbbles  will  remain  in  the  center  during  an  entire 

revolution  of  Aecomi^.  observing  through  the  slits  a fine  hair  or 

The  sights  may  next  betretea  y ,umb  Sh,lllLld  the  hair  appear  on  one 

S'Slt ”he  dght^ mmi  bfe  adjusted  by  filing  off  its  under  surface  on 

theade  that  following  manner:  Having  the  eye  nearly  in 

The  needle  ls^jnsted  mine  n -of  the  compass  circle,  with  a small 

the  same  plane  mth  the  ^adi l*  ^wire  brin^  cue  end  of  the  needle  in  line 

splinter  of  df^5onof  the  circle  as  the  zero  or  90°  mark,  and  notice 

with  any  prominent  divmon  oi  tne^  c ' h opposite  side:  if  it  does, 

if  the  other  end  fV^^?^^ethdee^^if  "ot.  ben¥  the  center  pin  by 

a? s s?.bSa  ris  ««■  .= 


MAGNETIC  VARIATION . 


39 


circle;  if  any  error  is  there  manifested,  the  correction  must  be  made  in 
the  center  pin  only,  the  needle  being  already  straightened  by  the  previous 
operation.  „ , 

When  again  made  to  cut,  it  should  be  tried  on  the  other  quarters  of  the 
circle,  and  corrections  made  in  the  same  manner  until  the  error  is  entirely 
removed,  and  the  needle  will  reverse  in  every  point  of  the  divided  circle. 


TO  USE  THE  COMPASS. 

In  using  the  compass,  the  surveyor  should  keep  the  south  end  toward  his 
person,  and  read  the  bearings  from  the  north  end  of  the  needle.  In  the  sur- 
veyor’s compass,  he  will  observe  that  the  position  of  the  E and  W letters  on 
the  face  of  the  compass  are  reversed  from  their  natural  position,  in  order 
that  the  direction  of  the  sight  may  be  correctly  read. 

The  compass  circle  being  graduated  to  half  degrees,  a little  practice  will 
enable  the  surveyor  to  read  the  bearings  to  quarters— estimating  with  his 
eye  the  space  bisected  by  the  point  of  the  needle. 

The  compass  is  usually  divided  into  quadrants,  and  zero  is  placed  at  the 
north  and  south  ends.  90°  is  placed  at  the  E and  W marks,  and  the  gradua- 
tions run  right  and  left  from  the  zero  marks  to  90°.  In  reading  the  bearing, 
the  surveyor  will  notice  that  if  the  sights  are  pointed  in  a N W direction,  the 
north  end  of  the  needle,  which  always  points  approximately  north,  is  to  the 
right  of  the  front  sight  or  front  end  of  the  telescope,  and,  as  the  number  of 
degrees  is  read  from  it,  the  letters  marking  the  cardinal  points  of  the  compass 
read  correctly.  If  the  E,  or  east,  mark  were  on  the  right  side  of  the  circle,  a 
N W course  would  read  N E.  This  same  remark  applies  to  all  four  quadrants. 
The  compass  should  always  be  in  a level  position. 


MAGNETIC  VARIATION. 

Magnetic  declination  or  variation  of  the  needle  is  the  angle  made  by  the 
magnetic  meridian  with  the, true  meridian  or  true  north  and  south  line.  It 
is  east  or  west  according  as  the  north  end  of  the  needle  lies  east  or  west  of 
the  true  meridian.  It  is  not  constant,  but  changes  from  year  to  year,  and, 
for  this  reason,  in  rerunning  the  lines  of  a tract  of  land,  from  field  notes  of 
some  years’  standing,  the  surveyor  makes  an  allowance  in  the  bearing  of 
every  line  by  means  of  a ver- 
nier that  is  so  graduated  that 
30  spaces  on  it  equal  31  on  the 
limb  of  the  instrument,  as 
shown  in  the  figure. 

To  Read  the  Vernier.— As  the 
compass  vernier  is  usually  so 
made  that  there . are  but  15 
spaces  on  each  side  of  the  zero 
mark,  it  is  read  as  follows: 

Note  the  degrees  and  half 
degrees  on  the  limb  of  the  instrument.  If  the  space  passed  beyond  the 
degree  or  half-degree  mark  by  the  zero  mark  on  the  vernier  is  less  than 
one-half  the  space  of  half  a degree  on  the  limb,  the  number  of  minutes  is, 
of  course,  less  than  15,  and  must  be  read  from  the  lower  row  of  figures.  If  the 
space  passed  is  greater  than  one-half  the  spacing  on  the  limb,  read  the  upper 
row  of  figures.  The  line  on  the  vernier  that  exactly  coincides  with  a line  on 
the  limb  is  the  mark  that  denotes  the  number  of  minutes.  If  the  index  is 
moved  to  the  right,  read  the  minutes  from  the  left  half  of  the  vernier;  if  moved 
to  the  left,  read  the  right  side  of  the  vernier. 

To  Turn  Off  the  Variation.— Moving  the  vernier  to  either  side,  and  with  it,  of 
course,  the  compass  circle  attached,  set  the  compass  to  any  variation  by 
placing  the  instrument  on  some  well-defined  line  of  the  old  survey,  and  by 
turning  the  tangent  screw  (slow-motion  screw)  until  the  needle  of  the  com- 
pass indicates  the  same  bearing  as  that  given  in  the  old  field  notes  of  the 
original  survey.  Then  screw  up  the  clamping  nut  underneath  the  vernier 
and  run  all  the  other  lines  from  the  old  field  notes  without  further  alteration. 

The  reading  of  the  vernier  on  the  limb  gives  the  amount  of  variation  since 
the  original  survey  was  made. 

The  accompanying  man  shows  the  general  course  and  direction  ofisogonic 
lines  (those  passing  through  points  where  the  magnetic  needle  has  the  same 


4C 


SURVEYING . 


declination),  in  all  parts  of  the  United  States  and  Mexico  for  the  year  1900. 
These  lines  are  drawn  full  when  compiled  from  reliable  records,  but  dotted 
in  other  places.  The  declination  is  marked  in  degrees  at  each  end  of  every 
alternate  line,  the  sign  + indicating  a west  declination,  and  the  sign  — an 
east  declination.  The  yearly  variation,  or  change  of  declination,  for  the 
period  1895-1900  is  marked  in  numerous  places  on  the  map.  The  annual 
change  in  declination  is  given  in  minutes;  a -l-  sign  signifies  increasing  west 
or  decreasing  east  declination,  a — sign  the  reverse  motion.  Stations  to  the 
right  of  the  agonic  curve,  or  curve  of  no  declination,  have  west  declination, 
and  those  to  the  left,  east  declination.  The  large  black  circles  or  dots 
indicate  the  capitals  of  the  several  states. 

The  use  of  this  chart,  is  quite  simple.  The  declination  for  any  place 
within  its  borders  is  either  found  by  inspection  or  by  simple  interpolation 
between  the  two  adjacent  curves;  the  value  found ‘is  for  1900.  For  any 
other  year  (and  fraction),  a reduction  for  secular  change  between  the  epoch 
and  given  date  must  be  applied.  The  annual  change  of  the  declination 
during  the  period  1895-1900,  expressed  in  minutes  of  arc,  is  indicated  in 
the  chart  ( + for  increasing  west  or  decreasing  east  declination  and  — for 
the  reverse  motion).  The  amount  varies  in  time,  but  not  sufficiently  during 
a brief  interval  of  years  to  cause  any  serious  inaccuracy,  and  the  values  given 
on  the  chart  can  be  used  for  a number  of  years  to  come  for  all  practical 
purposes;  its  variation  with  geographical  position  must  be  estimated  from 
the  map. 


THE  TRANSIT. 

The  transit  is  the  only  instrument  that  should  he  used  for  measuring  angles 
in  any  survey  where  great  accuracy  is  desired.  The  advantages  of  a transit 
over  a vernier  compass  are  mainly  due  to  the  use  of  a telescope.  By  its  use 
angles  can  be  measured  either  vertically  or  horizontally,  and,  as  the  vernier 
is  used  throughout,  extreme  accuracy  is  secured. 

The  illustration  shows  the  interior  construction  of  the  sockets  of  a transit 
having  two  verniers  to  the  limb,  the  manner  in  which  it  is  detached  from  its 

spindle,  and  how  it 
can  be  taken  apart 
when  desired.  The 
limb  b is  attached  to 
the  main  socket  c. 
which  is  carefully 
fitted  to  the  conical 
spindle  h,  and  held 
in  place  by  the  spring 
catch  s. 

The  upper  plate  a, 
carrying  the  compass 
circle,  standards, 
etc.,  is  fastened  to  the 
flanges  of  the  socket 
k , which  is  fitted  to 
the  upper  conical 
surface  of  the  main 
socket  c.  The  weight 
of  all  the  parts  is  sup- 
ported on  the  small 
bearings  of  the  end 
of  the  socket,  as 
shown,  so  as  to  make  as  little  friction  as  possible  where  such  parts  are 
being  turned  as  a whole. 

A small  conical  center,  in  which  a strong  screw  is  inserted  from  below,  is 
brought  down  firmly  on  the  upper  end  of  the  main  socket  c,  thus  holding  the 
two  plates  of  the  instrument  securely  together,  and.  at  the  same  time,  allow- 
ing them  to  move  freely  around  each  other.  The  steel  center  pin  on  which 
the  needle  rests  is  held  by  the  small  disk  fastened  to  the  upper  plate  by 
two  small  screws  above  the  conical  center.  The  clamp  to  limb  d /,  with 
clamp  screw,  is  attached  to  the  main  socket.  The  instrument  is  leveled  by 
means  of  the  leveling  screws  l and  placed  exactly  over  a point  by  means  of 
the  shifting  center.  The  plummet  is  attached  to  the  loop  p. 

The  verniers  on  a transit  differ  from  those  on  a compass  in  detail  only. 


90 


80 


1 

70° 


ADJUSTING  TUN  TRANSIT. 


41 


The  principle  is  the  same.  The  transit  vernier  is  so  divided  that  30  spaces  on 
it  equal  in  length  29  on  the  limb  of  the  instrument.  The  method  of  reading 
it  is  practically  the  same  as  reading  a compass  vernier,  except  that  of 
the  transit  the  vernier  is  made  with  all  of  the  30  divisions  on  one  side  of  the 
zero  mark. 

Each  division  of  the  vernier  is  therefore  or,  in  other  words,  1 minute 
shorter  than  the  half-degree  graduations  on  the  limb. 

In  the  figure  the  reading  is  20°  10'.  If  the  zero  on  the  vernier  should  be 
beyond  20i°  on  the  limb  of 
the  transit,  and  the  line 
marked  10  should  coincide 
with  a line  on  the  limb,  the 
reading  would  be  20°  40'. 

In  case  the  12th  line  from 
zero  should  coincide  with  a 
line  on  the  limb,  the  read- 
ing would  be  20°  42',  etc. 

In  some  transits,  the 
graduated  limb  has  two 
sets  of  concentric  gradua- 
tions, the  zero  in  both  being 
the  same,  and,  while  the  outside  set  is  marked  from  0°  each  way  to  90°,  and 
thence  to  0°  on  the  opposite  side  of  the  circle,  the  other  set  is  marked  from 
0°  to  360°  to  the  right,  as  a clock  face.  The  inside  set  has  the  N,  S,  E,  and  W 
points  marked,  the  0°  of  the  inside  set  being  taken  as  north. 

The  interior  of  the  telescope  is  fitted  up  with  a diaphragm  or  cross- wire 
ring  to  which  cross-wires  are  attached.  These  cross-wires  are  either  of 
latinum  or  are  strands  of  spider  web.  For  inside  work,  platinum  should 
e used,  as  spider  web  is  translucent  and  cannot  readily  be  seen.  They  are 
set  at  right  angles  to  each  other  and  are  so  arranged  that  one  can  be 
adjusted  so  as  to  be  vertical  and  the  other  horizontal.  This  diaphragm  is 
suspended  in  the  telescope  by  four  capstan-headed  screws,  and  can  be  moved 
in  either  direction  by  working  the  screws  with  an  ordinary  adjusting  pin. 
The  transit  should  not  be  subjected  to  sudden  changes  in  temperature  that 
may  break  the  cross-hairs.  In  case  of  a break,  remove  the  cross-hair 
diaphragm  and  replace  the  broken  wire. 

The  intersection  of  the  wires  forms  a very  minute  point,  which,  when 
they  are  adjusted,  determines  the  optical  axis  of  the  telescope,  and  enables 
the'surveyor  to  fix  it  upon  an  object  with  the  greatest  precision. 

The  imaginarv  line  passing  through  the  optical  axis  of  the  telescope  is 
termed  the  line  of  collimation,  and  the  operation  of  bringing  the  intersection  of 
the  wires  into  the  optical  axis  is  called  the  adjustment  of  the  line  of  collimation. 

All  screws  and  movable  parts  should  be  covered,  so  as  to  keep  out  acid 
water  or  dust.  If  this  is  not  done,  the  mine  work  will  soon  use  up  a transit. 
The  vertical  circle  on  the  transit  may  be  a full  circle  or  a segment.  The 
former  is  to  be  preferred,  as  it  is  always  ready  without  intermediate  clamp 
screws.  If  the  dip  of  a sight  is  to  be  taken,  the  tape  must  be  held  at  the 
transit  head,  and  stretched  in  the  line  of  sight.  If  the  pitch  of  the  ground  is 
to  be  taken,  the  point  of  foresight  must  be  at  the  same  height  as  the  axis  of 
the  transit,  and  the  sight  will  then  be  parallel  to  the  surface.  The  angle  of 
dip  is  read  “ plus”  or  “minus,”  as  it  is  above  or  below  the  horizontal  plane. 
If  we  have  the  dip  of  a sight,  and  the  distance  between  the  transit  head  and 
the  point  of  sight,  we  can  get  the  vertical  and  horizontal  components  of  that 
distance  from  the  table  of  sines  and  cosines. 


ADJUSTMENTS  OF  THE  TRANSIT. 

The  use  of  a transit  tends  to  disarrange  some  of  its  parts,  which  detracts 
from  the  accuracy  of  its  work,  but  in  no  way  injures  the  instrument  itself. 
Correcting  this  disarrangement  of  parts  is  called  adjusting  the  transit. 

First  Adjustment.— To  make  the  level  tubes  parallel  to  the  vernier  plate. 

Plant  the  feet  of  the  tripod  firmly  in  the  ground.  Turn  the  instrument 
until  one  of  the  levels  is  parallel  to  a pair  of  opposite  leveling  screws;  the 
other  level  will  be  parallel  to  the  other  pair.  Bring  the  bubble  in  each  tube 
to  the  middle  with  the  pair  of  leveling  screws  to  which  the  tube  is  parallel. 
Next  turn  the  vernier  plate  half  way  around;  that  is,  revolve  it  through  an 
angle  of  180°.  If  the  bubbles  have  remained  in  the  middle  of  the  tubes,  the 
levels  are  in  proper  adjustment.  If  they  have  not  remained  so,  but  have 


42 


SURVEYING. 


tAwarrl  pither  end  bring  them  half  way  back  to  the  middle  of  the 
tfibes  bv  means  of  the  capstan-headed  screws  attached  to  the  tubes,  and  the 
tu + t? hflpt  hv  the  leveling  screws.  Again  turn  the  vernier  plate 

through  180°  and  if  the  bubbles  do  not  remain  at  the  middle  of  the  tubes, 
the  correction.  Sometimes  the  adjustment  is  made  by  one  trial,  but 
usually  it  is  necessary  to  repeat  the  operation.  Each  level  must  be  adjusted 

SePSeMndy  Adjustment  —To  make  the  line  of  collimation  perpendicular  to  the 

and  carefully  leveled,  sight  to  a pin 
or  *.  about  400  ft.  distant,  ^nearly  level 


G 

B- 


&00' 


scope;  that  is,  tarn  it  over  on 
its  axis  until  it  points  in  the 
opposite  direction,  and  set  a 
point  at  about  the  same  dis- 
tance, which  will  be  at  D. 


^mestrallhtlinlwith  A K It  maybe  necessary  to  repeat  the  operation 
t0  horizontal  axis  of  the  telescope  parallel  to  the 

sSf  S.-';Fs  sas  .W”lSsx 

plamn  turn  over  the  telescope,  and  turn  the  plate  around  suffi 
Sfvtoto  take  an  approximately  accurate  sight  upon  the 
r»m'  n t ^4  Then  clamp  the  instrument  and  again  take  an  exact 
Sght  to 'the  po?nt  I PNext  depress  the  telescope,  and  set  another 
P fha  PTonud  which  will  come  at  G.  The  distance  is  l is 
dcmbfe  the  Serror  of  adjustment.  Correct  the  error  by  raising 
O?  lowering  one  end  of  the  telescope  axis  by  means  of  a small 

'5A  -d  have 

[hfstakes  driven  down  until l the . rod jading  ^ the^ame  on  both  stakes. 

gives  equal  rod  readings  on  both  stakes. 

THE  CHAIN  OR  STEEL  TAPE  AND  PINS. 

The  chain,  which  is  gene^l^50  or  10^ft.  lon|,  should  temah^oOhneel^ 


CHAIN  AND  PINS. 


43 


provided.  These  handles  should  be  attached  to  short  links  at  each  end,  and 
the  combined  length  of  each-of  these  short  links  and  one  handle  should  be 
exactly  1 ft.  The  handles  should  be  attached  to  the  short  link  in  such  a 
manner  that  the  chain  may  be  slightly  lengthened  or  shortened  by  screwing 
up  a nut  at  the  handle.  It  should  be  divided  every  10  ft.  with  a brass  tag,  on 
which  either  the  number  of  points  represents  the  number  of  tens  from  the 
front  end,  or  the  number  of  tens  may  be  designated  by  figures  stamped  on 
the  tags. 

When  a chain  is  purchased,  one  that  has  been  warranted  as  *'  Correct, U.  S. 
Standard,”  should  be  selected,  and,  before  using  it,  it  should  be  stretched  on 
a level  surface,  care  being  taken  that  it  is  straight,  and  no  kinks  in  it,  and 
the  extremities  marked  by  some  permanent  mark.  These  marks  can  be 
used  in  the  future  to  test  the  chain.  It  should  be  tested  frequently,  and  the 
length  kept  to  the  standard  as  marked  when  it  was  new. 

In  chaining,  the  chainmen  should  always  remember  the  axiom  that  a 
straight  line  is  the  shortest  distance  between  two  points.  Ordinarily,  the  chain 
should  be  held  horizontally,  and  if  either  end  is  held  above  the  ground,  a 
plumb-bob  and  line  should  be  used  to  mark  the  end  of  the  chain  on  the 
ground.  If  used  on  a regular  incline,  the  chain  may  be  stretched  along  the 
incline,  and,  by  having  the  amount  of  declination,  the  horizontal  and 
vertical  distances  may  either  be  calculated  or  found  in  the  Traverse  Table. 

For  accuracy,  steel  tapes  are  now  almost  exclusively  used  by  the  leading 
mining  engineers,  on  account  of  their  greater  accuracy  as  compared  with 

Ch  The  steel  tape  is  simply  a ribbon  of  steel,  on  which  are  marked,  by  etching, 
or  other  means,  the  different  graduations,  which  may  be  down  to  inches  or 
tenths  of  a foot,  or  may  be  only  every  foot.  It  is  wound  on  a reel,  and  may 
be  any  desired  length  up  to  500  ft.  . . , _ 

A well-made  tape  should  not  vary  ft.  in  100  ft.,  at  any  given  standard 
of  temperature.  The  steel  of  the  tape  should  not  be  too  high  in  carbon,  or  it 
will  be  brittle  and  liable  to  snap  on  a short  bend,  nor  should  it  be  of  too  soft 
steel,  or  it  will  stretch  when  strongly  pulled.  . , 

Careful  gunsmiths  can  make  and  repair  steel  tapes  with  a high  degree  of 
accuracy  and  fully  as  reasonably  as  the  instrument  makers.  For  outside 
work  tapes  1,000  ft.  long  have  been  made,  but  500  ft.  will  be  found  as  long  as 
can  well  be  used  in  a mine,  owing  to  the  lack  of  long  sights,  and  to  the 
increased  weight  of  so  long  a tape.  The  average  length  is  300  ft.  The  300  ft. 
are  divided  into  10-ft.,  5-ft.,  2-ft.,  or  1-ft.  lengths,  as  desired,  and  the  tenths 
and  hundredths  of  a foot  are  read  by  means  of  a pocket  tape  or  measuring 
pin  Sometimes  there  is  an  extra  division  before  the  zero  mark,  which  is 
divided  into  feet  and  the  first  foot  into  tenths.  With  such  a tape,  a distance 
can  be  accurately  measured  to  tenths,  or  even  quite  approximately  to 

hundredths  of  a foot.  ......  ....  , 

The  ends  are  fitted  with  eyes  on  swivel-joints,  to  prevent  straining  by 
twisting.  Handles  of  various  forms  have  been  devised  to  enable  the  tape  to 
be  stretched,  or  to  clamp  a broken  end.  Some  parties  use  ordinary  springs 
to  prevent  overstraining,  and,  in  certain  cases,  spring  scales  are  used,  and 
the  same  degree  of  tension  can  be  readily  produced,  and,  m this  way,  the 
exact  amount  of  sag  can  be  calculated  for  any  length,  and  the  necessary 
correction  made.  To  keep  a mark  on  the  tape  for  frequent  reference,  si  clip 
(made  by  bending  sharply  on  itself  a piece  of  steel  £ in.  X 3 in.)  is  slipped 
upon  the  tape,  where  it  will  remain  unless  subjected  to  considerable  force. 
Reels  for  winding  the  tape  are  made  of  iron  of  wood,  and  vary  greatly  in 

size  and  shape.  „ ,,  „ , 

When  distances  do  not  come  at  even  feet,  the  fractional  part  of  the  foot 
should  always  be  noted  in  tenths.  Thus,  53  ft.  and  6 in.  should  always 

be  noted  as  53.5  ft.  . , _ , , , , 

Pins  —pins  should  be  from  15  to  18  m.  long,  made  of  tempered-steel  wire, 
and  should  be'pointed  at  one  end,  and  turned  with  a ring  for  a handle. 
When  using  a 50-ft.  chain,  a set  of  pins  should  consist  of  eleven,  one  of  which 
should  be  distinguished  bv  some  peculiar  mark.  This  should  be  the  last  pm 
stuck  by  the  front  chainman.  When  all  eleven  pins  have  been  stuck,  the 
front  chainman  calls  “Out!”  and  the  back  chainman  comes  forward  and 
delivers  him  the  ten  pins  that  he  has  picked  up,  and  he  notes  the  “out.” 
When  giving  the  distance  to  the  transitman,  he  counts  his  “outs,”  each  of 
which  consists  of  500  ft.,  and  adds  to  their  sum  the  number  of  fifties  as  denoted 
by  the  pins  in  his  possession,  and  the  odd  number  of  feet  and  fractional  parts 
of  a foot  from  the  last  pin  to  the  front  end  of  the  chain. 


44 


SURVEYING. 


The  accuracy  and  value  of  a survey  depend  as  much  on  the  careful  work 
of  the  chainmen  as  on  anything  else,  and  no  one  should  be  allowed  to 
either  drag  or  read  the  chain  that  is  not  intelligent  enough  to  appreciate  the 
importance  of  extreme  accuracy.  , , . 

Pins  are  generally  used  in  outside  work,  where  they  can  be  easily  stuck 
into  the  ground,  readily  seen,  and  avoided,  and  the  chances  of  their  being 
disturbed  are  slight.  Inside  work  generally  contains  S9  many  chances  of 
error  in  their  use  that  they  are  usually  abandoned  m favor  of  other 
methods.  If  the  sight  be  longer  than  the  length  of  the  tape,  it  is  usua*  to 
drive  a tack  in  a sill  or  a collar  at  a point  intermediate  between  the  stations, 
and  take  a measurement  to  the  tack  from  each  station,  with  the  dip  01  the 
sights;  or  a tripod  is  set  up  in  the  line  of  sight,  and  the  horizontal  distance 
is  measured  from  each  station  to  the  string  oi  the  plumb-bob  under  the 
trinod  The  first  method  is  the  more  accurate. 

Plumb-Bob.— The  plumb-bob  takes  the  place  of  the  transit  rod  m under- 
ground work,  as  the  stations  are  usually  in  the  roof,  and  strings  are  hung  from 
them  to  furnish  foresights  and  backsights.  Plumb-bobs  vary  m weight  and 
shape.  At  various  times  and  in  various  countries  where  mine  surveys  have 
been  made,  the  idea  ot  sighting  at  a flame  has  been  considered,  and,  from 
rough  methods  of  setting  a lamp  on  the  floor  on  foresight  and  backsight, 
there  have  arisen  various  forms  of  plummet  lamps.  The  idea  is  to  continue 
the  practice  of  sighting  to  a flame,  but  to  make  that  flame  exactly  under  the 
station,  and  to  avoid  the  difficulty  in  sighting  to  the  string  of  the  plummet 
The  idea  is  good,  but  there  has  never  been,  devised  a plummet  lamp  that 
would  be  as  free  from  error  under  all  circumstances  as  the  old-fashioned, 
plummet,  so  that  the  majority  of  the  best  engineers  have  gone  back  to  the 
plummet.  The  best  plummet  is  the  one  that  combines  the  least  surface  with 
the  greatest  weight,  and  the  ordinary  shapes  used  for  outside  work  are  the 
best  for  inside  also.  In  a “ windy  ” place,  a hole  can  be  dug  m the  ballast 
of  the  track  and  the  “ bob  ” let  into  this  shelter  where  it  will  be  unaffected 
bv  the  air.  The  cord  is  best  illuminated  by  placing  a white  paper  or  card- 
board behind  it  and  holding  the  lamp  in  front  and  to  one  side.  Kie  string 
shows  as  a dark  line  against  a white  ground,  and  there  is  less  difficulty  m 
finding  it  than  when  the  light  is  placed  exactly  behind  it,  and  in  this  way  a 
careless  man  cannot  burn  the  string  by  poking  the  flame  against  it.  The 
white  background  will  also  illuminate  the  cross-hairs  of  the  transit.  The 
backsight  “ bob  ” can  be  made  of  lead,  as  there  are  no  “ centers  to  be  set  by 
this  man  A number  of  varieties  have  been  made  for  the  foresight,  to  aid  him 
in  “ center  setting  ” ; but  all  get  out  of  order  easily.  A quick  man  will  do  as 
good  work  with  the  old-style  bob,  and  have  none  of  the  accidents  common 
to  the  others.  In  general,  it  may  be  said  that  the  instruments  used  for  outside 
work  will  be  sufficient  for  mine  work  also. 

The  clinometer,  or  slope  level,  is  a valuable  instrument  for  side-note  work; 
but  it  is  not  accurate  enough  for  a survey,  and  its  place  is  taken  by  the 
vertical-  circle  on  the  transit.  There  are  two  styles  of  clinometer,  with  a 
bubble  and  with  a pendulum.  The  latter  is  the  old-fashioned  and  more 
accurate  German  “Gradbogen”  that  is  found  on  some  old  corps.  The  bubble 
variety  is  much  more  easily  rendered  worthless  by  the  breaking  of  the  bubble 
tube  and  in  general  is  not  so  accurate  as  the  other  style,  which  consists  of  a 
semicircular  protractor  cut  out  of  thin  brass  and  furnished  with - books i at 
each  end,  that  it  can  be  hung  on  a stretched  string  so  that  the  string  v ill 
pass  through  the  0°  and  180°  points.  The  dip  is  read  by  a pendulum  swung 
from  the  center  of  the  circle.  If  made  sufficiently  large  it  will  readily  read 
to  Quarter  degrees.  By  inclining  the  string  parallel  to  the  surface  and 
taiSngflieclinometer,  the.  dip  will  be  obtained.  A pocket  instrument 
combining  a compass  and  clinometer  can  be  obtained  from  any  dealer  in 
surveying  instruments.  . 

FIELD  NOTES  FOR  AN  OUTSIDE  COMPASS  SURVEY. 

Call  place  of  beginning  Station  1.  . 

Stations.  Bearings.  Distances . 

1_2  N 35°  E 270.0 

At  1 + 37  ft.  crossed  small  stream  3 ft.  wide. 

At  1 + 116  ft.  = first  side  of  road. 

At  1 + 131  ft.  = second  side  of  road.  , ^ . 

At  1 I 137  ft.  = blazed  and  painted  pine  tree,  3 ft.  left,  marked  for  a 
“go  by.” 


TRANSIT  S UR  VE  YING. 


45 


Station  2 is  a stake  at  foot  of  white-oak  tree, 
sides  for  corner. 

2-3  N 83i°  E 


blazed  and  painted  on  four 
129.0 


Station  3 is  a stake-and-stones  corner. 

3- 4  S 57°  E 222.0 

3  + 64  ft.  = center  of  small  stream  2 ft.  wide. 

3 + 196  ft.  = white  oak  “ go  by,”  2 ft.  right. 

Station  4 = cut  stone  corner. 

4- 5  S 34i°  W 355.0 

4 _ j- 174  ft.  = ledge  of  sandstone  10  ft.  thick,  dipping  27°  south. 

5- 1  N56i°W  323.0 

5 + 274  ft.  = ledge  of  sandstone  10  ft.  thick,  dipping  25°  south  (evidently 

continuation  of  same  ledge  as  at  4 + 174). 

Station  1 = place  of  beginning. 


TRANSIT  SURVEYING. 

To  Read  an  Angle.— The  angle  read  may  be  included  or  deflected.  If  we 
set  up  at  0 with  backsight  at  B and  foresight  at  C,  we  shall  find  that  there 
are  two  angles  made  by  the  line  C O with  the  line  BOA,  namely  the  included 
angle  B 0 C,  and  the  deflected  angle  CO  A. 

To  Read  the  Included  Angle.— Set  the  zeros  of  vernier  and  graduated  limb 
together  accurately,  and  clamp  the  plates.  Turn  the 
telescope  on  the  backsight,  with  the  level  bubble  down, 
and,  when  set,  fasten  lower  clamp  so  as  to  fix  both 
clamped  plates  to  the  tripod  head.  Loosen  the  upper 
clamp  and  turn  the  telescope  to  C and  set  accurately. 

The  vernier  will  read,  for  example,  ‘‘45°  left  angle.” 

To  Read  the  Deflected  Angle.— Arrange  verniers  as  above, 
and  be  sure  and  turn  the  telescope  over  on  its  axis  till 
the  bubble  tube  is  up,  and  then  take  the  backsight  and 
fix  lower  clamp.  Turn  the  telescope  back  (this  is 
called  “ plunging”  the  telescope)  and  sight  to  foresight 
and  fix  as  before.  The  vernier  will  read  a ‘‘right  angle  of  135°.”  The  sum 
of  included  and  deflected  angles  must  always  be  180°. 

Note.— In  making  a survey  by  included  angles,  we  must  add  or  subtract 
180°  at  each  reading  to  have  the  vernier  and  compass  agree;  by  deflected 
angles,  they  will  agree  without  the  above  addition  or  subtraction,  and  the 
latter  method  is  generally  used.  

TO  MAKE  A SURVEY  WITH  A TRANSIT. 

By  Individual  Angles.— Set  vernier  at  zero  of  limb,  plunge  telescope,  and, 
when  set  on  backsight,  loosen  needle  and  read  bearing  of  the  line  from  back- 
sight to  set-up.  Plunge  telescope  back  and  set  on  foresight  and  read  both 
needle  and  vernier.  The  difference  in  needle  readings  should  agree  with  the 
vernier  reading  within  15',  as  local  attraction  will  affect  the  needle  equally 
on  both  sights.  , , , . 

Note.— Any  mass  of  iron  or  steel  that  may  and  will  be  moved  during  the 
readings  of  the  needle,  will  affect  the  same  and  destroy  the  value  of  the 
needle  as  a check.  The  tape  and  other  iron  materials  should  not  be  moved 
during  the  taking  of  angles. 

By  Continuous  Vernier.— Set  vernier  at  zero,  unclamp  compass  needle,  and, 
when  stationary,  turn  the  north  point  of  compass  limb  so  as  to  coincide  with 
the  north  point  of  the  needle.  Fix  lower  clamp,  plunge  telescope,  and  take 
backsight  by  loosening  upper  clamp.  The  vernier  and  needle  should  agree 
in  giving  the  magnetic  bearing  of  the  line  from  backsight  to  set-up.  Record 
this  in  note  book;  plunge  telescope,  and  take  foresight.  Needle  and  vernier 
should  agree  as  before.  After  making  record,  set  up  over  foresight  and  take 
sight  to  station  just  left  with  telescope  plunged,  having  first  seen  that  the 
vernier  reads  exactly  as  it  did  on  the  last  foresight,  as  a slip  in  carrying  the 
transit  from  one  station  to  another,  which  is  not  detected  at  the  time,  can 
never  be  checked  afterwards  when  the  final  work  is  found  to  be  in  error. 
The  foresight  is  taken  as  before.  On  every  sight  the  needle  and  vernier 
should  agree  if  there  is  no  local  attraction  of  the  needle. 

If  we  can  see  all  the  corners  of  a field  that  is  to  be  surveyed  from  a central 
point,  we  can  make  the  survey  by  setting  up  at  that  point,  and,  with  one 


46 


TR ANSI T SURVEYING. 


porner  as  a backsight,  take  all  the  other  corners  as  foresights  with  but  one 
set-up  and  by  measuring  from  this  point  to  all  of  the  corners;  or  we  can 
set  up’ at  any  corner  and  run  a line  of  survey  around  the  field.  This  latter 
method  is  called  meandering.  Both  methods  will  give  the  same  result  when 
plotted-  but  the  former  is  much  quicker,  as  the  boundaries  of  a tract  are 
freemen tlv  overgrown  with  bushes  that  must  be  cleared  to  allow  a sight, 
3 a SLtaapSnt  can  frequently  be  found  that  will  allow  a free  sight  to 
all  the  corners,  and  the  distance  can  be  measured  by  tape,  or  stadia.  As  the 
central  point  is  nearer  the  corners  than  they  are  to  one  another  it  follows 
that  a shorter  distance  must  be  chained  or  cut  in  the  case  of  a central  set-up. 
^^Outsid^'sm'veys^  be  made  for  many  purposes  It  matters  not  what 
the  purpose  is,  the  work  should  be  fully  and  accurately  done,  and  the  map 
should  contain  everything  that  will  throw  light  upon  the  subject.  If  the 
outside  work  is  to  be  connected  with  inside  surveys,  there  are  a number  of 
points  to  be  observed,  and  they  will  be  given  under  the  head  of  underground 

W°Meridians  or  Base  Lines.— The  surveys  must  be  based  on  some  meridian;, 
and  started  ’from  some  fixed  point.  There  are  four  kinds  of  meridians,  o 

blFirst™ t line  already  on  the  ground,  as  one  of  the  sides  of  the  tract  is 
taken  as  a base.  The  subsequent  work  is  ends  of  thl& 

line  and  all  angles  measured  are  taken  as  deviations  from  it. 

Second.— A stone  post  is  sunk  in  the  ground,  or,  better,  au  iron  J®  PJjJ 
into  rock  “in  place that  is,  not  loose  rock,  even  if  a large  bolder— at  such 
a distance  from  the  works  as  to  be  beyond  the  influence  of  moving ^.machinery 
and  a line  of  sight  is  taken  to  some  permanent  natural  object,  as  far  distant  as 
can  be  clearly  seen  under  adverse  circumstances,  as  cloudy  or  dark  weather. 
This  line  of  sight  is  the  base  line,  and  the  plug  is  the  origin.  N9  measurements 
of  distance  are  needed.  If  no  natural  objects  exist,  a station  is  se^.^P  a 
a distance  so  as  to  be  as  permanent  as  possible,  and  angles  are  turned  from 
this  to  other  points,  so  as  to  check  any  movement  m it.  Generally  there  are 
„ number  of  tall  chimneys,  church  spires,  etc.  to  be  found.  While  this  is 
preamble  to  the  first,  it  Jives  no  method  of  check  in  underground  work, 

anTiy/-The  magnetic  meridian  is  taken  as  the  base  line.  The  transit  is 
setup  over  a plug,  as  just  noted,  and  the  subsequent  work  is  as  described 
unde?  running  continuous  vernier.  As  the  needle  is  subject  to  constant 
Nation  this%ase  line  will  afford  a check  underground  only  for  a short 
time  after  the  meridian  is  established,  and  all  subsequent  work  can  be 
checked  only  by  applying  the  difference  between  the  variation  at  the  time 
nf  P^blishment  and  at  the  time  of  making  the  survey  If  the  time  of 
establishing  the  survey  should  be  lost,  the  base  line  would  become  no  better 

tha2WA  -The  traeame?idian  is  taken  as  a base.  The  true  north  and  south 
bnp  ruav  be  'determined  by  observing  the  North  Star,  Polaris,  or  by  observing 
Ihe  suny  The  N™Star  loes  not  lie  exactly  at  the  North  Pole,  but  revolves 
it  in  a small  circle.  There  are  two  times  m a day  when  it  is  exactly 

our ^transffe "do  ^o^hlvetheS  JmduatS  hmte 

S?  «edStsatar  in 

crosses  the  meridian.  . . 

The  true  meridian  will  give  us  an  invariable  base 
line  At  any  date  after  the  establishment  of  the  same, 
we  can  check  the  work  above  or  below  ground  by 
applying  the  variation  of  the  needle. 

To  Find  the  True  North  by  an  Observation  of  the  North 
Star,  Polaris,  at  Elongation.-This  star  has  a motion 
around  a small  circle,  the  azimuth  angle  of  winch 
from  the  north  is  known  for  different  latitudes.  The 
star  may  be  readily  found  by  following  the  line  of  the 
so-called  pointers  in  the  Big  Bear,  or  Dipper.  The 
time  of  the  greatest  eastern  or  western  elongation  is 
found  from  a table.  Some  10  minutes  before  this  time 
the  transit  is  carefully  set  up  and  leveled  over  a peg. 
The  cross-wires  are  made  to  bisect  the  star:  they  are 


jpo  laris 


\ 

\ 

\ 

\ 


l 

I 

1 

1 

I 

1 l 
\ 1 
\ ! 

\l 

\l 

V Observer 


THE  SO  LAX  ATTACHMENT. 


47 


illuminated  by  a light  held  under  the  reflector  fastened  on  the  object 
end  of  the  telescope.  The  star  is  followed  with  the  cross-wires  until  its 
motion  toward  the  point  of  its  greatest  elongation  ceases.  The  telescope  is 
lowered  vertically,  care  being  taken,  of  course,  not  to  move  it  horizontally, 
and  a peg  is  set  up  on  the  line,  say  300  ft.  or  400  ft.  distant.  The  next  morn- 
ing the  correction  is  made  for  the  star’s  azimuth.  These  corrections  are 
different  for  different  latitudes  and  different  years.  They  are  to  be  found  in 

the  nautical  almanac.  , ...  . , , , 

The  method  “by  equal  shadows”  may  be  used  with  considerable  accu- 
racv  if  we  take  a sufficiently  long  staff,  or  can  obtain  the  shadows  of  a 
tall  spire  on  a level  surface.  A vertical  staff  casts  equal  shadpws  at  the 
same  time  before  and  after  noon.  If  we  drive  a stake  at  any  time  before 
noon,  in  the  extremity  of  the  shadow  cast  by  such  a staff,  and  measure 
its  distance  from  the  staff,  we  have 
one  leg  of  an  angle.  After  noon  we 
wait  till  the  shadow  becomes  exactly 
as  long  as  the  distance  measured,  and 
drive  a stake  at  the  extremity  of  the 
shadow.  A line  bisecting  the  angle 
made  by  lines  drawn  from  these  two 
stakes  to  the  staff  will  be  in  the 
meridian. 

Establishing  a Meridian  Line  With  the 
Solar  Attachment— The  angle  from 
the  equator  to  the  horizon  of  a place 
is  its  latitude;  consequently,  from  the 
zenith  to  the  pole  is  the  colatitude , 
or  90o  _ latitude.  The  angular  dis- 
tance from  the  equator  to  the  sun  is 
the  decimation;  consequently,  from 
the  sun  to  the  pole  is  the  polar  dis- 
tance. The  angular  distance  from 
the  horizon  to  the  sun  is  the  sun’s  . , , 

altitude;  consequently,  the  zenith  distance  is  the  angular  distance  between 
the  sun  and  the  zenith.  . „ . A . , , 

Adjustments  of  Burt’s  Solar  Attachment.— After  the  instrument  has  been 
carefully  leveled,  the  zero  of  the  vernier  of  the  solar  is  placed  opposite  the 
zero  of  the  arc.  The  horizontal  plates  of  the  instrument  are  clamped,  and 
the  sun’s  image  brought  between  the  horizontal  lines  of  either  silver  plate 
bv  any  manipulation  of  the  instrument  and  attachment  possible,  keeping 
the  plates  horizontal  and  the  zero  of  the  vernier  opposite  the  zero  on  the  arc. 
When  the  image  is  accurately  between  the  horizontal  lines,  the  arc  is 
revolved  so  that  the  image  falls  on  the  other  plate;  this  must  be  done 
rapidly  as  the  sun’s  image  moves.  If  it  does  not  fall  between  the  lines,  half 
the  error  is  corrected  by  the  tangent  screw  of  the  solar  and  half  by  the 
tangent  screw  of  the  telescope.  The  operation  is  repeated  until  the  sun  s 
image  falls  between  the  lines  of  the  second  plate,  after  a revolution  of  the 
arc  it  having  been  made  to  fall  between  the  lines  of  the  first,  as  described. 
Near  noon  is  a good  time  to  make  this  adjustment,  as  the  sun’s  apparent 
motion  is  not  so  rapid.  The  zero  of  the  vernier  is  now  brought  opposite  to 
the  zero  of  the  arc  by  loosening  the  screws  that  fasten  the  vernier,  and 
sliding  it  as  may  be  necessary.  It  is  often  difficult  to  make  the  zeros  come 
exactly  opposite  each  other,  as  the  vernier  plate  is  apt  to  move  slightly 
when  the  screws  are  tightened  again.  The  second  adjustment  is  to  make 
the  tons  of  the  rectangular  blocks  of  the  solar  attachment  level,  when  the 
telescone  is  level  and  the  arc  of  the  solar  is  set  at  zero.  Level  the  transit 
carefully  as  before  described,  set  the  solar  at  zero  and  plac^  the  level, 
furnished  with  the  solar,  across  the  tops  of  the  blocks.  If  the  bubble  comes 
to  the  center  of  the  tube,  no  correction  is  needed;  if  it  does  not,  correct  the 
error  bv  turning  the  screws  under  the  hour  circle,  care  being  taken  m this 
as  in  ali  other  movements  of  these  adjusting  screws,  to  leave  them  tight  after 
the  correction.  Revolve  180°  and  correct  again  if  necessary.  Placing  the 
blocks  90°  horizontally  from  their  first  position,  go  through  the  same 
operation  as  described  until  in  all  positions  the  bubble  remains  centered. 

To  Use  the  Solar.— Before  this  instrument  can  be  used  at  any  given  place, 
it  is  necessary  to  set  off  upon  its  arcs  both  the  declination  of  the  sun,  as 
affected  by  its  refraction  for  the  given  day  and  hour,  and  the  latitude  of  the 
place  where  the  observation  is  made. 


48 


TRANSIT  S UR  VE  Y1NG. 


The  declination  of  the  sun  as  given  in  the  ephemeris  of  the  nautical 
almanac  from  year  to  year,  is  calculated  for  apparent  noon  at  Greenwich, 
England.  To  determine  it  for  any  other  hour  at  a place  in  the  United 
States,  reference  must  be  had.  not  only  to  the  difference  of  time  arising 
from  the  difference  of  longitude,  hut  also  to  the  change  of  declination 
during  that  time. 

The  longitude  of  the  place,  and  therefore  its  difference  m time,  if  not  given 
directly  in  the  tables  of  the  almanac,  can  be  ascertained  very  nearly  by 
reference  to  that  of  other  places  given  which  are  situated  on,  or  very  nearly 
on,  the  same  meridian. 

It  is  the  practice  of  survevors  in  states  east  of  the  Mississippi  to  allow  a 
difference  of  6 hours  for  the  difference  in  longitude,  calling  the  declination 
given  in  the  almanac  for  12  M.  that  of  6 a.m.  at  the  place  of  observation. 
Beyond  the  meridian  of  Santa  Fe,  the  allowance  would  be  about  7 hours; 
and  in  California.  Oregon,  and  Washington,  about  8 hours.  Having  thus 
the  difference  of  time,  we  verv  readily  obtain  the  declination  for  a certain 
hour  in  the  morning,  which  would  be  earlier  or  later  as  the  longitude  was 
greater  or  less,  and  the  same  as  that  of  apparent  noon  at  Greenwich  on  the 
given  day.  Thus,  suppose  the  observation  made  at  a place  5 hours  later  than 
Greenwich,  then  the  declination  given  in  the  almanac  for  the  given  day  at 
noon,  affected  by  the  refraction,  would  be  the  declination  at  the  place  of 
observation  for  7 a.m.  This  give  us  the  starting  point. 

To  obtain  the  declination  for  the  other  hours  of  the  day,  take  from  the 
almanac  the  declination  for  apparent  noon  of  the  given  day,  and,  as  the 
declination  is  increasing  or  decreasing,  add  to,  or  subtract  from,  the  decli- 
nation of  the  first  hour  the  difference  of  one  hour  as  given  in  the  ephemeris, 
that  will  give,  when  affected  by  the  refraction,  the  declination  of  the 
succeeding  hour.  Proceed  in  like  manner  to  make  a table  of  the  declinations 
for  every  hour  of  the  day. 

To  Find  the  True  North  With  the  Burt  Solar.— Find  from  an  ephemeris  or 
nautical  almanac  the  sun  declination  for  noon  of  the  day  of  observation  at 
Greenwich.  Find  the  declination  for  the  hour  of  observation  at  the  place 
of  observation  bv  first  figuringwhat  time  it  is  at  the  place  of  observation 
when  it  is  noon  at  Greenwich.  If  the  place  of  observation  is  west  of  Green- 
wich it  will  be  earlier  there;  if  east,  later,  and  in  either  case  the  difference 
will  be  one  hour  for  everv  15°  of  longitude.  If  the  place  is  west,  subtract  the 
hour  just  found  as  described  from  the  hour  of  the  observation,  and  multiply 
the  hourly  difference,  also  taken  from  the  ephemeris,  by  the  remainder.  If 
the  declination  is  increasing  from  the  equator  either  north  or  south,  add 
this  product  to  it;  if  decreasing,  subtract  it.  A table  of  refractions  is  given 
in  the  ephemeris  for  the  different  latitudes  and  the  different  hours  of  the 
dav.  This  refraction  is  to  be  added  if  the  declination  is  north,  and 
subtracted  if  the  declination  is  south.  Having  thus  ascertained  the  declina- 
tion, lay  it  off  on  the  declination  arc.  Set  the  colatitude  of  the  place  off  on 
the  vertical  arc  after  having  leveled  the  instrument  carefully  with  clamped 
horizontal  plates  at  zero.  Alwavs  in  solar  observations  it  is  well  to  level  by 
means  of  the  upper  telescope  bubble.  Now,  revolve  the  horizontal  plates  still 
clamped  and  also  the  declination  arc.  around  its  polar  axis  until  the  sun’s 
image  is  exactlv  between  the  horizontal  lines  of  the  silver  plates.  When  the 
sun’s  image  is  between  these  lines,  the  object  end  of  the  telescope  will  be 
pointing  north.  , _ 

To  Take  the  Latitude  With  Burt’s  Solar.— A few  minutes  before  apparent 
noon  clamp  the  plates  at  zero,  level  the  instrument  carefully,  and  set  the 
zero  of  the  vernier  opposite  the  zero  of  the  vertical  arc.  Lay  off  the  declina- 
tion, corrected  for  noon  at  the  place  of  observation  and  for  refraction,  on 
the  declination  arc,  and  set  the  time  mark  on  the  declination  arc  opposite 
XII  on  the  hour  dial.  Bring  the  sun’s  image  between  the  horizontal  lines 
of  the  silver  plate  bv  moving  the  plates  horizontally  and  the  telescope 
vertically,  clamp  both  plates  and  telescope  and  follow  with  the  tangent 
movements  the  rising  sun.  Be  careful  to  stop  when  the  sun  ceases  to  mount. 
For  a moment  before  apparent  noon  there  is  no  perceptible  motion  of  the 
image.  The  reading  on  the  vertical  arc  is  the  colatitude  of  the  place. 

The  colatitude  should  never  be  taken  this  way  for  direct-sight  calcula- 
tions for  while  it  satisfies  the  automatic  solution  of  the  true  north,  it  may 
not  be  accurate,  and  the  latitude  needed  for  direct-sight  calculation  should 
be  true  to  within  a minute.  With  the  Burt  solar  there  is  at  times  what  is 
called  a false  image  to  guard  against,  an  image  that  comes  between  the  lines 
of  the  silver  plates  when  the  object  end  of  the  telescope  is  not  pointing 


TRANSIT  S UR  VE  YINQ. 


49 


north  If  the  time  be  observed  on  the  hour  dial,  or  the  magnetic  north  be 
noticed,  no  error  need  ever  occur  on  this  score,  for  with  the  false  image  the 
time  will  be  out  considerably  and  also  the  magnetic  variation. 

General  Remarks.— With  the  base  line  located  and  the  survey  made,  we  see, 
by  coming  back  to  the  point  from  which  we  started  or  “ closing”  the  work, 
whether  it  be  correct  in  distance  or  angle.  If  it  be  in  error,  see  if  the  error 
can  be  located  (as  will  be  shown  under  plotting),  and  if  it  can  be  tound,  run 
those  parts  over  again;  if  not,  repeat  the  whole  survey.  Shoving  the  work, 
as  it  is  called,  or  “doctoring”  it  so  that  it  will  close,  is  the  poorest  practice 
that  an  engineer  can  engage  in,  as  all  subsequent  work  that  depends  on  a 
doctored  survey  must  be  doctored  to  tit  the  faulty  work — even  it  it  be  right 
in  itself.  Every  engineer  should  be  able  to  swear— not  that  he  “ thinks  the 
survey  is  accurate,”  but  “that  he  knows  it  to  be  so,”  if  he  should  be  called 
as  a witness  in  court.  One  of  the  causes  of  inaccuracy  is  haste. 

To  make  a complete  map,  the  engineer  should  first  make  a survey  around 
the  tract  to  be  worked,  locating  all  the  prominent  physical  features  and 
improvements.  If  he  can  do  so,  he  should  make  a topographical  map  of  the 
tract  at  once;  but,  if  time  is  limited,  by  running  the  vertical  as  well  as  the 
horizontal  angle,  he  can  carry  the  tidal  elevation  or  the  elevation  above 
some  assumed  datum,  to  every  station,  and  murk  it  on  the  map  at  that  point. 
Then  as  he  makes  subsequent  surveys,  he  can  gradually  get  data  enough  to 
make  a fairly  complete  topographical  map  in  course  of  time.  Every  ledge 
of  rock  in  place  should  be  located,  and  the  amount  and  direction  of  its  dip, 
as  well  as  the  character  of  the  rock,  should  be  marked  neatly  on  the  map. 
The  streams  of  water  on  the  tract  should  be  regarded  as  of  primary  impor- 
tance, and  should  be  located  with  exactness. 

With  a true  meridian  base  line  we  can  connect  maps  made  at  different 
places  with  little  trouble.  This  is  especially  useful  with  adjoining  mines 
connected  at  but  one  point.  Having  made  the  survey  and  come  home,  we 
must  examine  all  the  apparatus  and  see  if  the  instruments  are  out  of  adjust- 
ment, as  such  a fact  will  prevent  our  bothering  over  work  that  will  not 
close  It  will  assure  us,  also,  that  we  can  start  out  at  a moment’s  notice 
with  no  thought  of  the  adjustment  of  our  tools.  A famous  wit  said  that  the 
proper  time  to  strop  a razor  was  just  after  you  had  used  it,  as  you  then  knew 
how  much  it  needed  it.  The  same  will  apply  to  surveying  instruments  and 
tools— especially  for  underground  work.  Here  the  lamp  smoke,  powder 
gases,  mine  dust,  paint  smears,  acid  water  from  “droppers,”  and  the  other 
abominations  incident  to  underground  surveying,  especially  in  a coal  mine, 
will  so  cover  the  tools  that  they  would  be  useless  if  left  uncleaned  half  a 
dozqn  times.  As  soon  as  the  corps  comes  back  from  the  mine,  and  before 
the  clothes  are  changed,  the  tape  must  be  stretched,  tested, wiped,  and  oiled. 
It  can  be  inspected  to  see  if  marks  are  too  much  worn,  or  it  stands  in  need  of 
mending,  the  marking  pot  is  cleared  of  “muck,”  and  fresh  white  paint  is 
mixed,  if  the  corps  is  going  out  in  24  hours;  the  plummets  will  have  their 
strings  overhauled  and  freed  from  knots;  hatchets  will  be  sharpened,  and 
axes  ground,  pouches  overhauled,  and  a supply  of  tacks  or  “spads”  taken. 
Then  the  transitman  changes  his  clothes  and  sets  up  the  transit,  wipes  it 
with  a cloth  wet  with  alcohol,  so  as  to  remove  dirt,  oil,  and  paint.  If  water 
has  gotten  between  the  graduated  limb  and  compass  box,  the  verniers  must 
be  uncovered  and  the  whole  wiped  dry.  If  the  sulphureted  hydrogen  from 
the  powder  smoke  has  tarnished  the  silver  surfaces  of  any  of  the  graduated 
circles,  it  must  be  removed  with  whiting.  Alcohol  should  be  always  used 
instead  of  water,  as  it  will  quickly  evaporate  and  leave  the  parts  dry.  The 
telescope  glasses  are  then  wiped  with  soft  chamois  leather,  and  the  instru- 
ment is  tested  for  want  of  adjustment  before  putting  it  away  in  its  box. 
When  going  to  and  from  work,  the  transit  should  not  be  carried  on  the 
transit  head,  or  the  spindle  will  become  sprung.  Nor  should  it  be  carried 
with  the  arm  crooked  under  the  telescope,  as  the  weight  comes  on  the  axis, 
and  that  soon  gets  sprung  so  that  all  the  adjusting  in  the  world  will  not 
make  it  work  right.  When  carried  in  the  hand,  it  should  be  reversed  and 
the  hand  slipped  under  the  compass  plate  and  brought  over  so  as  to  clamp 
both  plates.  In  this  way  there  will  be  no  strain  on  any  part.  In  case  of  a 
“fall”  in  the  mine,  remember  that  the  transit  is  the  baby  to  be  protected, 
and  stand  a few  bumps  to  save  a strained  or  broken  instrument,  that  will 
end  the  work  for  some  time. 

‘ Plotting.— A “plot”  is  not  only  a piece  of  ground  with  bodies  of  water, 
roads,  vegetation,  etc.  upon  it,  but  refers  also  to  the  map  of  the  same  drawn 
to  a given  scale,  and  showing  all  of  the  above  natural  features.  Plotting  is 


50 


TRANSIT  S UR  VE  YING . 


the  making  of  such  a map  from  notes  of  a survey,  and  may  or  may  not 
require  the  permanent  placing  of  the  stations  on  the  map,  by  which  the 
survey  is  made.  In-  underground  work,  the  exact  location  and  the  retention 
of  those  stations  is  a matter  of  the  first  importance,  and  is  secondary  only  to 
the  exact  ploUing  of  the  side  notes.  The  scale  of  the  plot  is  generally 
as  large  as  will  show  the  points  of  interest  m the 
Pennsylvania,  the  maps  for  coal  mines  must  be  drawn  to  a scale  of  100  ft.  to 
an  inch  There  are  two  methods  of  plotting:  by  protractor,  and  by 
coordinates.  When  the  scale  is  sufficiently  large,  it  is  a matter  of  little  choice 
which  method  is  used,  if  the  work  be  carefully  done  with  exact  instruments, 
but  with  small  scales-100 . ft.  or  above,  to  the  inch— we  should  use  the 
method  bv  coordinates.  With  the  latter  scale,  the  prick  of  a pm  on  the 
paper  will^ represent  a foot  square,  or  a circle  slightly  larger  than  a foot 
m diameter.  If  the  next  station  is  to  be  located  from  the  pin  prick  of  the 
first,  and  that  is  exactly  located,  we  may  not  hit  the  exact  cenr-CT  9*^^ 
small  indentation.  In  fact,  the  chances  are  greatly  against  our  doing  so, 
and  the  location  of  the  second  station  will  probably  be  in  error.  If  we  have 
a bad  habit  of  placing  the  protractor  or  the  straightedge  against  one  side  of 
the  pin  pricks,  or  pencil  marks,  when  the  scale  is  large  we 
be  introducing  a “ personal  error,  as  it  is  called;  and  the  sum  of  all  the 
errors  made  at  each  of  100  stations  will  bring  our  final  point  very  much _out 
of  the  way.  On  this  account,  and  from  the  fact  that  no  protractor  that  is 
movable  can  be  used  without  the  chances  of  shppmg  while  the  angle  is  read 
or  marked,  has  led  all  careful  engineers  to  abandon  its  use  m favor  of  the 
method  by  coordinates.  When  the  scale  is  from  1 to  2o  ft.  to  an  inch  the 
errors  are  small  enough  to  make  little  chances  of  variation  in  a cl?seoften 
or  twelve  stations;  when  the  survey  is  of  short  sights  from  a mam  line  to 
points  where  no  further  work  is  to  be  done,  the  protractor  will  afford  a quick 

meTh°ere°i  a ?han?'e  of  error  in  both  methods  that  must  he  noted  here,  where 
the  survey  is  not  completed  at  one  time.  If  the  map  be  made  m a day  or 
two,  and  will  never  be  extended  by  subsequent  work,  there  will  be  no 
chance  of  error  from  a change  in  the  paper  on  which  it  is  made,  due  to 
moisture  or  dryness;  but  if  the  map  be  made  on  a series  of  very  damp  days, 
or  a series  of  very  dry  ones,  a change  in  the  weather  to  the  other  extreme 
will  swell  or  shrink  the  map.  The  general  tendency  in  a large  mine  map 
that  is  frequently  used,  and  is  rolled  and  unrolled  every  day for  ^ sg 
years,  is  to  stretching,  so  that  there  will  be  a variation  of  from  l to  5 ft  m 
1,000.  If  we  extend  a recent  survey  on  such  a map,  we  are  plotting  it  to  a 

different  scale  to  that  assumed  by  the  map  under,  ^wri 

noted.  The  paper  on  which  the  map  is  to  be  drawn  should  be  tacked  down 
to  the  table  or  board,  and  should  be  covered  with  squares  each  exactly  10  in. 
square.  The  sides  of  these  squares  should  be  the  meridians,  or  north  or  south 
lines,  and  the  tops  and  bottoms  should  run  due  east  and  west.  Mark  the  first 
station  on  the  paper,  set  your  parallel  ruler  or  T square  on  the  meridian  nearest 
it  and  with  the  protractor  produce  the  course  to  the  next  station.  Measure  the 
distance  with  a scale,  and  proceed  in  this  manner  to  plot  all  the  courses  using 
each  time  the  meridian  nearest  the  station  the  course  is  taken  from.  After  all 
the  stations  have  been  plotted,  fill  in  the  side  notes,  marking 
the  map  with  great  care  and  neatness.  Always  use  the  horizontal  distances. 
All  surveys  should  be  traversed,  and  all  plotting  should  be  eithei checked 
bv  the  traversing,  or  the  principal  stations  should  be  plotted  by  use  of  the 
traverse.  For  a large  mine  map  that  will  be  in  use  many  years,  muslin- 
backed  egg-shell  paper  must  be  used.  It  comes  in  a long  roll,  and  any 
reasonable  length,  and  a width  up  to  6 ft.  can  be  obtained. 

To  Calculate  the  Vertical  Distances.— When  making  the  survey,  read  the 
vertical  angles  to  all  stations.  If  the  angle  is  one  of  depression,  note  it  vuth 
a minus  sign  (— ) preceding  it.  If  it  is  an  angle  of  elevation,  precede  it  with 
a plus  sign  ( + ).  These  will  show  whether  the  vertical  distance  is  to  be 
added  to,  or  subtracted  from,  the  height  of  the  preceding  station. 

Having  the  horizontal  distance  and  the  vertical  angle: 

Distance  X tangent  of  vertical  angle  = vertical  distance. 

Having  the  pitch  distance  and  vertical  angle: 

Distance  X sine  of  vertical  angle  = vertical  distance. 

To  Calculate  the  Horizontal  Distance,  or  Latitude.— Pitch  distance  X cosine 
of  vertical  angle  = horizontal  distance.  . r 

Vertical  height, or  departure  h-  tang.of  vertical  angle  = horizontal  distance. 


TRANSIT  S UR  VE  YINQ. 


51 


Tv  Calculate  the  Pitch  Distance.— Horizontal  distance  — cosine  of  bearing, 
or  multiplied  by  secant  of  bearing  = pitch  distance. 

Vertical  distance  -i-  sine  of  vertical  angle,  or  multiplied  by  cosecant  of 
bearing  = pitch  distance. 

To  Calculate  the  Vertical  Angle.— The  horizontal  distance  --  the  pitch 
distance  = cosine  of  vertical  angle. 

Vertical  distance  -5-  pitch  distance  = sine  of  vertical  angle. 

Vertical  distance  -4-  horizontal  distance  = tangent  of  vertical  angle. 

Note.— Whenever  sines,  cosines,  tangents,  etc.  are  here  named,  they  mean 
the  natural  sines,  etc.  of  the  angle.  . 

Plotting  by  Coordinates.— In  describing  the  establishment  of  a meridian 
and  a fixed  point,  we  made  the  latter  a stone  post,  or  iron  plug  sunk  in. solid 
rock.  This  point  is  called  the  origin  of  coordinates.  We  have  the  principal 
meridian  passing  through  this  point  in  an  exact  north  and  south  direction, 
and  a secondary  meridian  or  base  line  passing  through  this  point  at  right 
angles  to  the  first,  or  in  an  exact  east  and  west  line.  Any  point  we  may 
select  on  the  map  will  be  a certain  distance  north  or  south,  and  east  or  west  of 
the  origin.  The  lines  drawn  from  this  point  at  right  angles  to  the  two  base 
lines  just  given  are  called  the  coordinates  of  that  jpoint,  and  we  can  plot  the 
point  when  they  are  given.  For  example,  the  coordinates  of  Station  24  are 
North  845.67,  and  East  890.12.  We  measure  890.12  ft.  east  of  the  origin  on  the 
secondary  meridian  and,  from  this  point,  measure 345:67  ft.  north  to  the  point 
desired;  or  we  can  measure  first  on  the  primary  meridian  to  the  north  and 
then  turn  off  a right  angle  to  the  east  and  reach  the  same  point.  In  any 
event  we  plot  the  position  ol'  each  station  independently  of  all  the  others, 
and  any  error  in  locating  one  is  not  carried  to  the  next.  When  two  stations 
are  plotted,  the  distance  between  them  on  the  map  should  be  exactly  what 
we  found  for  their  horizontal  distance  on  the  ground.  This  check  shows 
whether  our  plotting  is  correct.  This  is  also  called  traversing  a survey  if  the 
meridian  be  north  and  south,  and  in  books  on  surveying  there  are  printed 
traverse  tables , which  are  accurate  within  certain  limits,  but  not  so  accurate 
as  the  tables  of  coordinates  published  separately,  as  the  latter  are  carried  to  a 
greater  number  of  decimals.  Gordon’s  Traverse  Tables  will  enable  you  to 
find,  without  calculation,  the  coordinates  for  a distance  of  12  miles  with  a 
chance  of  error  of  only  half  an  inch,  which  is  much  more  accurate  than  the 
graduation  of  the  instruments  with  which  the  work  was  done. 

With  a north  and  south  meridian,  the  point  from  which  we  begin  to 
measure  angles— the  zero  point— is  the  north  point,  and  the  angles  are  read 
for  continuous  vernier  in  the  direction  of  the  hands  of  a watch.  The  sines 
of  angles  are  eastings  and  westings,  and  the  cosines  are  northings  and 
southings. 

To  Traverse  a Survey.— To  traverse  a survey,  means  to  determine  by  calcu- 
lation how  far  north  or  south  and  east  or  west  any  station  may  be  from 
another,  the  location  of  which  is  fixed.  To  do  this,  all  distances  must  be 
either  measured  horizontally,  or  calculated  to  horizontal  distances.  The 
horizontal  angles,  or  courses,  must  be  either  read  as  quadrant  courses,  or 
reduced  from  azimuth  to  quadrant  courses.  An  azimuth  course  is  one  that 
is  read  on  the  transit  which  is  graduated  from  0°  to  360°.  A quadrant  course 
is  one  read  in  the  quadrant  of  the  circle,  as  S 67°  W,  N 43°  E,  etc. 

Latitude  means  distance  north  or  south,  and  is  determined  by  the  first 
initial  of  the  recorded  course.  Thus,  if  a course  is  S 67°  W,  the  latitude  is 
south;  if  N 43°  E,  the  latitude  is  north. 

Departure  means  distance  east  or  west,  and  is  determined  by  the  last 
initial  of  the  recorded  course.  Thus,  if  a course  is  S 67°  W,  the  departure  is 
west;  if  N 43°  E,  the  departure  is  east. 

The  latitude  = distance  X cosine  of  bearing. 

The  departure  = distance  X sine  of  bearing. 

If  the  survey  is  a continuous  one  around  a tract,  and  ending  at  the 
place  of  beginning,  the  sum  of  the  northings  should  equal  the  sum  of 
the  southings,  and  the  sum  of  the  eastings  should  bqual  the  sum  of  the 
westings.  Or,  in  other  words,  the  sum  of  all  the  latitudes  north,  should 
equal  the  sum  of  all  the  latitudes  south;  and  the  sum  of  all  the  departures 
east,  should  equal  the  sum  of  all  the  departures  west.  It  is  evident  that  by 
coming  back  to  the  place  of  beginning  the  surveyor  has  traveled  the  same 
distance  north  as  he  has  south,  and  the  same  distance  east  as  he  has  west. 

The  most  accurate  way  to  construct  a map  is  to  traverse  the  survey  and 
place  all  stations  on  it  by  the  traversed  distances,  or  to  at  least  put  a 
number  of  the  principal  stations  on  the  map  by  the  traversed  distances,  and 


52 


transit  sur  veying. 


use  the  protractor  to 

the  survey  is  at  the  fixed  f ^ of  this  point  from  the 

pencil  sketch  to  find  the  aPPJP^i^eneraf  trend  of  the  property  itself, 
boundaries  of  the  property , ai ttf1?egor“|j„  upon  the  paper  so  that  all  of 
This  will  show  us  the  place  to  0 fd  P about  the  same  amount  of 

the  property  can  be  placed  on  tne  map,  anu  north  and  souih 

margin  on  all  sides.  It  will  also ^°hTs^  settled  mXthe  origin  by  a needle 
line must  take  on  the  paper  When  this  f tueQ^  mar  s 

point,  and  lay  the  straightedge  across  it «)  a quite  hard  pencil 

principal  meridian  and  draw  Then  lav  off  on  both  sides  of  the  origin 
brought  to  a very  hue  P0*™  • t h needle  points.  These  must  he  so 

distances  of  5 in.,  and  mark  the  an  err()P  of  one  hundredth  of  an 

accurately  located  that  there' ^^^dred  At  the  point  where  we  can  get 
inch  in  them,  or  °ne  ^ot  m f angles  to  the  principal  meridian,  lay 

the  longest  line  on  the  paper  at  right Qf  the  meridian,  and 
off  points  for  a right  angle  ac£ara  y f the  straightedge,  a lme  parallel 
draw  through  the  three  th^ accurately  into  5"  distances  as 

to  the  secondary  meridian  an^  lines  at  right  angles 

before.  Through  each  ot  the  points  thus  manw, ,1  squares 

to  the  lines  already  drawn,  until  the  paper  ^ accurately  ^ flvedlulldredth. 
5 in.  on  a side,  and  n0.ne  o^hem  extremities  ofthe  lines  passing  through 

Beginning  with  the  origin  mark  the  side  0f  the  north  and 

it  zero.  All  distances  to  the  east  o P tQ  that  pne;  those  to  the  left  are 
south  zero  line  are  marked  + P iine  are  marked  + 

marked  - . A1  distances above : the  east  anawes^  _ If  the  coordinates  of 
with  respect  to  that  line,  and  a d t measure  the  whole  east 


Stations. 

, Quadrant 
Courses. 

1 

Distances. 

Latitudes. 

Departures. 

S 

E 

W 

1-2 

2-3 

a-4 

4-5 

N35°E 
N 83°  30'  E 
S 57°  E 
S 34°  15'  W 

270 

129 

222 

355 

221 

15 

121 

293 

155 

128 

186 

200 

1 236 

414 

469 

200 

Totals. 


N 

S 

E 

W 

221 

155 

236 

283 

115 

469 

178 

269 

for  latitudes  and 

ine  iorcgumg  is  221  ft  north  and  155  it.  easx  oi  oiauuu  a, 

by  the  rule  given  under  tPe  heacl  tie  diyideit  int0  triangles  and 
same  number  of  stdes.  If  a^  nregi  these  areas  will  be  the  area  of 

‘ K 

wittfthe  greatest  ^arej owing0 to^iaWUty  to  error  through  very  slight  mac- 

curacies  of  measurement.  Tract.— If  the  seam  lies  flat, 

To  Find  the  Contents  of  a Seam  ofCoal  Under*  ^cthickness  of  the  seam  in 
multiply  the  area  of  the  ^act  “ square  leer  oy  i seam  in  feet.  if  the 

slam  is --  «nd  Us  area®  by  measuring  the  width  of  the  tract  on 

its  line 
the  hor 
This  w: 

byft^hiAnessTvill  give  thb  contente.^  .p  feet  x gp  Gr-  x 62 .5 


feet.  The  product  will  °e  “f  I1' me^uring  the  width  of  the  tract  on 

seam  is  an  inclined one,  hnd ^its 1 area .by  mea  ^ of  the  seam  by  dividing 

its  line  of  pitch  and  find  the  distance  on  tne  p ^ the  angle  of  inclination, 
the  horizontal  distance  measured  by  e^°sine  the  pitch  distance  by  the 
strict  Mid  youhwhl  have  the  area’o?  the  seam.  This  multiplied 

icufii'u  • 4-v»  a nAtitonrs  . ^ 


Tons  of  coal  = 


2,240 


LEVELING. 


63 


LEVELING. 

Instruments.— But  two  instruments  are  used— the  level  and  a leveling  rod. 
The  level  consists  of  a telescope  to  which  is  fitted,  on  the  under  side,  a long 
level  tube.  The  telescope  rests  in  a Y at  each  end  of  a revolving  bar,  which  is 
attached  to  a tripod  head  very  similar  to  that  used  tor  a transit.  The 
telescope  is  similar  to  the  telescope  of  a transit.  The  leveling  rod  is 
merely  a straight  bar  of  wood,  6 ft.  or  more  in  length,  divided  into  feet  and 
tenths  of  a foot.  A target  divided  into  four  equal  parts  by  two  lines,  one 
parallel  with  the  staff,  and  the  other  at  right  angles  to  it,  and  painted  red 
and  white,  so  as  to  make  it  prominent  at  a distance,  slides  on  the  rod  and  is 
provided  with  a clamp  screw.  The  center  of  the  target  is  cut  out  and  a 
vernier,  graduated  decimally,  is  set  in,  which  enables  the  rodman  to  read  as 
close  as  of  a foot. 

If  a long  rod  is  required,  it  is  made  of  two  sliding  bars,  which,  when 
closed,  are  similar  to  a single  rod,  as  described  above.  When  used  at  points 
where  it  is  necessary  to  shove  the  target  to  a greater  height  than  6 or  6£  ft., 
the  target  is  clamped  at  the  highest  graduation  on  the  front  of  the  rod,  and 
the  rod  is  extended  by  pushing  up  the  back  part,  which  carries  the  target 
with  it.  The  readings,  in  this  case,  are  made  either  from  the  vernier  on  a 
graduated  side,  or  a vernier  on  the  back.  The  rodman  must  always  hold  his 
rod  perfectly  plumb  or  perpendicular. 

To  Adjust  the  Level.— The  proper  care  and  adjustment  of  the  level  is  of  great 
importance.  A very  slight  error  in  adjustment  will  completely  destroy  the 
utility  of  any  work  done. 

To  Adjust  the  Line  of  Collimation. — Set  the  tripod  firmly,  remove  the  Y pins 
from  the  clips,  so  as  to  allow  the  telescope  to  turn  freely,  clamp  the  instru- 
ment to  the  tripod  head,  and,  by  the  leveling  and  tangent  screws,  bring 
either  of  the  wires  upon  a clearly  marked  edge  of  some  object,  distant  from 
100  ft.  to  500  ft. 

Then  with  the  hand,  carefully  turn  the  telescope  half  way  around,  so  that 
the  same  wire  is  compared  with  the  object  assumed.  . 

Should  it  be  found  above  or  below,  bring  it  half  way  back  by  moving  the 
capstan-headed  screws  at  right  angles  to  it,  remembering  always  the  invert- 
ing property  of  the  eyepiece;  now  bring  the  wire  again  upon  the  object,  and 
repeat  the  first  pperation  until  it  will  reverse  correctly.  Proceed  in  the 
same  manner  with  the  other  wire  until  the  adjustment  is  completed. 
Should  both  wires  be  much  out,  it  will  be  well  to  bring  them  nearly  correct 
before  either  is  entirely  adjusted. 

To  Adjust  the  Level  Bubble.— Clamp  the  instrument  over  either  pair  of 
leveling  screws,  and  bring  the  bubble  into  the  center  of  the  tube. 

Now  turn  the  telescope  in  the  wyes,  so  as  to  bring  the  level  tube  on  either 
side  of  the  center  of  the  bar.  Should  the  bubble  run  to  the  end,  it  would 
show  that  the  vertical  plane,  passing  through  the  center  of  the  bubble,  was 
not  parallel  to  that  drawn  through  the  axis  of  the  telescope  rings.  To 
rectify  the  error,  bring  it  by  estimation  half  way  back,  with  the  capstan- 
headed screws,  which  are  set  in  either  side  of  the  level  holder,  placed 
usually  at  the  object  end  of  the  tube.  Again  bring  the  level  tube  over  the 
center  of  the  bar,  and  adjust  the  bubble  in  the  center,  turn  the  level  to 
either  side,  and,  if  necessary,  repeat  the  correction  until  the  bubble  will 
keep  its  position,  when  the  tube  is  turned  half  an  inch  or  more  to  either  side 
of  the  center  of  the  bar.  The  necessity  for  this  operation,  arises  from  the 
fact  that  when  the  telescope  is  reversed,  end  for  end,  in  the  wyes  in  the 
other  and  principal  adjustment  of  the  bubble,  we  are  not  certain  of  placing 
the  level  tube  in  the  same  vertical  plane,  and,  therefore,  it  would  be  almost 
impossible  to  effect  the  adjustment  without  a lateral  correction. 

Having  now,  in  a great  measure,  removed  the  preparatory  difficulties,  we 
proceed  to  make  the  level  tube  parallel  with  the  bearings  of  the  Y rings.  To 
do  this,  bring  the  bubble  into  the  center  with  the  leveling  screws,  and  then, 
without  jarring  the  instrument,  take  the  telescope  out  of  the  wyes  and 
reverse  it  end  for  end.  Should  the  bubble  run  to  either  end,  lower  that  end, 
or,  what  is  equivalent,  raise  the  other  by  turning  the  small  adjusting  nuts, 
on  one  end  of  the  level,  until,  by  estimation,  half  the  correction  is  made; 
again  bring  the  bubble  into  the  center  and  repeat  the  whole  operation,  until 
the  reversion  can  be  made  without  causing  any  change  in  the  bubble.  It 
would  be  well  to  test  the  lateral  adjustment,  and  make  such  correction  as 
may  be  necessary  in  that,  before  the  horizontal  adjustment  is  entirely 
completed. 


54 


transit  s ur  verm 


To  Adjust  the  «... ,-Ha^ng - ef 

now  to  descnbe  that  of.  t0  thevertical  axis,  so  that  the  bubble 

level  into  a ^ entire  revolution ’of  the  instrument, 

will  remain  m the  ^"‘rt.iihe  hrectly  over  the  center  of  the  bar,  and  clamp 
To  do  this,  bring  the  level  tube  directly  o v before  over  two  of  the  leveling 

the  telescope  hrmt1>7?neket  leve?^ the  fubbie,  and  turn  the  instrument  halt 
screws,  unclamp .the  wcket  level^ne  dudd 'tbe  ^me  position  with  respect 

way  around,  so  that  the  ievei  ba  > the  bubble  run  to  either  end,  bring 
to  the  leveling  beneath^  Should^the  wome  ^ bar;  now  move  the 

ill^cop^vefthe^ther  sit  of level! ^^^-ews,  bring  t^hbteagin  into 

If^crewf ’succes’Sv!?®  until  thl adjustment  is  very  nearly  perfected,  when 

brought  precisely  to  its  i ormer  atuat  • made  and  the  sockets  well 

completely  adjusted,  ! f the  11 ^men  P P bubble  wlll  reverse  over  each 

fitted  to  each  other  and  tne  tnpou  . . b unable  to  make  it 

pair  of  screws  m auy^m-  f^ond  the  engmee  c y t e 

S"  “ Sm  prob.il,  b.'  1.  Ur.  imperfecttuu  «,  rh. 

interior  spindle.  __tQ  of  the  ievel  have  been  effected,  and  the  bubble 
After  the  adjustments  oi -tne  socket,  the  engineer  should 

remains  in  the  center  m an  P n(j  sighting  upon  the  end  of  the 

carefully  tmn  the  telescope  he  w>  ^ Jong  each  side  of  the  wye, 

level,  which  has  theQ^rrivz®^{!1  ^possible  Whin  this  has  been  secured, 

make  the  tube  as  n^lye^c^asposb  vertieal  e(Jge  of  a building, 

he  may  observe,  through  the  teiesc  p , he  should  loosen  two  of 

and  the  adjustments  of  the  level  will 

be  complete.  ^otrnmpnt  the  legs  must  be  set  firmly 

To  Use  the  Levf  .-^en  usmg  the  ms^ment,  me ^gs^  ^ be 

into  the  ground,  and  neither r the > na ^ ^ brought  over  each  pair  of 

g££  sting  the  wdil“c^y  to  tJ*%&  the  object  distinctly  in  view, 

SO  that  all  errors  of  Pa^^.xt?iay  1 ^^fln^bserver  is  moved  to  either  side  of 
This  error  £*&**%* telescope  in  which  the  foci  of  the  object  and 
the  center  of  1£e  <7^®°®  Brlciselfupon  the  cross-wires  and  object;  m such 
eyeglasses  are  not  brought  precisely  up  surface,  and  the  observation 

a case  the  wires  will  appear  to n»Te  5™ Les  the  wires  and  object  should  be 
will  be  liable  to  inaccuracy.  spider  lines  will  appear  to  be  fastened 

brought  toto  view  so  i^rfe^y  that  the £P to™  hoWever  the  eye  is  moved 
to  the  surface,  and  will  lernain  m i n fi  ly  set  in  the  tripod  head  as 
If  the  socket  of  the  11  s rument ■becomes  so  nrmij  e shoufd  place  the 
to  be  difficult .of  remove tor l the ^ binary  way  toe  e „ aud  a 

^eS  u"^  ^ to  the  blr,  Scire  also  to  hold  his  hands  so  as  to 

grasp  it  the  moment  it  is  free.  carefully  made  and  vertical  angles 

Field  Work.  If  the  survey  has  heen  camuiiy  ^ ^ where  extreme 
taken  at  every  sight,  leveling  will  oe  nece  * In  most  cases  of 

accuracy  in  regard  to “eta^ng  thickness  of  strata, 
practical  work  at  ^ide  rpad  etc.,  the  elevations  calculated  by  the 

general  rise  or  fall  of j an  made  roa . , - Qugh,  but  there  are  frequently 
use  of  the  vertical  angle  will  be  close  e g g^ccegs  in  certAin  work.  In 
instances  when  leveling ; must  ^donet  transit  telescope  is  supplied 

ihs  note  book  ruled,  the  levelman  » 

ready  to  proceed  with  the  work. 


FIELD  WORK. 


55 


The  rodman  holds  the  rod  on  the  starting  point,  the  elevation  of  which  is 
either  known  or  assumed.  The  levelman  sets  up  his  instrument  somewhere 
in  the  direction  in  which  he  is  going,  but  not  necessarily,  or  usually,  in  the 
precise  line.  He  then  sights  to  the  rod  and  notes  the  reading  as  a backsight 
or  +■  (plus)  sight,  entering  it  in  the  proper  column  of  his  note  book,  and 
adding  it  to  the  elevation  of  the  starting  point  as  the  “ height  of  instrument.” 
The  rodman  then  goes  ahead  about  the  same  distance,  sets  his  rod  on  some 
well  defined  and  solid  point,  and  the  levelman  sights  again  to  the  target, 
which  the  rodman  moves  up  or  down  the  rod  till  it  is  exactly  bisected  by  the 
horizontal  cross-hair  in  the  telescope,  as  he  did  when  giving  the  backsight. 
This  reading  is  noted  as  a foresight  or  — (minus)  sight.  The  foresight 
subtracted  from  the  height  of  instrument  gives  the  elevation  of  the  second 
station.  The  rodman  holds  this  latter  point,  and  the  levelman  goes  ahead 
any  convenient  distance,  backsights  to  the  rod,  and  proceeds  as  before.  In 
this  case  we  have  assumed  that  levels  are  only  being  taken  between  regular 
stations  or  two  extreme  points. 

If  a number  of  points  in  close  proximity  to  each  other  are  to  be  taken, 
the  rodman,  after  giving  the  backsight,  hoids  his  rod  at  each  point  desired. 
The  readings  of  any  number  in  convenient  sighting  distance  are  taken  and 
recorded  as  foresights,  and  any  descriptive  notes  are  made  in  the  column  of 
remarks.  These  are  each  subtracted  from  the  height  of  instrument,  and  the 
elevation  found  is  noted  in  column  headed  elevation.  After  all  the  inter- 
mediate points  are  taken,  the  rodman  goes  ahead  to  some  well-defined  point, 
which  is  called  a “turning  point”  (T.  P.)  in  the  notes.  The  elevation  of 
this  is  found  and  recorded.  The  rodman  remains  at  this  point  until  the 
levelman  goes  ahead,  sets  up  and  takes  a. backsight.  This  backsight  reading, 
added  to  the  elevation  of  the  turning  point,  gives  a new  height  of  instrument 
from  which  to  subtract  new  foresights,  and  thus  obtain  the  elevation  of  the 
next  set  of  points  sighted  to. 

When  running  levels  over  a long  line,  the  levelman  should  set  frequent 
“bench  marks.”  These  are  any  permanent  well-defined  marks  that  can  be 
readily  found  and  identified  at  any  future  time.  By  leveling  to  them  he  has 
secured  the  elevation  of  points  from  which  to  start  any  subsequent  levels 
that  may  be  necessary.  A good  bench  mark  can  always  be  made  on  the  side 
or  root  of  a large  tree  or  stump  by  chopping  it  away  so  as  to  leave  a wedge- 
shaped  projection  with  the  point  up.  Drive  a nail  in  the  highest  point  of 
this,  to  mark  where  the  rod  was  held,  and  blaze  the  tree  or  stump  above  the 
bench  mark.  In  this  blaze,  either  cut  or  paint  the  number  of  the  bench 
mark,  which  should,  of  course,  correspond  with  the  number  in  the  note 
book.  In  the  mines,  prominent  frogs  or  castings  in  the  main  roads,  if 
permanent,  make  good  bench  marks. 


Level  Notes. 


Station. 

B.  S. 

i 

F.  S. 

H.  Inst. 

Elev. 

Remarks. 

1 

100. 

Assumed  elevation  of  Station  1. 

3.412 

103.412 

2 

4.082 

99.33 

Station  2 of  survev.  See  page 

Vol 

6.791 

96.621 

Sight  taken  to  ground  at  N.  E.  cor. 

John  Smith’s  house. 

3 = T.  P. 

4.862 

98.55 

Station  3 of  survey  noted  above. 

11.698 

110.248 

4 

9.817 

100.431 

Station  4 of  survey  noted  above. 

B.  M.l 

6.311 

103.937 

B.  M.  1 is  on  north  side  of  large 

white  oak. 

5 

6.427 

103.821 

Station  5 of  survey  noted  above. 

In  underground  leveling,  extreme  care  must  be  observed  to  record  the 
algebraic  signs  of  the  readings,  which  show  whether  the  level  rod  was  held 
in  its  usual  position,  indicated  by  a + sign  or  the  absence  of  any  sign,  or 
upside  down,  indicated  by  the  — sign. 

Proof  of  Calculations.— The  calculations  are  proven  by  adding  together 
the  backsights  and  also  the  foresights  taken  to  turning  points  and  last 


56 


UNDERGROUND  SURVEYING. 


station.  Their  difference  equals  the  difference  of  level  between  the  starting 
point  and  last  station.  Thus: 

Foresights.  Backsights. 

4.862  3.412 

61427  11-698 


11.289 


15.110 

11.289 

a 821  = 108.821  — 100.0  or  3.821. 


TRIGONOMETRIC  LEVELING. 

for  the  leveling  of  mine  slopes  and 
pitching  rooms  where  the  Y level  can- 
not be  used  with  any  advantage  or 
accuracy.  By  reading  the  angles  and 
by  checking  the  measurements  a very 
high  degree  of  accuracy  can  be  ob- 
tained in  trigonometric  leveling. 

Case  1.  Assume  the  elevation  of  A 
to  be  100  ft.  A.  T.  With  the  transit  set 
up  over  A and  properly  leveled,  sight 
to  a point  C on  a rod  so  that  B C 
equals  A D.  Measure  the  vertical  angle 

■I  AQ  I Q 

Case  2.  Assume  the  elevation  of 
station  A in  the  -roof  of  a mine  to  be 
100  ft  A.  T.  Then  with  the  transit 
set  up  directly  under  A and  properly 
leveled  sight  to  a point  C upon  the 
plumb-line  suspended  from  the  station 
B,  measure  the  vertical  angle  X,  m- 
dined  distance  D C,  and  roof  distance 
B C From  this,  the  distance  C F — 
n CY  sin  X.  The  elevation  of  B is 
then  found  as  follows:  The  elevation 
of  B = the  elevation  of  A AJJ-t 

diagrams  the  most  complex  modifi- 

cations  can  be  worked  out. 

Trigonometric  Level  Notes. 


Station. 

Vertical  1 
Angle. 

Inclined 

Distance. 

Vertical 

Distance. 

Height  of 
Instrument. 

Roof 

Distance. 

Eleva- 

tion. 

A 

A- B 
B - C 
C -D 
D—  E 

H — h 1 1 

100 

100 

100 

100 

+8.72 

+3.49 

—5.23 

-6.98 

2' 

3' 

4' 

2' 

3' 

2' 

3' 

V 

+100 

109.72 

112/21 

105.98 

98.00 

UNDERGROUND  SURVEYING. 

been  grouped  together  for  convenience  of  reference. 


STATIONS. 


57 


The  Establishment  of  Stations.— As  this  is  the  most  important  duty  of  an 
engineer  in  surface  work,  so  it  takes  the  first  place  in  work  underground,  as 
the  accuracy  of  the  work  depends  on  the  location  of  the  stations,  while  its 
rapidity  depends  on  using  the  fewest  number  consistent  with  completeness. 
It  also  stands  to  reason  that  the  fewer  the  numbe’r  of  stations,  the  fewer  the 
chances  of  error.  In  underground  work,  stations  should  be  located  under 
the  conditions  of  permanence,  freedom  from  destroying  agencies,  and  ease  of 
access.  Temporary  stations  for  a single  sight  need  not  fill  all  these  require- 
ments. We  establish  them  generally  in  the  roof  of  the  mine— less  frequently 
in  the  floor.  In  the  former  case  we  must  establish  a “ center”  before  each 
set-up  of  the  transit,  and  thus  underground  differs  from  surface  work.  The 
first  surveys  were  made  with  lamps  set  on  the  floor,  sighted  to,  and  then  set 
over.  Permanence  was  secured  by  driving  iron  nails  or  tacks  in  the  sills  of 
the  track  or  sets  of  timber.  As  acid  water  soon  destroyed  these,  they  were 
followed  by  copper  tacks  or  brads,  and  all  were  witnessed  by  notches  cut  on 
both  sides  of  the  sill,  as  in  outside  work,  and  by  a vertical  paint  mark  on  the 
solid  wall,  with  the  number  of  the  station.  This  method  is  faulty,  as  the 
tracks  in  crooked  gangways  are  seldom  placed  where  one  can  get  the  longest 
sight,  and,  as  they  are  the  traveling  ways,  the  stations  run  the  chance  of 
being  knocked  out  by  passing  men  or  mules,  and  the  whole  track,  on  a curved 
incline,  is  generally  sprung  by  every  loaded  trip.  As  the  sights  must  be  as 
long  as  carefulness  of  work  will  allow,  we  put  them  generally  in  the  roof,  as 
that  offers  the  greatest  area  for  a choice,  and  is  not  under  foot.  Any  settling 
of  the  roof  so  as  to  affect  the  accuracy  of  the  station  would  be  equally  effect- 
ive in  destroying  the  accuracy  of  a station  in  the  floor.  We  therefore  choose 
places  that  will  be  least  affected  by  subsequent  work,  and  put  the  stations  in 
collars,  lids  or  wedges  of  props,  in  the  props  themselves,  when  they  have 
incline  sufficient  to  allow  the  transit  to  be  set  under  them,  or  in  the  roof 
itself.  Wherever  set,  they  should  not  project  far  from  the  surface,  and  thus 
be  liable  to  be  brushed  away  in  a low  gangway  by  cars  with  topping  higher 
than  usual,  or  knocked  away  by  flying  fragments  from  a shot,  if  near  the 
working  faces.  Top  stations  have  a mark  about  them  to  call  attention  to 
their  location.  It  is  generally  a circle,  unless  there  are  other  corps  at  work 
in  the  same  mine  that  use  the  circle,  and  the  stations  of  the  two  surveys 
would  be  confused  if  marked  alike.  In  this  case  a corps  selects  some  easily 
made  figure,  as  a triangle,  square,  etc.  If  two  surveys  use  the  same  station, 
the  mark  of  the  second  survey  is  placed  around  that  of  the  first,  and  the 
“ Remarks  ” give  “ Station  No.  234  of  L.  & S.  corps,”  etc. 

Kinds  of  Stations. — The  simplest  top  station  is  a shallow  conical  hole,  made 
with  the  point  of  the  foresight  man’s  hatchet,  which  is  dug  into  the  top  rock 
and  rotated,  and  is  called  by  some  a jigger  station.  Corps  using  these  entirely 
have  a jigger  consisting  of  a steel-pointed  extension  rod,  with  an  offset  hold- 
ing a paint  brush.  The  rod  is  long  enough  to  allow  the  point  to  be  driven 
into  the  roof  at  any  height,  and  its  rotation  marks  a circle  with  the  brush, 
which  is  also  used  to  mark  the  number  beside  it.  Centers  are  set  under  such 
stations  and  sights  are  given  by  another  tool— also  called  a jigger.  This  is  an 
extension  rod,  beyond  the  upper  end  of  which  projects  a piece  of  sheet  iron 
shaped  like  an  isosceles  triangle,  with  the  upper  and  smaller  angle  cut  off  so 
as  to  form  an  end  one-quarter  of  an  inch  broad,  and  in  this  end  is  cut  a 
U-shaped  groove. 

The  sights  are  given  and  the  “ centers  ” set  by  putting  the  plummet  cord 
in  this  groove,  and  placing  the  end  in  the  “jigger  hole”  in  the  roof.  The 
cord  must  be  more  than  twice  the  length  of  the  section  of  the  place,  as  it 
must  be  held  in  the  hand,  run  over  the  jigger  notch,  and  hang  vertically  to 
the  plummet,  which  must  come  to  the  floor  when  the  stations  are  set.  The 
rod  and  cord  are  held  in  the  left  hand,  and  the  right  is  free  to  steady  the 
“bob,”  give  sight,  or  set  the  center.  The  advantage  of  this  method  lies  in 
the  quickness  with  which  -the  centers  are  set  and  the  sights  given,  and  the 
ease  with  which  the  highest  stations  are  reached.  The  disadvantages  are 
the  impossibility  of  making  the  jigger  hole  perfectly  conical,  so  that  the  jig- 
ger can  be  set  in  the  same  place  on  two  successive  sights,  and  the  plummet 
cord  will  hang  exactly  in  the  same  place. 

Second.— Common  shingle  nails  are  driven  into  collars,  or  cracks  in  the 
roof.  The  end  of  the  plummet  line  is  noosed  and  put  over  the  head.  This 
causes  an  eccentric  hanging  of  the  plummet  that  may  cause  an  error  in  back- 
sight and  foresight  of  the  width  of  the  nail  head,  which  will  be  quite  appreci- 
able in  a short  sight.  To  do  away  with  this  error,  a variety  of  nails  ( called  spads , 
spuds , etc.)  are  made  of  iron  or  copper.  Iron  will  not  corrode  in  dry  mines, 


58 


UNDERGRO  UND  S UR  VE YING. 


k rrmoli  cheaper  The  simplest  is  made  by  hammering  out  the  head  of  a 
horsesSe  or  mule^shoe  nail,  punching  a hole  in  the  flattened  head  for  insert- 
ing the  cord  and  cutting  off  the  point,  so  as  to  make  the  finished  spad  an 
inch  Ion0-  This  will  bring,  the  head  near  the  surface  without  having  to  drill 
toodeena  hole  and  will  make  them  unfit  for  lamp  picks  as  they  are  very 
handv  for  such  purposes,  and  thousands  have  been  pulled  out  to  this  end. 
Anv  blacksmith  can  furnish  them  for  less  than  1 cent  each.  They  are 
driven  broadside  to  the  line  of  sight,  or  they  will  be  liable  to  the  same  objec- 
tion as  the  shingle  nail.  To  remove  all  chance  of  eccentricity,  a form  is 
made  with  a shoulder  in  which  a hole  is  drilled  parallel  to  the  length  of  the 
nail  The  practice  of  using  staples  for  stations  is  antiquated  though  gi\  en 
iii  the  last  editions  of  soml  modern  textbooks-and  should  never  be  used 

wh^,adC^In : SSta  Of  spads  are  driven  into  a crack  of  the  roof;  but 
such  stations  cannot  be  called  permanent , as  the  same  force  that  made  the 
crack  will  tend  to  open  it  and  let  the  nail  drop.  Even  if  this  does  not  hap- 
pen we  shall  have  the  water  in  a wet  mine  coming  in  by  these  cracks,  and 
rotting6 the  nails,  or  the  rock  at  the  sides  of  the  crack,  and  m a month  after 
tVip  nlnoixiff  of  tli6  st&tion.  it  will  b6  unfit  for  usg*  . , 

Fourth -Into  a hole  drilled  in  the  roof,  a wooden  plug  is  driven,  and  into 
thiswe  drive  the  spad.  The  swelling  wood  clamps  the  same  and  prevents 
i ccnfong  out  as  readily  as  it  was  put  in.  The  plugs  are  made  of  well-dried 
and  are  carried  bv  the  man  that  sets  the  stations.  The  first 
holes  were  made  by  a jumper,  and  the  plugs  were  2 in.  square  and  6 m.  long. 
The  modern  holes  are  usually  made  by  a fn 


will  do  the  work  without  bendin 
slates  or  clays;  but  an  ordinary 


atthe  shank.  Such  drills  can  be  used  in 
„rill  and  hammer  must  be  used  in  harder 

U1w^  fhe  roof  is  too  poOT  to  hJld  them.  Such  stations  should  be  checked  in 
they  are  used,  if  we  wish  to  swear  to  the  accuracy 

in  the  qu^ndary^of  tl^man^vhose^^mpanyi worked  ac^ossthSr  liSe  beSuse 

wood  shoepeg  is  ci  . d A corq  wm  Soon  rot,  and,  if  m the 

plummet  is  tied  to  the  lower  for  whip  lashes,  while  the  wire  is 

S5r!Te™anSi!  bu?fven  this  will  be  pulled  out  by  catching  in  the  topping 

0f  spads  is  dispensed  with,  and  all  the  stations  put  in  rock 

Lastly.  a twist  drill  makes  a vertical  hole  1 m.  deep, 

roof  where  poss  b . ♦ ta^en  the  foresight  man  puts  a steel  clip  with 

Int°  h^?es  Thf  is  made  by  bending  upon  itself  a thin  piece  of  steel 
serrated  edges.  This  is  mane  d to|ether  it  wm  go  into  the  hole,  and 

& in.  wide.  -When the senas  are  ^esse^  -js  hold  the  clip  in  the  hole  so  that 
the  spring  of  the  sides  the  ® through  a hole  in  the  center  of  the 

it  is  hard  to  pul]  out  oord^passes  tnmi *gua_no  matter  how  the  clip 

bend  and  is,  ^ d pressing  together  the  ends  of  the  clip.  This  is 

is  inserted.  ]t remov  ea  uy  p |in|  as  there  is  no  eyehole  to  be  freed 

the  easiest  and  Q nc]e.sVaLd  ld  untied  The  hangingof  the  plummet 
from  dirt  and  no  knot  to  be  tied  and  manea.  fn  a|  long  asF  the  roof 

takes  a fraction  of !a ^^naVthe  pXng  of  the  holes  inclined  .to  the 

vcTc  Jbyl  careleS mamand  the  many  roofs  that  are  unfit  for  pierc.ng 

with  a twist  drill  ho,l]d  have  some  regular  way  pf  witnessing  our 

Marking  St  • vertical  line  on  the  rib  calls  attention  to  a station  m 
stations.  I"  general,  ^vert  o f station  has  the  mark  around  it.  as  has 

the  floor  newthe  sirte  marKea.  * jc  fl  e If  three  regular  corps  are 
been  described  a^it  ^s  som  g the  same  mines,  as  the  company 

engaged  m the  ^“.tgi^ividual  operator,  and  the  private  corps  that  is 
corps,  the : corps i of : the  nm  p of  the  land  owners,  they  must  use 

The  most  common  are  the  circle,  square,  and 


STATIONS. 


59 


triangle.  If  the  “ circle  ” corps  puts  in  the  station,  it  has  a circle  about  it. 
The  next  corps  uses  it  and  puts  a square  about  it  and  notes  “ Sta.  472  = to 
Sta.  742  of  ( ) Corps.”  The  third  corps  uses  it  and  puts  a triangle  about 
the  square,  and  notes  “ Sta.  617  = to  Sta.  472  of  ( ) Corps,  and  Sta.  742  of  ( ) 

Corps*.”  If  the  first  corps  uses  the  station  again,  it  notes  the  numbers  given 
by  the  two  other  corps,  and  these  three  numbers  will  aid  in  identifying  it  if 
one  or  two  of  the  numbers  are  lost. 

Distinguishing  Stations.— Each  station  must  be  lettered  or  numbered  so  that 
it  can  be  readily  recognized  when  the  subsequent  surveys  are  made.  When 
set  it  may  have  been^at  the  end  of  a gangway,  while  six  months  later 
the  gangway  has  been  "driven  hundreds  of  feet  from  that  place,  chambers 
have  been  turned  off  in  what  was  solid,  and  the  place  be  so  utterly  unlike 
its  former  state  that  nothing  but  a fixed  mark  belonging  to  that  station 
alone  will  enable  us  to  recognize  it.  The  methods  of  distinguishing  stations 
vary  widely.  In  one  place  the  writer  found  that  each  gangway  and  room 
had  a Station  1 at  its  beginning,  and  the  various  stations  numbered  1 were 
designated  “ Grog  Run  1,  2,  3,  etc.”;  “ Pat  James  Gangway  1,  2,  etc.”;  and  so 
on  through  the  map,  that  showed  between  fifty  and  one  hundred  stations 
numbered  1,  so  that  a new  engineer  would  have  had  to  learn  the  mine 
thoroughly  before  he  could  extend  a survey.  Another  way  is  to  use  Al, 
A2,  etc.,  up  to  A100,  and  so  through  the  alphabet  to  avoid  running  up  too  high 
in  numbers.  A third  was  lettering  the  various  sections  of  the  mine  A,  B, 
C,  etc.,  and  the  numbers  begin  with  1 in  each  and  run  up  indefinitely. 

All  of  the  above  have  disadvantages,  as  powder  or  lamp  smoke,  mud, 
mold,  or  the  misplaced  ingenuity  of  small  boys  may  so  obliterate  or  obscure 
a mark  that  it  will  be  recognized  only  by  association  with  its  immediate 
neighbors,  and  these  may  have  shared  the  same  fate.  You  may  have  only  a 
part  of  the  mine  map  with  you,  and  because  the  system  of  marking  strives  to 
get  along  with  as  few  symbols  as  possible,  you  have  to  go  to  the  office,  when 
there  would  have  been  a chance  of  deciphering  the  mark  if  there  had  been 
a number  of  figures  to  it.  The  best  practice,  therefore,  courts  large  numbers, 
begins  with  Station  0 at  the  mouth  of  the  slope  or  drift,  or  the  foot  of  the 
shaft,  and  numbers  consecutively  in  each  bed.  In  a short  time  three  figures 
are  reached,  while  in  old  mines  the  numbers  require  four  digits.  The 
chances  of  obscuring  such  a mark  are  lessened,  while  the  chances  of  our 
deciphering  it  are  increased. 

Centers.— When  the  station  is  in  the  roof,  there  must  be  something  for  the 
transit  to  set  over,  as  it  is  easier  to  do  so  than  to  set  under  a station,  and  much 
more  accurate  as  instruments  are  now  made.  The  set-up  is  made  over  a 
“ center.”  At  first,  a cross  scratched  on  the  floor  or  on  a loose  piece  of  slate, 
a daub  of  white  lead  on  the  same  with  a small  piece  of  coal  placed  under 
the  point  of  the  plummet — when  that  had  been  steadied— or  finally,  a nail 
driven  into  a block  and  afterwards  pointed,  were  used.  All  of  these,  except 
where  the  mark  was  on  the  solid  floor — if  they  were  large,  enough  co  be 
stable— were  in  the  way  of  the  observer’s  feet,  while,  if  small,  they  were  so 
light  as  to  be  readily  displaced.  It  must  be  noted  here  that  it  is  not  so  much 
the  errors  that  we  can  foresee  and  detect  that  influence  the  accuracy  of  the 
work  in  our  own  eyes,  but  the  chances  of  error  from  accidents  that  we 
cannot  control  and  that  cannot  be  readily  detected.  To  avoid  the  above 
chances,  we  make  the  centers  as  small  and  as  heavy  as  we  can— in  other 
words,  we  make  them  of  lead.  A hole  If  in.  in  diameter  and  i in.  deep  is 
bored  in  a thick  plank,  a brad  is  set  in  its  center  with  the  head  down;  the 
hole  is  filled  with  melted  lead  and  the  brad  is  slightly  raised  to  surround  the 
head  with  lead,  and  held  with  pincers  in  a vertical  position  till  the  lead  has 
set.  The  brad  is  cut  off  I in.  above  the  lead  and  pointed.  This  ’‘center” 
combines  weight  and  small  size,  and  is  generally  used. 

Paint.— White  lead,  or  Dutch  white,  thinned  with  linseed  oil,  is  ordinarily 
used.  It  is  carried  in  a covered  tin  pail  holding  a pint.  The  cover  nas  a 
hole  large  enough  to  admit  the  brush.  The  pail  generally  has  to  be  cleaned 
out  after  each  day’s  work,  as  the  brush  gathers  dirt  every  time  it  is  used.  In 
case  the  paint  is  to  be  kept  for  a number  of  days,  it  must  be  covered  with 
water,  which  can  be  poured  off  before  using.  If  the  ordinary  paint  brush 
has  too  long  bristles,  it  can  be  shortened  and  kept  from  wearing  by  winding 
with  fine  wire  to  the  proper  length.  The  top  should  be  wiped  clean  and 
dry  with  a piece  of  cotton  waste  before  the  paint  is  applied,  or  the  white 
will  be  so  discolored  as  to  be  scarcely  visible,  or  if  the  top  is  dirty  it  will 
flake  off,  and  the  numbers  be  lost. 


60 


SURVEY  NOTES. 


KEEPING  NOTES. 

Taking  Note,— Complete  no^e^shoul<^be^teten^a^d^recor^dneatly^i^ 

Every  ledge  of  rock  should ibe noted , its “a  separate  book  for 
transit  note  s^an'd  for  ^denotes,  andwhere  many  collieries  are  operated,  a 
separate  set  of  books  should  be for  ■ Jgc: ^Sterile' following  things:  The 
However  the  to  check  the  vernfer,  the 

numbers  of  the  stations,  the  MJ1  distance  measured,  either  flat  or  on 

vernier  reading,  the  dip  ot  tne  si  gnu  f the  ground;  the  height  of 

the  dip;  the  height  ot  the  axis  ot _thetramnt  Necessary  remarks  to 

l^eight'of Srumelt),  H.  R-  (hci^hl  of  tod,  or  poml  to  which 

sight  was  taken),  .^^^^starting  a survey,  there  should  he  entered  the 
At  the  top  of  .g  tQ  be  done;  the  names  of 

name  of  the  mme  work  and  those  that  were  taken  from  the 

the  regular  corps  employed  fO“he  wotk,  ai  used.  the  date  of  the  work, 

mine  to  point  out  work  or  assist;  thyn^mmenlsuseo  u e where  such 

and,  in  case  it  he  the  ° Such  hooks  are^complete  records,  and 

work  was  noted  must , oe  set -down  Such  boo«a  eg  Pfg  of  the  kind  of 

Xkdon1ina4seTlawsuit  “quires  Inch  testimony  by  showing  the  number 
of  men,  the  instruments  "^“^hetam«eE^toy of  keeping  these 
Transit  and  Side  Not.es-~Pe^a^^Pthods  arrange  themselves  into  groups, 
an^spec\mens  of  foS^oups  will  be  shown,  as  the  most  common  in  use  m 

the^jsT-The  side  notes  of  each  sight  follow  the  transit  notes  of  that  sight, 
V»v  the  side  notes  in  the  same  hook. 

Y Fourth. — Each  set  of  notes  has  a separate  hook  sets  o£ 

The  last  method  is  *ke  best-^en  “t  X same  time,  such  a method  is 
notes,  and  where two men .do • the ^^^g^ate^et  of  hooks  for  ordinary 
imperative.  Each  mine  should  have  a ftPara"fy;fthe  engineer  reference 
work  and  special  work,  and  |^c  a pract^c  a|d  if  the  party  makes  surveys 
notes  m a portable  form.  Unless  tms  ’ succeedmg  surveys  m any 

in  twenty  different  n^^es^  the  no  f t bQth  must  be  carried.  This 

ssars?a  ssus.ss'." 

looked  up,  and  the -notes  found.  outside  survey  is  secondary  to  the 

The  taking  of  side  nnderiTund  work,  of  ordinary  character,  the 

instrumental  work;  while  m unde  , are  built  the  sjde  notes.  The 

lines  of  the  survey  are r skeletons  upo  hich  ^ the  forms  for  taking  them 
side  notes  are  therefore  of  the^ hi ig  tbe  underground  work,  so  that 

the'mapper* can6 reproduce  themkith fu  11  y even  if  he  may  never  have  been 

inside.  Qnrmose  we  are  setting  up  at  6;  with  backsight  at 

„•  &ht  = ffiP  27'  left;  and  that  the  drstance  b e 

is  421.76  ft.  measured  on  a pitch  ol  + 4 50  . 

First  Form: 


Sta. 


Needle. 
B.  S. 


S 25°  30'  W 


Vernier. 

Needle. 
F.  S. 

Pitch. 

Dist. 

Sta. 

A 

B 

L 85°  27' 

L 85°  26' 

S 60°  0'  E 

+ 4°  35' 

421.76 

c 

FORMS  FOR  NOTES . 


61 


Fig.  1. 


differences  of  level  as  measured 
filled  in  at  the  office,  to  make  the 


This  is  read:  “ Set-up  at  6;  backsight  at  a;  foresight  to  c;  first  reading  of 
vernier  under  A;  second  (check)  reading  under  B;  check  reading  by  needle 
computed  from  foresight  and  backsight  needle,  etc.”  Some  note  the 
readings  of  one  vernier  at  A,  and  the  opposite  one  at  B,  and  take  only 
one  sight.  The  last  column  for  stations  is  sometimes  omitted,  and  the  first 
widened,  so  that  the  three  can  be  entered  as  fol- 
lows: “o-6-c.” 

Second  Form.—' This  differs  from  the  first  in 
having  but  one  column  for  the  venier  reading, 
which  is  not  noted  until  two  readings  agree, 
and  also  in  omitting  the  last  column  for  sta- 
tions, as  noted  above.  In  some  cases  the  line 
is  indicated  by  but  two  stations,  the  one  set  up 
at,  and  the  foresight,  as  in  the  angle  given 
above,  b-c  To  note  the  backsight,  the  previous 
line  is  always  taken,  and  under  “Sta.”  we  put 
“a-5,”  and  the  needle  reading. 

Third  Form. — In  this  case  a continuous  ver- 
nier is  carried  and  the  readings  are  put  in 
the  second  column,  with  the  needle  course  on 
foresights  as  a check  in  the  third.  In  the  column 
for  stationsonly  the  station  at  which  the  set-up 
is  made  is  noted  on  the  line  with  the  readings 
for  that  set-up — the  backsight  going  on  the  pre- 
vious, and  the  foresight  on  the  following,  lines. 

Fourth  Form. — This  is  also  a form  for  record- 
ing a continuous  vernier,  as  well  as  the  deflected 
angle.  The  right-hand  page  is  for  noting 
by  level  or  transit.  Certain  columns  are 

book  complete  as  a reference  in  mapping,  or  in  the  mine.  This  form  is 
advocated  “/or  its  compactness  but  there  is  such  a thing  as  too  much  of 
that  article,  as  there  is  no  room  on  either  page  for  remarks,  while  in  all  the 
other  systems,  the  right-hand  page  is  set  aside  for  this  purpose. 

Fifth  Form.— Where  the  leveling  is  performed  by  the  transit,  and  each 
sight  is  taken  with  that  end  in  view,  the  level  notes  are  added  to  any  form 
of  transit  notes  chosen  and  they  are  recorded  as  shown  in  table  on  page  56. 
These  figures  are  used  to  calculate  the  differences  in  elevation,  as  shown  by 
the  pitch  of  the  sight.  The  minus  signs  show  that  the  points  noted  are 
below  the  stations.  If  the  station  were  in  the 
+5  * floor,  the  sight  would  have  a plus  sign.  A contin- 

uous vernier  can  be  used  with  this  form. 

Forms  for  Side  Notes.— In  every  case  the  notes 
should  convey  to  the  man  that  plots  some  idea  of 
the  form  of  the  place  surveyed.  An  accurate  sketch 
cannot  be  made  unless  the  whole  locality  can  be 
seen  at  a glance— which  is  seldom,  if  ev6r,  the  case— 
and  yet  we  must  not  go  to  the  other  extreme  and 
write  down  the  notes  without  a sketch;  yet  that  is 
what  is  frequently  done,  and  may  be  simply  noted 
+ $/  — 4 6 as  the  first  form,  and  put  aside  as  a faulty  method 

with  no  good  points. 

♦ 72 — 5 7 Second  Form  — In  this,  see  Fig.  1,  as  in  a sketch 

made  as  a person  advances  with  no  definite  idea  of 
the  arrangement  of  the  work,  there  is  too  frequently 
is  a running  of  the  sketch  off  the  page— on  one  side  or 
the  other,  and  a cramping  of  certain  parts.  Insert- 
ing the  figures  on  the  line  of  survey  confuses  the 
;»  one  that  plots  if  the  sketch  is  distorted  or  cramped. 
As  the  hands  of  the  note  man  are  dirty  from  rub- 
bing along  the  tape,  to  find  the  numbers, it  generally 
happens  that  the  sketches  are  smeared  and  blurred 
' so  that  they  are  hard  to  decipher  when  the  notes 

Fig.  2.  are  most  clearly  kept,  and  a method  that  encourages 

cramping,  confusion,  or  obscurity  must  be  rejected. 

Third  Form. — There  is  no  attempt  made  at  sketching  in  this  form,  Fig.  2, 
but  the  red  line  in  the  center  of  the  page  of  the  note  book  is  taken  as  the  line 
of  survey,  and  the  next  parallel  lines  on  either  side  are  taken  as  the  boundaries 
of  the  solid  on  either  side.  The  only  figures  on  each  side  of  the  red  line  are 


O 238  [167. 
+ 157  — 
+ /S? 
+Mo 
4 I/O 


+ 30 
+ 20 


+ 16 — » 5 
+ 14 
0,23  r 


L 


LJ 


:n 


62 


SURVEY  NOTES. 


thP  distances  from  the  line  to  the  solid,  while  the  “pluses”  at  which  they 
were  taken  are  noted  at  the  side  of  the  page,  and  the  exact  distance  betw eei q 
^ two  stations  is  enclosed  in  the  parallelogram.  This  method  at  the 
pluses  155  and  157  calls  attention  to  a point  where ^a^c^ev?r^e 

' cans  & tlmpUla^e^s  to  Sve|e 

32SJ5J&  .5  MX'SK 

corner  as  ttefirst  ortart  ^*X>f  the 

;^«id  tm  thi 

whethe^^ataei^ehe<10^or  100* ftf  dSant.^  onVcan1%™^d”°n™tes^  W 

accurately  taken,  and  two  persons  accurately  plotting  such  notes  will  reach 

th\«^  Notes —These  are  kept  as  in  outside  work,  as  has  been  before  stated 

iilssasssssa 

§gE| gfekSSHSSSs^SE 

proper  degree.  For  rough  measurements,  the  length  of  the  winding  rope 
betBy  on^of  these  ^ mShodsw^lS'cate  a bench  mark  below,  that  is  connected 

ImUon^W^  must1  bear  In  mind  that  roof  stations  are  almost  certain  to 

kn  Whenever  we  begin  a level  survey,  we  must  measure  the  distance  between 
roofand  fkmr'and^e' it  if  agrees  w&  the notes  . U»  differs,  we  must  note 
the  fact  under  the  original  notes,  as  a check  for  future  work. 


STOPE  BOOKS. 

By  Joseph  Barrell.* 

Tn  lare-e  metal  mines,  where  the  veins  are  more  or  less  vertical  and  great 
volumes  of  SI  are Extracted  from  between  the  levels,  it  becomes  important 
to  fldoDt  such  a system  for  recording  the  shape  and  location  of  the  stopes  that 
at  anyPfuture  time  the  engineers  may  he.  able  to  give  precise  information 

coimeming  them,^withou^ente^ng^tt^mine  for^^m  purjms^.^^  means  for 

sketches  Udth  the  transit  work  of  the  drifts  and  also  the  various  Boors  with 
one  another  othetical  map  of  a portion  of  two  levels  Figs.  2, 3,  and  4 
^Ksed^X^okl  rilled %°t\e ^er^nically 

or 


#See  “Mines  and  Minerals,”  OctoDer,  1899,  page  97, 


STOPE  BOOKS. 


63 


fifth  line  to  be  heavier.  Each  square  will  represent  a square  set,  giving  an 
actual  scale  of  about  20  ft.  to  the  inch.  A smaller  scale  does  not  show  enough 
detail,  and  a larger  one  is  not  necessary  for  this  class  of  work. 

The  most  convenient  size  for  the  bound  books  is  11  in.  long  by  5i  in.  wide. 
Only  the  right-hand  leaves  are 
numbered,  so  that  when  open 
a page  extends  entirely  across 
the  book,  20  in.,  showing  400  ft. 
of  the  length  of  the  vein  and 
wide  enough  for  two  floors  on 
one  page.  The  floors  imme- 
diately above  each  other  must 
follow  on  consecutive  pages; 
thus,  on  the  first  double  page 
will  be  400  ft.  of  the  sill  floor 
and  first  floor,  on  the  second 
page  the  second  and  third 
floors,  and  on  the  seventh  page 
the  twelfth  and  thirteenth 
floors.  The  eighth  page  is 
reserved  for  cross-sections  of 
the  vein,  and  the  ninth  for  the 
long  upright  section,  these  two 
being  shown  by  Figs.  3 and  4. 

The  next  400  ft.  of  the  same 
drift  will  be  shown  on  page  10, 

so  that  it  joins  on  to  page  1 on  one  side  and  to  page  19  on  the  other,  and 
in  this  way  the  work  of  one  level  is  kept  together.  For  convenience,  the 
book  should  be  indexed  by  placing  a projecting  tag  with  the  number  of  the 
level  on  each  page  of  the  drift  floor. 

Having  now  a general  idea  of  the  arrangement  of  the  work  in  the  book,  it 
remains  for  us  to  determine,  precisely,  how  to 
place  it  and  how  to  show  the  relation  to  the 
transit  surveys.  First,  it  is  necessary  to  have 
some  reference  line  on  the  vein.  For  this 
purpose  draw  on  the  map,  through  the  center 
of  the  shaft,  a line  perpendicular  to  the  strike 
of  the  vein,  as  shown  in  Fig.  1.  Scale  off  from 
the  map  the  distance  at  which  it  cuts  the 
transit  course  from  the  nearest  station.  Then, 


by  adding 


the  known  distances  between  sta- 
tions to  this,  we  obtain  the  surveyed  distance 
of  apy  point  on  the  drift  from  our  reference 
line.  Select  the  middle  or  end  of  a page  in 
the  stope  book  for  the  zero  or  reference  line, 
such  that  the  drift  will  go  most  conveniently 
in  the  book,  and  on  the  upper  line  locate  the 
survey  points  at  their  proper  distances  from  it, 
as  in  Fig.  2.  The  vertical  location  of  any  part 
can  be  told  when  the  dimensions  of  the  tim- 
bering are  known.  In  this  instance  the  drift 
is  7 ft.  10  in.  high,  and  each  of  the  following 
12  floors  are  7 ft.  2 in.  If  the  levels  are  exactly 
100  ft.  apart,  the  thirteenth  floor  will  conse- 
quently be  6 ft.  2 in.  in  height. 

The  Stope  Book  in  the  Mine.— Having  indi- 
cated in  the  office,  by  a regular  system,  the 
place  for  everything  that  will  be  found  in  the 
mine,  the  next  step  is  to  proceed  to  the  details 
of  sketching.  The  location  of  the  stations  on 
the  top  line  of  the  drift-floor  pages  shows  on 
what  vertical  line  they  should  lie  in  the 
sketch;  but  the  fact  that  each  square  must 
be  kept  as  representing  a square  set,  and  that 
any  or  all  of  them  may  not  be  exactly  to  our 
scale,  will  cause  the  location  made  in  the  mine  to  vary  slightly  from  that 
made  in  the  office.  Any  such  discrepancy  must  be  taken  upon  the  edge 
ot  the  page.  Therefore,  proceed  to  the  station  nearest  the  center  pf  the  pag© 


64 


UNDERGROUND  SURVEYING. 


and  locate  it  as  nearly  as  possible  under  its  position  at  the  top,  remembering 
tha/t  the  sets  of  timber,  no  matter  how  irregular,  must  be  represented  as 
Snares  Now  walk  along  the  drift,  watching  the  character  of  one  side  at  the 
lino  of  the  floor  sketching  while  walking,  counting  the  sets,  and  indicating 
the  Posts bfdots of  the  plncil.  Check  up  the  number  of  sets  on  each  station 
and  Continue to the  end  of  the  drift.  Sketch  the  other  side  in  coming  back, 

. , Aniinfing  the  sets  a second  time,  from  station  to  station,  a further 
checkyis"d8n^n  the  wort°On  the  ’correctness  of  the  sketches  of  the 

driHa^inVhnihedhthedrilh'clfmb  to  theSr^floor  and  locate  the  set  climbed 
through  the  same  distance  east  or  west  of  the  reference  line  as  °n  the  drift 
belowg  see  Fig  2.  Since  the  chutes  and  manways  will  ordinarily  not  step  off 

PTonnd  floor  against  tke  hanging  wall.  It  is  well  to  start  with  10,  since  then, 

t^cl^e'^^O'^is^^roi^lllan^toat^rtramines^e'Mmbering^nthe  first 
SOOT  On  the  thfrteen*  floor,  in  this  instance,  as  shown  in  Fig.  3,  the  man- 
wav  is  in  row  19  In  such  a manner  each  floor  is  completely  located  with 
reference  to  the  drift  below  and  ultimately  with  the  transit  survey. 

The  ease  and  rapidity  of  the  work  will  depend  on  the  character  of  the 
mine.  Much  is  gained  by  practice,  the  work  ™t  being 

Knt  q ruinsp  for  sketching  being  made  ever>  tittn  or  tenm  sei,  01  wuwevei 
Sere  a Change  in  the  character  of  the  wall.  In  drifts  such  as  are  usually 
~ ® .ppr.™  q nfin  tn  q nm  ft  of  sketching  is  a good  day’s  work.  The  sketch 
Should  be  tekenat^some^  definite  horizon,  and  that  of  the  floor  level  is  best. 
Features  of  constant  recurrence  must  be  represented  by  conventional  signs. 
Features  ot  constant  ^ in  Fi  % c enclosed  by  a square  indicates  a 

chute  passing  through  the  floor;  up  means  a ladder 
up;  M,  a manway  down.  A full  line  indicates  a 
rock  wall,  a broken  line,  lagging;  cross-hatching 
represents  filling;  a dashed-and-dotted  line,  the 
presumed  limit  of  filled  workings,  etc.  It  is  ot 
importance  to  indicate  irregularities  m the  tim- 
bers. If  it  is  a short  set,  write  S within  the  square; 
if  a long  set,  L,  giving  the  length  if  necessary.  If 
there  should  be  an  angle  in  the  timbering  so  that 
there  may  be  a set  more  on  one  side  of  the  dntt 
than  on  the  other,  represent  it  by  a wedge-shaped 
opening,  as  shown,  being  the  appearance  ot  the 
drift  if  it  were  straightened  out.  In  sketching,  it  is 
essential  to  accuracy  that  the  attention  be  held 
to  a few  things  at  a time.  On  reaching  the  top  ot 
the  raise  the  plan  views  are  completed,  each  floor 
having  been  sketched  on  the  way  up.  On  descend- 
ing- turn  to  page  8 and  sketch  the  cross-section  of 
+v»o  rnflmvflv  as  shown  in  Fig.  3.  Each  set  is  still  represented  by  a square, 
althOTgh  the  sets  are  higher  than  wide,  but  since  that  fact  is  known  it  can 

leaThe  stonebook  is  taken  through  the  mine  and  brought  up  to  date  at  the 

monih  the tot  &p Should  have  a notch  cut  in  it  and  the  same  indicated  in 
theTkiKi™„  Section  -The  view  of  the  vein  that  will  he  of  most  general  use, 


Fig.  3. 


THE  LONG  SECTION. 


65 


mine  or  the  office,  but  it  is  a little  better  to  determine  the  limiting  points  in 
the  mine.  The  transit  stations,  chutes,  and  raises  should,  of  course,  be 
located  upon  it  as  common  points  with  the  map,  connecting  the  two.  The 
final  long  section  is  drawn  by  merely  piecing  together  the  several  parts 
from  the  stope  book  and  drawing  them  horizontally  and  vertically  to  the 
same  scale. 

Since  a vein  is  quite  an  irregular  surface,  the  question  arises  as  to  what 
modification  of  a vertical  projection  will  give  the  most  accurate  and  con- 
venient representation  of  it.  That  devised  by  Mr.  A.  A.  Abbott,  of  which 
the  essential  feature  is  the  horizontal  adjustment  space  left  between  the 
levels,  is  shown  in  Fig.  4.  At  our  reference  line,  in  this  case  the  projection 
of  the  shaft  upon  the  vein,  the  zero  points  of  the  levels  are  placed  over  each 
other.  But  owing  to  the  warpings  in  the  vein,  a raise,  such  as  No.  201, 
started,  in  this  case,  40  ft.  east,  will  not  break  through  on  the  similar  point 
of  the  level  above.  The  simplest  way  in  which  to  allow  for  these  discrep- 
ancies is  to  draw  the 
levels  more  than  their 
true  distance  apart  by 
the  width  of  an  adjust- 
ment space,  lay  out 
each  level  at  its  true 
length,  and  draw  the 
raises  perpendicular  to 
them  provided,  of 
course,  that  the  raises 
only  step  off  along  the 
dip  and  not  along  the 
strike.  All  these  fea- 
tures can  be  appreci- 
ated by  studying  Figs. 

1,  2,  3,  and  4 in  con- 
nection with  each 
other.  Lines  corre- 
sponding to  the  height 
are  ruled  on  the  sides 
of  the  drawing,  and 
the  floor  on  which  the 
work  is  being  done  is 
ascertained  by  means 
of  a parallel  ruler. 

Such  a view  approxi- 
mates to  a development 
of  the  vein  horizon- 
tally, but  vertically  to 
a projection , since  the 
vein  is  projected  on  a 
series  of  vertical  planes  passing  through  the  transit  courses.  The  drifts  are 
shown  at  their  true  lengths,  but  the  heights  are  the  vertical  distances  and 
not  the  lengths  up  the  dip. 

The  long  section  will  be  brought  up  to  date  every  3 or  6 months,  and  the 
portions  of  the  veins  extracted  during  the  interval  indicated  by  cross- 
hatching  or  tinting.  In  the  illustration,  the  ore  bodies  are  cross-hatched  to 
bring  them  out  more  clearly,  but  to  do  this  on  the  regular  map  would 
involve  erasures  with  every  extension  in  the  workings.  In1  the  mine,  a 
hard  and  sharp  drafting  pencil  will  be  used,  but  pencil  markings  in  a book 
constantly  in  use  soon  become  faint  and  blurred.  It  is  necessary  to  go 
through  the  book  at  intervals  and  ink  in  everything  with  waterproof  draw- 
ing ink.  Two  colors  can  be  used  with  advantage,  red  for  all  transit  lines 
and  survey  figures,  and  black  for  the  stopes  and  those  symbols  relating  to 
them.  If  there  are  several  splits  to  a vein,  sometimes  worked  together  and 
sometimes  not,  the  work  on  the  different  splits  can  be  readily  distinguished 
on  the  long  section  by  using  red  for  the  hanging-wall  split,  and  blue  for  that 
of  the  foot-wall.  If  old  filling  is  taken  out,  such  as  ore,  as  frequently  hap- 
pens, the  parts  extracted  can  be  cross-hatched  in  red,  and  thus  a record  of 
both  the  first  and  second  extractions  preserved. 

The  value  of  these  methods  over  mere  sketches  made  without  system  lies 
in  their  accuracy.  Where  the  timbering  is  irregular,  the  accuracy  of  the 
results  depends  largely  upon  the  time  and  care  taken  in  the  work. 


66 


UNDERGROUND  SURVEYING. 


MINE  CORPS. 

The  method  of  dividing  the  work  in  an  underground  survey  depends  on 
the  size  of  the  corps.  We  will  therefore  consider  the  work  of  each  man, 
in  order  to  get  the  right  number  for  the  corps.  The  chief  of  the  party 
should  be  where  he  can  do  the  most  good,  and  where  he  can  plan  the 
work  for  his  subordinates.  The  principal  point  ot  the  survey  is  the 
setting1  of  the  stations  so  as  to  do  the  work  thoroughly  with  the  fewest 
set-ups  and  thus  diminish  the  chances  of  error  in  instrumental  work. 
The  chief  should  locate  the  stations  and  add  all  the  necessary  signs 
to  show  how  the  work  is  to  be  done.  The  transitman  should  not 
have  his  attention  distracted  from  his  particular  work  by  questions  as  to 
procedure  He  should  work  untrammeled.  The  chief,  therefore,  should  not 
run  transit.  Upon  this  basis  the  ideal  mine  corps  works,  and  such  a corps 
consists  of  at  least  four,  and  better  five,  men  from  the  office .and  three  from 
the  mine.  It  is  divided  into  two  sections.  The  chief  takes  the  men  supplied 
bv  the  mine— one  or  more  of  whom  are  acquainted  with  the  work  done  since 
the  last  survey— and  locates  the  stations;  the  transitman  follows  with  the 
second  section,  to  measure  angles  and  distances.  By  this  time  the  stations 
are  set  and  the  chief  takes  his  men  after  the  transit  party  and  gets  the  side 
notes  with  a check  measurement  of  the  distances  between  stations. 

Such  a corps  goes  to  the  end  of  the  former  survey  and  identifies  the  last 
two  stations.  The  transitman  prepares  to  set  up  at  the  last,  while  the  chief 
and  partv  goes  as  far  as  he  can  see  the  light  from  the  last  station,  or  to  some 
intermediate  point  from  which  one  or  more  sights  are  to  be  taken.  He  then 
stops  and  sends  a man  along  each  place  where  a sight  must  be  taken,  as  long 
as  their  lights  are  plainly  seen  from  top  to  bottom  where  he  is  standing,  and 
over  this  place  he  marks  a point  for  a station  to  be  inserted,  and  generally 
inserts  it  himself  unless  he  be  pushed  by  work,  and  must  leave  it  for  another 
to  do  when  he  places  a circle  about  the  dot,  places  the  number  at  the  side, 
and  as  many  arrows  as  there  are  new  stations,  the  longer  arrow  generally 
pointing  to  the  sight  to  be  last  taken  and  where  the  transit  is  to 
y s be  set  up  next.  Leaving  a backsight  at  the  point  just  set, 

“ he  sets,  successively,  stations  at  the  points  where  the 

foresight  men  have  stood,  in  the  manner  just  described, 
until  he  has  covered  the  new  work— the  mine  boss  or  some 
intelligent  miner  going  with  him  to  give  him  an  idea  of 
the  “lay  of  the  ground,”  so  that  the  work  can  be  covered 
with  the  fewest  number  of  stations.  Sometimes  the  chief 
takes  the  side  notes  and  measures  the  distances  between 
stations  as  fast  as  they  are  set.  In  a pitching  place,  a circu- 
lar brass  protractor  with  small  plummet  is  hung  at  the 
center  of  a stretched  tape,  to  give  the  angle  at  which  the 
tape  is  held;  this  serves  as  a check  to  the  measurements 
of  the  transit  party,  which  are  taken  as  the  basis  of  the 
work,  and  the  other  measurements  are  solely  as  checks. 

In  flatwork,  both  measurements  should  coincide. 

In  a small  corps,  and  where  time  is  of  little  importance,  the  foresight 
man  puts  in  the  stations  ahead  of  the  transit,  and  while  he  is  so  doing  the 
transitman  takes  the  side  notes.  Sometimes  the  side  notes  are  taken  by  the 
Se  man whill  one  of  the  party  is  taking  the  transit  to  the  next  station 
and  setting  it  up  for  the  next  sight.  There  are  about  as  many  variations 
from  these  two  methods  as  there  are  corps.  . r . 

The  foresiaht  man  should  be  intelligent  and  active,  as  the  amount  of  work 
done  in  a day  depends  on  his  ability  to  keep  ahead  of  the  transitman.  Some  of 
the  latter  are  fast  enough  to  keep  two  foresight  men  on  the  jump.  His  duty 
is  to  set  the  center  for  the  next  set-up  under  the  station,  and  also  place  the 
tripod  if  three  are  used  in  the  work,  to  give  the  sight  and,  in  some  corps,  to 
carry  the  front  end  of  the  tape  and  assist  in  taking  the  distance.  In  some 
corps  he  also  carries  the  bag  with  tools  for  setting  stahons,  so  that  he  gen- 
erally has  a load  that  makes  rapidity  of  movement  difficult  and  anything 
that  will  diminish  the  weight  carried  will  tend  to  quicken  the  work. 

The  raDiditv  with  which  good  work  is  done  varies  considerably,  but  it 
depends  on  the  activity  of  transitman  and  foresightman,  and  a good  corps 
should  have  no  trouble  in  making  twelve  set-ups  an  hour  and  taking 
two  or  three  sights  from  each  set-up  It  vanes  also  with  the  distances 
between  stations.  The  saving  of  time  should  never  be  sought  at  the  expense 
of  accuracy  in  the  work;  it  is  to  be  gained  by  rapidity  of  moving  about,  in 


SURVEYING  METHODS. 


67 


setting  transit,  center,  etc.,  and  in  hanging  plummets  to  give  sight.  The 
foresight  man  and  backsight  man  should  be  in  position  to  give  sight  before 
the  transitman  is  ready,  so  that  he  can  turn  his  instrument  on  one  or  the 
other  and  find  them  in  position.  The  slowest  parties  were  those  that  carried 
empty  powder  kegs  (in  the  days  when  loose  powder  was  allowed  inside) 
for  seats,  and  spent  the  greater  part  of  the  time  sitting  on  them. 

The  backsight  man  has  little  to  do  inside,  and  to  compensate  for  this,  he 
is  the  one  that  cleans  and  oils  the  tape,  gets  out  new  plummet  strings,  and 
sees  that  the  tools  are  ready  for  the  next  work,  as  soon  as  the  corps  gets  to 
the  office. 

The  transitman  cleans  the  transit,  unless  the  corps  has  subordinates  that 
can  be  trusted  with  so  delicate  an  instrument.  The  blackening  from 
sulphureted  hydrogen  is  rubbed  from  the  silvered  surfaces  with  whiting, 
and  the  oil  or  paint  smears  are  removed  with  alcohol.  Alcohol  should  be 
used  instead  of  water  for  cleaning  the  instruments,  and  especially  the  lenses, 
which  are  wiped  with  jewelers’  cotton  or  soft  chamois  skin. 


SURVEYING  METHODS. 

Outside  Surveys.— We  have  spoken  of  the  points  necessary  to  include  in 
the  survey  outside,  and  how  the  base  line  is  established.  It  remains  to  call 
attention  to  several  points  that  must  be  known  before  the  surface  plant  can 
be  protected  from  settling,  from  the  removal  of  the  deposit  below.  The 
exact  location  of  all  buildings,  lakes,  ponds,  rivers,  railroads,  etc.  is  not 
only  necessary  for  the  making  of  a correct  map;  it  is  necessary  for  the 
determination  of  the  amounts  and  location  of  the  beds  that  must  be  left 
untouched  by  the  subsequent  mining.  Here  must  be  mentioned  an  error 
that  generally  governs  the  location  of  the  retaining  pillars  to  support  the 
above  and  prevent  damages  to  themselves  or  to  the  mine.  The  settling  of 
the  ground  would  make  all  bodies  of- water  leak  into  the  mine,  and  also 
destroy  to  a greater  or  less  degree  all  surface  plant,  as  well  as  throw  out  of 
plumb  all  shafts  or  other  openings  for  hoisting,  if  it  did  not  close  them 
entirely.  The  usual  custom  is  to  extend  vertical  planes  through  the  bound- 
ary lines  of  such  objects,  and  leave  untouched  all  parts  of  the  superincum- 
bent beds  embraced  by  those  planes.  This  is  accurate  only  when  the  strata 
are  horizontal  or  vertical,  as  beds  settle  normally  to  the  planes  of  the  strata 
and  not  in  a vertical  line  in  case  the  open  spaces  are  stowed.  If  the  spaces 
are  left  open,  they  are  first  filled  by  falls,  and  then  the  settling  goes  on 
according  to  the  above  rule.  No  cut  is  necessary  to  show  the  method  of 
settling,  and  the  place  where  the  bed  is  to  be  left  untouched  may  be  found 
as  follows:  Draw  a vertical  section  through  the  point  to  be  supported , and  also 
the  underlying  bed  on  the  line  of  the  dip  of  the  bed— the  section  being  accurately 
drawn  to  any  scale.  Draw  through  the  extremities  of  the  object  to  be  supported, 
lines  to  the  bed,  which  will  make  right  angles  with  it.  The  space  included  will 
give  the  dimension  of  the  pillar  measured  along  the  dip  of  the  bed,  and  the 
dimensions  of  the  object  taken  at  right  angles  to  the  first  plane  will  give  the  other 
dimension  of  the  pillar. 

Inside  Surveys.— As  the  beds  of  anthracite  lie  at  all  angles  with  the  hori- 
zontal plane,  the  methods  of  surveying  them  vary  accordingly,  and  can  be 
divided  into  flat  and  pitching  work.  Flat  work  is  where  the  beds  have  so 
slight  a dip  that  the  cars  can  be  drawn  to  the  face  of  the  room,  and  where 
there  is  nothing  to  prevent  a sight  to  that  face  from  the  gangway.  The 
variations  in  the  methods  of  work  in  this  case  depend  on  the  accuracy  with 
which  the  work  must  be  performed,  as,  in  some  cases,  the  workings  are 
approaching  the  boundary  line  of  the  property,  and  the  sides  of  the  rooms 
must  be  located  accurately.  In  general,  the  rooms  are  driven  at  right  angles 
to  the  gangway,  unless  the  dip  is  too  great  to  haul  a car  to  the  face  on  that 
line,  when  they  are  inclined  to  the  gangway  at  an  acute  angle.  The  width 
of  the  rooms  in  fiat  work  is  generally  uniform  where  the  roof  is  good,  but 
where  the  roof  is  poor  the  entrance  is  harrowed  for  a short  distance  (to  better 
support  the  gangway)  and  then  widened  to  the  full  width,  or  the  whole  is 
driven  to  the  limit  narrow,  and  the  side  is  robbed  when  the  top  is  drawn, 
and  the  whole  room  caves  in.  This  last  must  be  surveyed  before  the  robbing 
begins. 

The  most  accurate  method  of  survey  is  to  run  a line  along  the  gangway 
and  put  a station  at  the  entrance  of  each  room,  whence  a sight  is  taken 
to  the  face.  This  may  be  varied  by  putting  the  stations  at  alternate  rooms 


68 


SURVEYING 


and  measuring  through  the  cross-cuts  to  get  the  thickness  of  the  pillars  of 
the  intermediate  rooms,  or  placing  stations  at  every  third  room  and  measur- 
ing the  thickness  of  pillars  and  width  of  rooms  that  intervene;  or,  finally,  by 
running  out  the  gangway  with  as  few  sights  as  possible  and  paying  no  atten- 
tion to  the  positions  of  the  rooms  in  setting  stations,  thence  up  to  the  last 
room  to  the  face,  and  back  through  the  cross-cuts  nearest  the  face  to  the 
former  work,  where  a tie  is  made.  When  opportunity  offers,  sights  are  made 
from  the  face  of  the  rooms  to  the  stations  in  the  gangway  for  immediate  ties. 
In  case  a gangwav  and  airway  have  been  driven  considerably  ahead  of  the 
rooms,  it  is  always  necessary  to  run  lines  out  each  and  tie  at  the  last  cross- 
cut. This  must  be  done  in  every  case  where  the  gangway  is  approaching  the 
boundary  line,  or  old  workings  that  have  been  abandoned  and  are  full 
of  water!  In  addition  to  this  check  the  miners  must  keep  bore  holes  20  ft. 
ahead  in  the  line  of  the  gangway,  and  every  20  ft.  must  drive  others  from 
the  corners  of  the  heading  at  an  angle  of  30°  with  the  line  of  the  gangway. 
In  this  way  there  will  be  no  danger  of  running  into  “a  house  of  water,  as 

the  Cornish  miners  call  it,  if  the  survey  be  inaccurate. 

Pitching  Work.— When  the  bed  pitches  so  that  a car  cannot  be  run  to  the 
face  and  when  there  is  a good  deal  of  firedamp  in  the  mine,  it  is  generally 
difficult  to  see  from  the  gangway  to  the  face,  where  the  roof  is  good  and  the 
room  straight,  as  a buggy  track  or  chute,  or  both— when  the  pitch  is  slight 
fill  up  the  room,  and,  where  the  pitch  is  great,  the  gangway  pillars  generally 
run  across  the  face,  or  there  is  a “battery”  shutting  off  the  bottom  of  the 
room  so  that  the  face  can  be  reached  only  by  several  sights.  Where  the 
roof  is  poor,  the  obstructions  are  increased,  as  the  rooms  are  driven  narrower 
or  if  wide,  have  center  props  and  stowing  m the  center.  If  the  coal  is  full  of 
slate  or  if  the  partings  are  thick,  a large  part  of  the  room  is  taken  up  with 
piles’ of  “ gob,”  and  with  a very  poor  roof  the  body  of  the  room  that  has  been 
worked  out  is  filled  with  the  fallen  roof,  and  the  coal  sent  out  through  the 
triangular  man  wavs,  where  it  is  almost  impossible  to  take  a sight.  ^ 

Work  of  this  kind  is  surveyed  by  lines  out  gangway  and  back  through  the 
faces  of  the  rooms  which  are  generally  clear,  even  if  the  bodies  of  the  rooms 
Se  filled  with  the  fallen  top.  Where  chance  favors  sights  are  taken  to  the 
aangwav;  but  this  very  seldom  happens,  as  the  two  lines  are  as  effectually 
seoarated  as  if  in  different  mines.  From  the  stations  in  the  faces,  lines  are 
run  down  the  rooms  as  far  as  possible  to  get  their  direction  and  to  locate 
the  cross-cuts  The  very  worst  case  of  all  is  where  two  l^eds  are  separated 
hv  a thin  nartina  of  rock  and  the  gangway  is  driven  in  the  lower  one  alone, 
roomr in ^ the  upper  one  being  worked  by  rock  chutes  into  the  rooms 
below,  or  into  the  chutes  from  those  rooms.  This  °f  work  is  hard  o 
ventilate  and  to  survev  where  the  rooms  above  are  ventilated  by  the  air 
lystem  ohhe  lower  beds;  but  is  readily  mapped  where  there  is  an  air  system 

f°rniosLbIurvev.s,-To  diminish  the  chance  of  error  and  to  furnish  a ready 
check  the  survey  must  be  closed  upon  itself  or  some  part  of  a former  surye> 
withe^ryuvllvenew  stations.  With  good  work the  error close 
Should  not  exceed  1',  and  the  error  m position  shouMbe  ^ectffied  bv 
Errors  must  not  be  “balanced  they  must  be  detect® d a id  rectified  Dy 
running  the  line  again,  if  they  are  not  readily  sejen  *0™  must  be 

given.  If  an  incorrect  survey  be  balanced,  each  su^doeot  one  m 
altered  to  fit  this ‘incorrect  work,  though  it  may  aI^hecf 

never  know  where  our  work  really  stands.  It  well,  tbeT^^ 
the  work  in  arc  as  soon  as  we  make  a close  and  before  the  party  leaves  me 
place,  as  it  is  easy  to  rerun  the  work  then. 


CONNECTING  OUTSIDE  AND 


INSIDE  WORK  THROUGH  SHAFTS  AND 

SLOPES. 


As  the  dip  of  the  bed  increases,  it  is  less  easy  to  make  % connection  and 
the  chances  of  accuracy  diminish.  In  a survey,  B.  ^0^-^”ftfcaneu)ar 

locates  the  station  with  regard  to  former  work  The  greatest  angular 

accuracy  for  a given  value  of  R is  where  T er^.  ffn^  — O and  ^ cosine 
Angle.  As  the  pitch  or  vertical  angle  of  sight  increases,  the  above  cosine 

diminishes  until,  at  a vertical  sight,  R.  Cos.  vert.. Anflko~+[u n mi difficulty 
In  the  case  of  an  adit  level,  or  a slope  of  less  than  45  , there ^ no  diffic  y 
bevond  the  want  of  absolute  rigidity  m setting  up  the  transit,  and  the 
danger  of  moving  it  in  going  about  it.  The  difficulty  increases  mo  e p > 


SHAFTS  AND  SLOPES. 


69 


than  does  the  pitch,  and  as  R.  Cos.  Vert.  Ang.  diminishes,  though  R be  fixed, 
the  chances  of  error  increase.  When  the  slope  reaches  60°  there  is  an 
impracticability  in  running  a line  down  a slone,  as  the  lme  of  collimation  of 
the  telescope  strikes,  the  graduated  limb  of  the  instrument.  We  can  use 
a prismatic  eyepiece  and  see  up  the  slope;  but  cannot  look  down.  As  we 
have  assumed  that  it  is  unnecessary  to  use  an  additional  telescope,  we  shall 
have  to  run  the  line  by  intermediates.  Set  up  at  the  bottom  of  the  slope 
where  the  longest  sight  up  the  same  can  be  secured  and  backsight  on  a 
station  of  the  underground  work;  or  set  a backsight  for  the  occasion  (both 
stations  will  afterward  be  connected  with  the  work  below).  With  the 
prismatic  eyepiece,  sight  up  the  slope  on  a line  that  will  give  the  longest 
sight  and,  at  the  same  time,  afford  a good  intermediate  place  to  set  up 
the  transit,  as,  on  a pitch  of  60°  or  more,  it  is  absolutely  necessary  that  the 
legs  of  the  transit  should  be  set  solidly  (in  holes  in  the  floor,  or  between  the 
sills  of  the  track)  so  that  they  will  not  be  moved  by  subsequent  walking 
about  it.  By  this  method,  all  the  sights  will  be  taken  from  one  side  alone, 
and  the  tripod  legs  can  be  shortened  to  make  the  sight  possible  without 
building  a standing  place— if  the  man  be  short-legged. 

Call  this  station  A;  at  the  foot  of  the  slope  locate  B,  where  the  transit  can 
be  readily  set  up,  and  as  far  up  the  slope  as  we  can  see  (this  distance  must  be 
at  least  100  ft. ),  and  in  a continuation  of  A B,  locate  C.  Set  up  at  B and  take 
foresight  to  C\  locate  D under  the  same  conditions  that  governed  the  placing 
of  B,  and,  in  a continuation  of  the  line  B D,  place  E.  Set  up  at  with 
foresight  at  E,  and  locate  F and  G as  before.  The  survey  is  carried  by  the 
intermediates  B,  D,  F,  etc.,  to  the  top,  by  a series  of  foresights  to  C,  E,  G,  etc. 

Shafts.— The  term  shaft  in  American  coal-mining  practice  is  applied  only 
to  vertical  openings,  though  in  metal  mining,  both  in  this  country  and 
abroad,  it  is  also  applied  to  highly  inclined  slopes.  For  such  shafts,  most  of 
the  methods  given  in  the  textbooks  are  worthless,  as  they  are  for  transit 
work  and  R.  Cos.  Vert.  Ang.  in  rare  cases  may  be  as  great  as  20  ft.,  while  R 
varies  from  100  to  1,500  ft.  Again,  to  sight  down  a shaft  necessitates  the 
erection  of  a temporary  (and  therefore  more  or  less  unsteady)  support  for 
the  tripod  of  the  transit,  and  the  chances  of  variation  in  its  position  as  we 
stand  on  different  sides  of  it  are  so  great  that  we  cannot  feel  sure  that  a 
movement  has  not  taken  place  that  will  vitiate  the  work. 

In  sighting  up  a shaft  of  greater  depth  than  100  ft.,  there  is  annoyance— if 
not  danger — from  dripping  water  or  the  fall  of  more  solid  substances.  In  a 
wet  shaft  the  object  glass  is  instantly  covered  with  water,  and  a sight  is 
impossible.  We  must  also  have  a platform  to  stand  upon,  and  we  cannot 
feel  sure  that  this  will  be  perfectly  rigid.  From  all  these  considerations  the 
methods  with  a transit  are  never  used  by  engineers  in  the  anthracite  regions, 
and  the  connections  are  made  as  follows: 

When  the  bottom  of  the  shaft  can  be  reached  by  an  adit  or  slope  in  a 
roundabout  route  of  such  length  as  to  render  errors  in  measurement  of  dis- 
tance of  great  importance,  the  angles  are  carried  by  a transit  with  as  long 
sights  as  possible,  and  no  distances  are  measured,  from  a point  on  the  surface 
in  the  shaft  to  a point  vertically  below  it  in  the  mine.  Sometimes  the  guide 
of  the  cage  is  taken  when  it  has  been  recently  set,  as  the  guides  are  plumbed 
into  position;  but  the  better  way  is  to  suspend  an  iron  plummet  by  a copper 
wire:  sink  the  former  in  a barrel  of  water  so  as  to  lessen  the  tendency  to 
swing  on  account  of  the  pull  upon  the  “ bob  ” and  wires  from  the  air-cur- 
rents, or  falling  drops  in  a wet  shaft.  The  top  of  the  barrel  is  covered  with 
two  pieces  of  plank  with  a semicircular  groove  of  3 in.  radius  cut  out  of  the 
middle  for  the  passage  of  the  wire,  to  catch  the  substances  whose  fall  upon 
the  water  would  cause  waves.  The  heavier  the  plummet  and  the  lighter 
the  wire,  the  less  the  tendency  to  swing.  This  wire  can  be  sighted  at  by 
parties  above  and  below  at  the  same  time,  and  the  swing  can  be  bisected 
to  get  the  position  of  the  wire.  A number  of  sights  that  agree  can  be  taken 
as  accurate. 

When  the  shaft  is  the  only  way  to  get  below  from  above,  it  must  be 
plumbed  with  two  or  more  wires  suspended  as  just  described.  With  two 
wires,  they  are  so  hung  that  an  instrument  can  be  set  up  below  in  a line 
passing  through  them  produced,  and  at  a sufficient  distance  from  them  to 
insure  an  accurate  sight;  with  more  wires,  the  station  below  can  be  located 
at  any  point  whence  all  the  wires  can  be  seen. 

Case  1. — Two  wires  are  used,  which  are  located  as  far  apart  as  possible. 
Two  pieces  of  scantling  c d and  ef,  Fig.  1,  are  spiked  across  the  opposite  corners 
of  two  compartments  of  a shaft  to  allow  the  cages  to  pass  up  and  down 


70 


SURVEYING. 


e<cc 


Fig.  1. 


without  interference.  The  station  X is  (roughly)  located  in  a line  through 
the  corners  x,  x and  is  connected  with  the  outside  survey.  From  this  station 
locate  in  the  line  Jm  two  spads  for  holding  the  wires  of  the  plumh-bobs 
These  are  driven  up  to  the  head  in  the  scantlings  m such  a way  that  the  line 
of  sight  passes  through  the  center  of  the  holes  m their  heads.  M.easure  the 
distance^  Xa  and  a b This  completes  the  work  of  the  survey  aboveground. 

The  light  copper  wire  is  rolled  upon  a 
reel,  and  one  end  is  fastened  to  a light 
plumb-bob  to  keep  it  free  from  coils  or 
kinks  in  descending.  It  can  thus  be 
readily  lowered  without  accident. 
When  at  the  bottom,  the  upper  end 
is  fastened  in  the  spad  and  the  heavy 
“bob”  applied  to  the  bottom  and 
placed  in  the  empty  barrel.  The  cages 
are  then  run  slowly  up  and  down, 
with  an  observer  on  each  to  see  that  the  wires  hang  free  from  top  to  bot- 
tom By  this  time  the  wire  will  have  stretched  so  that  it  will  be  straight, 
and  if  there  be  any  slack,  it  is  taken  up,  the  barrel  is  filled  with  water,  and 
+he  top  boards  put  in  piace.  As  a last  check,  measure  the  distance  between 
the  wires  below  and  see  if  it  agrees  with  the  distance  above. 

Lining  inbelow  a point  Fon  the  line  a &,  make,  a hole  in  the  roof  two 
inches  in  diameter,  and  drive  in  a broad  plug.  Setting  up  transit  under 
Y we  sight  at  the  wires  a and  b alternately..  A number  of  methods  for  illumi- 
nating the  wires  have  been  used,  and  are  given  in  textbooks.  The  writer  has 
always  found  those  depending  on  a sight  of  the  wire  across  the  flame  of  a 
lamp  the  hardest  to  obtain,  and  concludes  from  experience  that  the  method 
of  illuminating  the  wires  for  mine  surveying  is  the  best  for  this  also.  A large 
white  target  is  placed  behind  both  wires  and  illuminated  by  a large  lamp 
with  a reflector  behind  it.  The  wire  stands  out  black  against  it  and  can  be 
followed  across  the  target.  As  there  is  considerable  distance  between  the 
wires  and  as  the  transit  is  comparatively  near  them,  there  will  be  small 
chauce  of  getting  a sight  of  one,  when  the  telescope  is  focused  upon  the 
other  aid  fo  the  focus  has  to  be  set  between  them.  This  gives  a hazy  sight 
at  each  but  both  are  shown  against  the  white  background. m strong  relief. 
After  the  transit  head  is  shifted  so  that  the  lipe  of  sight  coincides.  aPPr°-p- 
mately  with  both,  focus  upon  them  alternately  and  see  if  the  line  the 

swing  of  each.  If  so,  the  work  is  done;  if  not,  the  shifting  of  the  transit 
headgmu  st  follow  till  the  end  is  attained.  It  frequently  requires  two  or  more 
hours  of  steady  observation  to  complete  the  work,  and,  when  it  seems  as  if 
the  proper  point  were  secured,  one  of  the  wires  will  show  by  its  swaying  that 
it  has  been  deflected  from  the  vertical  by  a peculiar  slant  of  wind,  and  the 
result  obtained  must  be  checked  again.  When  you  are  through  there  is  no 
absolute  certainty  that  the  point  you  have  marked  is  m the  accurate 
extension  of  the  line  ab  at  the  surface.  Having  decided  on  the  proper  place, 
vou  drive  a spad  into  the  plug  overhead;  hang  a plumb-bob  to  it,  and  see  if 
it  be  over  the  axis  of  the  transit,  as  shown  by  the  screw  on  the  telescope.  If 
not  drive  the  spad  so  that  the  point  of  the  bob  does  so  hang,  and  the  station 
F is  said  to  be  in  the  line  a b.  Measure  Ya  and  the  angles  to  any  station  of 
the  underground  survey;  the  line  a b is  connected  with  the  surveys  at  day- 
light and  below,  and  the  plumb-bobs  may  be  removed.  . 

Criticism  of  the  Above  Method.-l.  As  has  been  stated  there  is  no  absolute 
certainty  that  the  point  Y is  in  the  line  a b prolonged,  and  this  want  of 
eertaintv  should  not  exist  in  so  important  a measurement. 

2 The  work  must  be  performed  by  daylight,  and  the  length  of  time 
neeessarv  to  complete  it  makes  it  impossible  to  work  the  shaft  for  at  least 
half  a day,  and  may  cause  annoyance  to  the  operators  or  if  you  working 
for  a lessee,  lead  them  to  refuse  to  let  you  have  the  use  of  the  shaft  at  tne 

“TTma^beha^d  ^obtafnhong  sight  below  on  any  .line  running 
through  the  larger  axis  of  the  shaft.  Any  shorter  line  would  give  too  shorta 
base  line  and  would  increase  the  chances  of  error.  To  avoid  these,  another 

meCA°SE  S2  — Fi g11™  sho ws* the  top  set  of  timbers  in  a shaft  of  two  hoisting 

compartments  down  which  it  is  desired  to  carry  a known  course  or  mend- 
fa™ on  the  surface  to  the  entry  below.  First  find  out  which  side  of  the 
shaft  is  best  adapted  for  setting  up  the  transit,  as  the  point  to  be  marked  m 
the  mines  will  be  vertically  under  the  point  on  the  surface;  consequently. 


SHAFTS  AND  SLOPES, 


71 


NORTH 


the  side  with  the  widest  opening  leading  from  the  foot  of  the  shaft  should 
1)6  selected 

Having  carried  the  meridian  to  a convenient  point  near  the  top  of  the 
shaft,  and  having  found  that  the  south  side  of  the  shaft  is  the  most  accessi- 
ble, determine,  with  an  ordinary  string,  the  location  of  the  point  A,  from 
which  the  hangers  for  the  plumb-lines  wil  be  exactly  located  by  means  ot 
the  transit.  Now  mark  with  chalk  on 
the  timbers  where  the  strings  cross. 

These  marks,  though  not  accurate, 
serve  as  guides  in  setting  the  hangers. 

Make  a permanent  station  at  the  point 
A and  carry  the  meridian  to  it. 

The  hangers  can  be  made  of  strap 
iron,  \ in.  thick  by  2 in.  wide,  and  at 
least  16  in.  long.  In  one  end  of  the 
iron,  have  a jaw  with  a fine  cut  at  the 
apex,  or  a drill  hole  just  large  enough 
to  contain  the  wire  to  be  used  for 
plumbing.  There  should  be  two  or 
three  countersunk  holes  in  the  hanger, 
through  which  to  fasten  it  to  the  tim 
bers  by  means  of  heavy  wire  nails  A 
top  view  of  the  hanger  is  shown  m 
Fig.  2. 

In  most  shafts  there  is  a space  from 
2 to  4 in.  wide  between  the  ends  of 
the  cage  and  the  sides  of  the  timbers;  i A . 

and  in  order  to  hoist  and  lower  the  cage  to  see  that  the  wires  are  hanging 
freely,  it  is  best  to  set  the  hangers  in  such  a position  on  the  timbers  that 
the  wires  will  hang  in  the  middle  of  the  space. 

Fasten  the  hangers  permanently  over  the  chalk  marks  previously  maae 
on  the  north  side  of  the  shaft,  wuth  the  jaws  pointing  toward  A,  and  on  the 
south  side  of  the  shaft  the  outer  end  of  the  hanger  may  be  fastened 
temporarily. 

Now  set  the  transit  over  the  station  at  A,  take  the  backsight,  foresight  on 
the  wire  hole  of  the  hanger  C and  set  the  wire  hole  of  the  hanger  B on  the 
same  line.  Record  this  course  and  foresight  on  the  wire  hole  of  tne  hanger 
E fixing  as  before  the  wire  hole  of  the  hanger  D in  the  same  line.  Record 
this  course,  and  then  the  meridian  to  be  carried  into  the  workings  below  is 
established.  Measure  carefully  and  record  the  distances  A to  B,  A to  G, 
and  B to  C,  the  distances  A to  D A to  E,  and  D to  E , and  finally  the  dis- 
tances B to  D and  C to  E.  The  necessity  of  taking  all  these  measurements  is 
for  the  purpose  of  establishing  a point  at  the  bottom  of  the  shaft  vertically 
below  A,  and  checking  the  work  in  the  office.  , , . ... 

The  transit  party  can  now  descend  to  the  bottom  of  the  shaft,  taking  with 
them  four  buckets  of  oh,  the  weights  or  plumb-bobs  to  be  attaches  to  the 
wire,  and  all  the  surveying  instruments,  leaving  a responsible  party  on  the 
surface  to  handle  the  wires.  Having  arrived  at  the  bottom  ci  the  shatt, 
have  the  cage  hoisted  3 ft.  above  the  landing,  throw  several  planks  across 
the  timbers  on  which  to  set  the  buckets  of  oil,  signal  to  the  man  on  top  to 
lower  a wire  and  to  fasten  it  securely,  passing  it  through  the  wire  hole  ot 
the  hanger;  now  attach  the  plumb-bob  and  adjust  the  wire  to  such  length 
that  when  sustaining  the  full  weight  of  the  plumb-bob.  the  latter  will  not 
touch  the  bottom  of  the  bucket.  Insert  the  weight  in  the  oil,  using  care 
not  to  leave  the  full  weight  on  the  wire  with  a jerk,. but  let  tne  weight 
down  slowly,  so  that  the  wire  receives  the  full  strain  gradually.  Set  the 
three  remaining  wires  in  a similar  way. 

After  the  wires  have  been  hanging  a few  minutes  with  the  weights 
attached,  the  latter  may  move  from  one  side  to  the  other  ot  the  buckets. 
Watch  this  carefully  and  keep  moving  the  buckets  until  all  the  weights 
hang  perfectly  free,  then  leave  everything  alone  until  the  wires  become 
steady.  The  cages  can  now  be  hoisted  and  lowered  for  the  purpose  of 
examining  the  wires  to  see  that  they  hang  free  and  plumb,  care  being 
that  the  cages  are  not  brought  so  close  to  the  landings  as  to  disturb  the 
hangers  at  the  top,  or  the  buckets  at  the  bottom.  . 

To  find  a point  vertically  below  A,  stretch  a string  along  the  wires  B,  C , 
being  careful  not  to  touch  them;  stretch  another  along  the  wires  D,  E\ 
thent  with  a plumb-line,  determine  a point  on  the  bottom  vertically  below 


72 


SURVEYING . 


the  intersection  of  the  strings.  Measure  the  distances  A B,  A D,  B Dy  and 
C E and  compare  them  with  the  corresponding  distances  at  the  top  of  the 
shaft.  If  these  distances  compare  favorably,  the  wires  are,  in  all  probability, 
steady,  and  the  work  of  determining  the  desired  course  with  the  transit 
may  now  be  begun.  _ . , . 

Set  the  transit  up  over  the  point  of  intersection  just  found;  backsight  on 
the  wires  B,  C;  foresight  on  the  wires  D,  E,  and  compare  the  included  angle 
and  the  distances  with  the  corresponding  angle  and  distances  at  the 
surface.  If  these  do  not  correspond,  move  the  transit  in  the  direction 

necessary  to  increase  or  decrease  the  angle 
or  distances,  as  the  case  may  be.  Repeat 
this  operation  until  the  exact  point  verti- 
cally below  A is  determined. 

A simple  device  that  is  of  great  advan- 
tage is  to  have  three  links  from  an  ordinary 

—B  trace  chain  placed  in  the  wires  on  the  side 
toward  the  transit,  and  a few  feet  above 
the  buckets.  This  not  only  enables  the 
wires  to  turn  freely,  but  also  enables  the 
transitman  to  sight  through  one  of  the  links 
to  the  wire  beyond,  whereby  he  can  place 

II  the  transit  in  exact  line  with  the  wires  more 

O ' I easily  than  if  the  links  were  not  there. 

i I Case  3.— Two,  three,  or  four  wires  are 

/ \ I employed.  They  are  secured  and  hung  as 

/ \\  I before,  and  are  located  in  the  angles  of  the 

/ 1\\  J compartments  x,  xf  x,  x,  Fig.  3.  These  are 

/ \ \ connected  with  four  stations  A,  B,  C , D , the 

/ \ \ lines  A B and  C D being  at  right  angles  to 

\ Tll\  one  another  for  convenience  in  the  subse- 

\ icw  aftl  quent  calculation,  and  are  connected  with 

\ I II  /I  I the  outside  survey.  From  A and  B,  taking 

\U/  AB  as  a base  line,  the  points  x,  x , x,  x are 

\ I / located.  The  same  is  repeated  from  C and 

\/  D,  taking  CD  as  a base  line.  We  thus  have 

, four  locations  of  each  wire.  These  are  tab- 

7 '  *  1 * * * * * 7 ulated,  and  any  variations  in  a reading 

must  be  followed  by  a repetition  of  the 
same.  The  mean  of  the  readings  gives  the 
location.  (Subsequently,  the  subject  of  cab 
culating  work  will  be  taken  up.)  It  can  be 
briefly  stated  here  that  the  bearings  of  each 
wire  to  each  of  the  others,  as  referred  to  the 
base  line  of  the  survey,  are  then  calculated 
and  the  distance  between  the  wires  accu- 
rately measured.  This  finishes  the  work  at 
daylight.  , x - 

There  may  be  two  general  types  of 
arrangements  ot  the  bottom  of  the  shaft, 
and  both  arrangements  have  been  sketched 
and  lettered  similarly.  The  first  is  a case 
when  the  shaft  is  arranged  across  the  dip 
of  the  bed,  and  the  second  is  parallel  to  the 
same.  In  both  cases  O and  7 are  taken  as 
far  apart  as  possible,  and  all  the  wires 
x ' x , x , x located  from  each  station  with 
reference  to  the  other.  The  distances  between  the  wires  above  and  below 
are  also  accurately  measured  as  a check.  There  wih  be 
and  7 from  the  four  wires,  and  the  mean  of  these  is  taken  as  the  co rrect  one. 
In  every  case  of  angle  measurement  mentioned,  a senes  of  readmgsofeach 
angle  is  taken  upon  different  parts  of  the  graduated  limb  to  avoid  instru- 
mental errors,  and  the  mean  of  these  taken  as  the  true  reading.  te 

locations  of  0 and  7,  the  course  between  them  as  referred  to  the  mean  base 
line,  is  calculated,  and  07  is  the  base  line  for  the  underground  work  The 
angle  readings  above  and  below  can  be  made  at  the  same  time  with  differ- 
enf  instruments,  and,  in  taking  the  readings  below,  it  is  not  ^essa^to 
wait  for  absolute  quiet  in  the  wires,  as  that  is  seldom  foun^;  f i^th  a 
can  be  bisected  by  the  cross-hair,  and  the  readings  are  duplicated  until  a 


Fig 


SHAFTS  AND  SLOPES 


73 


constant  result  is  secured.  By  this  method  a greater  accuracy  and  speed  is 
obtained,  and  the  angles  below  can  be  accurately  measured,  no  matter  how 
the  shaft  may  be  arranged. 

The  T-Square  Method.*— This  ingenious  method  of  taking  the  line  under- 
ground is  especially  valuable  in  shafts  with  several  small  compartments  or 
in  cramped  places  where  one  cannot  line  in 
with  the  wires. 

The  wires  are  placed  in  separate  com- 
partments and  as  far  apart  as  possible.  The 
apparatus  is  made  by  the  carpenter,  and 
consists  of  a straightedge  and  T squares.  The 
former  is  merely  a planed  pine  board  about 
8 in.  X$  in.  and  a'foot  longer  than  the  distance 
between  the  wires.  It  rests  approximately 
horizontally  on  slats  tacked  across  the  shaft 
for  supports.  It  is  brought  to  about  an  } or 

in.  from  each  wire  and  then  nailed  to  the 
slats  sufficiently  to  prevent  slipping.  One 
man  should  be  at  each  wire.  The  T squares 
are  most  serviceable  if  made  with  a mov- 
able head  clamped  by  a thumbscrew,  and 
of  planed  pine,  about  *2£  in.  X i in.  Except 
in  cramped  quarters,  the  T squares  will  be 
set  at  right  angles,  and  should  be  placed  together  in  clamping  to  insure 
that  each  is  set  at  precisely  the  same  angle. 

Fig.  4 shows  a cramped  position  such  as  sometimes  arises  and  in  which 
the  movable  head  gives  more  latitude  in  working.  After  clamping,  the 
T squares  are  slid  along  the  straightedge  until  close  to  the  wire,  but  not 
touching  it,  and  are  there  clamped  by  a “G”  clamp,  both  "men  working  at  one 
T square.  The  ends  of  the  T squares,  C and  D,  must  be  supported  on 
blocks  so  that  the  T squares  lie  approximately  in  the  same  horizontal  plane; 
Everything  up  to  the  next  step  need  be  only  approximately  and  quickly 
placed,  but  now  the  greatest  care  must  be  exercised  in  measuring  out  equal 
distances,  A C and  B D , from  the  wires.  If  the  wire  vibrates,  determine  the 
middle  of  its  swing  by  a pencil  or  pin.  Hold  a footmark  (not  the  end  of  the 
tape)  opposite  the  wire  on  the  T square,  measure  out  an  even  number  of 
feet,  and  mark  the  point  with  a sharp  pencil,  and  insert  a pin.  This  done 
for  both  wires  gives  us  the  parallelogram  A B D C\  in  which  the  only  essential 
is  that  C D should  be  exactly  parallel  to  A B,  the  line  of  the  wires.  Now  set 
the  transit  over  the  most  convenient  of  the  two  points,  as  D.  To  get  the 
azimuth  of  D C , and,  consequently,  the  line  of  the  wires,  sight  on  a known 
point  E for  a backsight,  and  measure  the  angle  EDC.  Establish  another 
point  as  F , on  the  line  of  the  backsight,  in  order  that  its  course  may  be 
preserved  after  the  instrument  and  T square  are  removed. 

By  this  means  the  closing  angle  at  E may  be  read  after  the  wires  are 
removed  from  the  shaft.  Underground,  the  method 
is  the  same,  except  that  D C is  the  known  course, 
and  is  used  as  the  backsight.  To  give  the  coordinates 
of  the  instrument  at  D with  the  greatest  precision, 
the  angle  ADC  and  the  distance  A D should  be 
HIGS-Siircd 

Surveying  Slopes  or  Inclined  Shafts. — Where  a single 
sight  reaches  from  top  to  bottom  of  the  shaft,  the 
problem  is  simple  enough.  A station  can  be  estab- 
lished on  the  inside  of  the  foot-wall  plate  at  the  collar 
and  others  in  similar  positions  at  each  level.  The 
instrument  set  up  over  any  station  can  command  the 
whole  shaft  and  the  level  opposite. 

Fig.  5.  Where  the  shaft  is  sunk  on  several  dips,  the  survey 

is  a much  more  difficult  matter.  Fig.  5 illustrates 
cases  of  common  occurrence.  The  shaft  may  be  divided  into  sections  like 
A DEB,  which  are  convex  downwards,  and  others  such  as  E B C,  which 
are  concave  downwards.  As  a rule  a set-up  can  be  avoided  at  the  convex 
knuckles  if  desired,  and  need  only  be  made  at  those  that  are  concave. 

Bent  Plumb-Line  Method.— A may  be  invisible  from  B,  but  the  survey  may  be 


• #See  “Mines  and  Minerals,’’  January,  1899,  page  242. 


74 


SURVEYING. 


carried  from  one  point  to  the  other  by  the  ingenious  method  of  the  bent 

^ The  most  complicated  example  which  can  arise  is  shown  in  Fig.  5. 
Establish  a station  at  A,  the  foot- wall  side  of  the  collar,  the  center  point 
being  a small  nail  head  projecting  horizontally.  Attach  a long  plumb-lme 
to  this  and  carry  the  other  end  to  B.  Here  it  will  probably  be  necessary  to 
use  a small  screw-eye,  with  its  head  turned  into  the  vertica 
shaft,  for  the.  center  point.  Pass  the  plumb-line  through  this  and  draw  it 
fairly  tight.  Now  attach  a plumb-bob  at  an  intermediate  point  and  regulate 
the  tautness  so  that  the  line  is  clear  at  all  points. 

The  curves  in  the  shaft  may  be  such  that  two  plumb-bobs  may  have  to  be 
hung,  as  at  D and  E.  and  even  a third  may  become  necessary 

The  plumb-line,  perhaps  100  ft.  long,  is  apt  to  be  disturbed  by  the  air- 
currents,  and  it  is  often  better  to  mark  a point  on  a convenient  timber  near 
1),  and  another  near  E,  so  close  to  the  string  that  there  is  no  doubt  of  the 
points  lying  in  exactly  the  same  vertical  plane  as  the  plumb-lme.  If  these 
points  be  once  established,  the  string  and  weights  can  be  taken  out  of  the 
shaft,  leaving  us  four  points  in  the  same  vertical  plane,  and  whose  horizontal 
projections  lie  in  the  same  course.  , . ...  „ 

Now  set  up  at  A and  measure  the  azimuth  angle  from  the  backsight  to  D, 
thereby  Riving  the  bearing  from  A to  B.  If  D should  be  Invisible  from  B, 
depress  the  telescope  after  sighting  on  D and  locate  the  point  N m the  same 
vertical  plane,  and  so  situated  that  it  is  visi  ble  from  both  l and  B.  Measure 
the  vertical  angle  and  distance  to  N.  Now  set  up  at  B,  use  the  course  B E for 
a backsight,  and  foresight  to  C.  Measure  the  vertical  angle  and  distance 
B N It  is  seen  that  B N might  have  been  used  as  a backsight,  and  E only 
serves  as  an  additional  check.  N is  really  an  intermediate  station,  but  since 
it  lies  in  the  course  A B,  a set-up  ttnw  is  unnecessary  In  simple  cases,  it  is  a 
very  convenient  method  of  car:  ying'  a survey  from  the  surface  to  the  first 
level  and  a longer  horizontal  projection  of  the  sight  Ab  can  be  secured 
than  if  a set-up  were  made  in  the  shaft  at  D\  but  in  complicated  cases,  such 
‘as  the  one  shown,  it  may  often  be  quicker  to  make  the  extra  set-up  than 
to  use  the  plumb-line.  In  all  sights  for  determining  azimuth  keep  the 
vertical  angles  as  low  as  possible,  and  the  horizontal  projection  of  the 

C°UMethod'by  a Single  Wire  in  the  Shaft  -Stretch  a rather  fine  wire,  free  from 
kinks  down  the  shaft,  as  shown  in  Fig.  6.  being  careful  that  it  touches 
nowhere  in  the  shaft.  Take  two  plumb-bobs  provided  with  fine  round 
strings.  Suspend  one  from  A and  the  other  from  B so  that  they  nearly  touch 
the  same  side  of  the  wire  MN.  In  order  to  have  the  plumb-lines  as  far  apart 
as  possible,  the  line  at  B must  be  quite  long  and  a can  of  water  should  be 
provided  to  keep  the  bob  from  swinging.  The  plumb-line  is  fastened  to  a 
nail  B nearly  in  the  proper  position.  Have  a bar  of  wood  with  a block 
fastened'  to  it  placed  to  one  side  of  B and  a little  below  it. 
The  block  must  have  a hole  so  that  a small  screw  bolt  can 
easily  screw  through  it.  A spool  is  run  on  the  bolt  having  a 
small  groove  turned  in  it  and  being  sandpapered  and  greased 
so  that  the  string  will  slip  easily  as  the  bolt  is  turned.  Now, 
place  the  transit  in  line  with  the  two  plumb-bobs  as  m an 
ordinary  case  of  shaft  plumbing.  Repeat  this  operation  below. 
The  plumb-bobs  in  both  cases  hang  in  the  same  vertical  plane 
and  thus  the  true  bearings  are  found  underground.  Even  the 
plumb-lines  could  be  dispensed  with,  but  the  method  would 
not  then  be  so  accurate.  The  instrument  would  be  set  nearly 
in  the  vertical  plane  passing  through  the  wire,  leveled  and 
sighted  at  M.  Dip  the  telescope  until  the  lowest  point  on  the 
wire  is  visible,  note  the  amount  by  which  the  cross-hair  and 
wire  fail  to  coincide  and  shift  the  instrument  accordingly.  But 
if  this  method  were  tried,  the  two  points  sighted  at  would  not  be  nearly  so 
far  apart  horizontally  as  the  plumb-lines,  and  any  error  in  leveling  wou  .d 
also  vitiate  the  result.  This  method  of  the  single  wire,  however,  provides 
no  way  of  obtaining  the  coordinates. 


Fig.  6. 


NOTES  ON  MAPPING. 

There  are  no  general  rules  governing  the  minutiae  of  map  making,  so 
that  it  may  be  well  to  note  some  of  the  variations  in  practice.  In  some 
offices  the  area  excavated  is  shown  by  a light  wash  of  India  ink  in  addition 


NOTES  ON  MAPPING. 


75 


to  the  ink  line  bounding  the  solid  area.  This  makes  a striking  map,  and 
the  workings  stand  out  prominently.  If  the  survey  were  never  to  be 
extended  and  the  map  were  simply  made  to  show  a particular  state  of  the 
workings,  there  would  be  no  objection  to  the  practice;  but  as  such  extern 
sions  have  to  be  made,  and  old  pillars  removed  or  cut  up,  it  requires  con-' 
siderable  skill  to  tint  the  extensions,  and  especially  the  surfaces  when 
erasures  have  been  made,  so  as  to  produce  an  effect  uniform  with  the  old 
tinted  surface,  especially  as  that  tint  has  been  deepened  by  frequent  han- 
dling. For  these  reasons  many  offices  omit  the  tint  on  the  map,  but  some  tint 
the  back  of  the  tracing  used  by  the  corps,  or  sent  to  the  mine  inspector. 

It  is  an  open  question  whether  the  ends  of  the  chambers  (breasts,  rooms) 
and  gangways  (entries,  levels)  should  be  closed  with  ink.  It  is  well  to  be 
able  to  show  on  your  map  where  the  faces  of  the  workings  were  at  any  given 
time.  Some  place  the  date  of  each  survey  at  the  ends  of  the  gangways  at 
each  posting,  and  of  every  fourth  or  fifth  chamber,  and  thus  note  the  rapid 
ity  with  which  the  mine  is  worked.  Others  use  various  colors  to  denote  th.e 
successive  postings  of  the  survey,  and  place  across  the  ends  of  gangways  ana 
chambers.the  color  appropriate  to  the  survey  that  located  them. 

Wnere  there  are  a number  of  beds  worked  from  the  same  shaft,  slope,  or 
adit,  the  workings  are  frequently  vertically  above  one  another,  and  their 
location  on  the  same  map  causes  confusion  unless  care  be  taken.  One  ot  the 
methods  used  to  distinguish  between  each  bed  is  to  line  in  the  areas  worked 
with  a color  appropriate  to  that  bed.  In  this  way,  three  or  four  beds  have 
been  plotted  on  the  same  map.  A better  way  is  to  make  a map  for  each  bed 
and  to  combine  the  various  beds  on  the  tracings  for  the  officers  and  the  mine 
inspector.  Each  bed  on  this  is  lined  with  its  color,  and  tinted  with  a wash 
of  the  same  color  on  the  back  of  the  tracing  on  the  parts  excavated. 

The  lines  of  survey  are  lightly  drawn  bet  ween  stations  with  red  ink,  and 
the  stations  denoted  by  minute  circles  of  the  same  color  as  that  used  for  that 
particular  seam.  The  survey  lines  should  never  cut  the  circumference  of  the 
circle,  as  such  a procedure  might  cause  doubt  as  to  the  exact  location  of  the 
station  i n case  measurements  were  made  on  the  map.  Stations  are  numbered 
as  in  the  mine,  and  beneath  each  is  placed  the  elevation  above  or  below  tide 
of  the  roof  of  the  mine.  If  the  stations  are  numerous  and  the  elevations  fre- 
quently taken,  such  a map  would  furnish  the  means  of  ascertaining  the 
shape  of  the  bed  by  running  contours  through  points  of  equal  elevation. 
This  plan  was  used  by  a number  of  engineers  and  was  adopted  by  the  Second 
Geological  Survey  of  Pennsylvania  in  making  their  mine  sheets.  The  adop- 
tion of  the  scale  of  100  ft.  to  the  inch,  under  the  ventilation  law,  also  fur- 
nished that  survey  with  a means  of  tracing  and  connecting  adjoining 
properties  and  their  workings,  as  had  been  frequently  done  by  large  com- 
panies having  adjacent  collieries,  and  the  maps  of  the  anthracite  regions  ol 
the  Second  Geological  Survey  of  Pennsylvania  have  been  thus  compiled  from 
tracings  of  office  maps,  with  little  or  no  inside  work  by  the  corps  of  the  survey. 

The  ground  areas  of  all  buildings  are  tinted  a uniform  red. 

All  railroad  tracks  are  represented  by  red  lines. 

All  bridges,  etc.,  and,  in  fact,  any  improvements  built  by  man,  are  to  be 
colored  red. 

In  the  mine,  the  stations  are  represented  by  a small  circle  (o)  with  the 
number  in  black  beside  it. 

The  lines  of  survey  are  drawn  between  the  circumferences  of  tne  circles 

marking  the  station  'o o,  so  as  to  leave  the  centers  uncolored.  The 

elevations  above  tide  are  marked. 

All  small  bodies  of  water  are  tinted  with  Prussian  blue;  all  large  bodies 
with  indigo — as  Prussian  blue  is  too  vivid  for  large  areas  of  tint. 

It  is  the  custom  to  allot  a color  to  each  bed,  and  make  each  bed  on  the 
general  tracing  in  its  color.  In  this  way  all  the  beds  may  be  mapped  on  the 
same  tracing,  and  can  be  distinguished  though  the  workings  may  all  under- 
lie the  same  area.  Various  colors  are  sometimes  used  to  denote  the  extent 
of  the  workings  at  the  given  postings. 

The  paper  on  which  the  map  is  made  should  be  of  the  best  quality,  as 
frequent  changes  in  the  workings,  and  the  removal  of  portions  of  old  pillars, 
necessitate  many  erasures.  Ordinary  paper  will  not  work  well  after  erasure 
and  subsequent  handling,  and  the  best  practice  is  to  use  cloth-backed  egg- 
shell paper. 

It  remains  to  note  that  the  temperature  and  humidity  of  the  office,  and  of 
the  place  where  the  maps  are  stored,  should  vary  as  little  as  possible.  As  the 
scale  is  small,  any  variation  in  the  paper  by  contraction  or  expansion  will 


76 


SURVEYING. 


affect  the  scale  on  which  the  map  was  originally  laid  out,  and  will  affect  it 
unequally,  as  the  paper  is  not  homogeneous.  This  can  be  seen  by  making 
measurements  on  old  maps  to  check  work  done  in  former  times.  In  almost 
every  case  the  500'  squares  are  slightly  in  error.  This  must  be  guarded 
against  in  case  measurements  are  taken  from  the  map.  It  is  best  to  calculate 
the  distances  wanted  from  the  coordinates  of  the  ends  of  the  lines,  and 
insure  absolute  accuracy.  _ , ,. 

A good  map  is  the  sign  of  a good  draftsman.  The  title  should  be  subordi- 
nate to  the  map.  It  is  common  to  see  the  fifty-cent  map  of  a small  area 
smothered  under  a gorgeous  ten-dollar  title.  The  lettering  should  be  neat 
and  appropriate,  and  a style  should  be  adopted  that  can  be  readily  thrown 
off — as  time  is  quite  an  item  in  the  money  made  by  mapping. 

A neat  title,  the  judicious  use  of  tints  over  the  area  excavated,  and  good 
lettering  of  minor  objects  will  add  dollars  to  the 
& value  of  a map.  A small  outlay  of  taste  and  care 

will  make  a beautiful  tracing  out  of  a ragged  one, 
and  double  its  value. 

Locating  Errors. — Errors  in  arc  or  distance  are 
easily  located  by  the  method  of  coordinates.  The 
transitman,  at  the  completion  of  a closed  survey, 
should  sum  the  angles  and  see  if  it  be  360°.  Thus, 
before  leaving  the  mine,  a check  will  be  established 
on  the  transit  work.  In  case  of  a variation  from 
360°,  the  notes  are  examined  to  see  if  the  needle 
readings  show  a similar  variation  with  the  vernier. 
In  case  the  notes  are  incomplete,  or,  if  a continuous 
vernier  has  been  carried,  we  table  the  work  before 
leaving  the  mine  and  locate  the  error  as  follows:  Fig.  7 represents  a close  of 
four  stations  and  an  angular  error  at  c.  Starting  from  a we  table  as  follows: 


Sta. 

Course. 

Dist. 

N 

s 

E 

w 

Sums. 

N 

S 

E 

W 

a 

b 

d (d’) 
a ( a ") 
b 

N 

E 

S 30  E 
S 60  W 
N 30  W 

100 

100 

100 

100 

100 

86.58 

50 

100 

50 

86.58 

100 

100 

13.42 

36.58 

100 

150 

63.12 

There  is  an  error 
course  a 6 by  30°. 
Reversing  the  order 


in  close  of  30°,  as  the  course  a"  b differs  from  the 
of  tabling,  and  correcting  each  course  by  30°,  we  have: 


Unon  comparing  the  sums  of  the  northings  and  southings  and  eastings 
and  westings  in  both,  we  find  that  c is  the  only  station  for  which  they  agree. 
Here  the  error  occurred.  The  location  of  c from  either  direction  was  cor- 
rect and  what  followed  incorrect.  From  this  we  can  deduce  the  rule: 

To  Find  an  Error  in  Arc.— Table  the  close  from  any  station  m both  directions 
back  to  the  initial  station.  The  station  which  has  a similar  sum  of  eastings 


NOTES  ON  MAPPING. 


77 


and  westings  and  northings  and  southings  in  both  tablings  is  the  one  at 
which  the  error  was  made. 

With  two  or  more  errors  nothing  can  he  done. 

Errors  in  Distance— These  maybe  found  in  a close  by  tabling.  Suppose 
we  have  a square  abed  so  placed  that  the  magnetic  meridian  passes 
through  b d.  Let  the  distance  c d be  incorrect. 


The  first  location  of  a is  southings  0,  westings  0;  the  second  location  is 
southings  35.35,  westings  35.35.  The  westings  are  sines  and  the  southings 
cosines,  as  stated  before.  As  sin  -f-  cos  = tang  of  course  referred  to  the  base 
line,  we  divide  35.35  by  35.35  and  obtain  1 as  the  natural  tangent  for  45°,  and, 
as  the  error  was  in ‘southings  and  westings,  the  course  on  which  the  error 
was  made  is  S 45°  W.  The  amount  of  the  error  is  found  by  dividing  the  error 
in  eastings  or  westings  as  tabled  by  the  sine  of  the  course  just  found,  or  the 
error  in  northings  or  southings  by  the  cosine  of  the  same.  Both  results 
will  agree,  35.35  -r-  70.71  = .50.  Reducing  the  measured  distance  by  this 
amount,  we  find  the  tabulation  shows  an  accurate  close.  From  this  we 
deduce  the  rule:  _ 

To  Find  an  Error  in  Measurement— Divide  the  difference  between  the  east- 
ings or  westings  of  the  two  locations  by  the  difference  between  the  northings 
or  southings  of  the  same.  The  quotient  will  be  the  tangent  of  the  course  on 
which  the  error  was  made.  The  extent  of  the  error  is  found  by  dividing  the 
error  in  eastings  or  westings  (as  tabled)  by  the  sine  of  the  above  course,,  or 
the  error  in  northings  or  southings  by  the  cosine  of  the  same. 

Locating  Special  Work.— This  last  principle  may  be  used  for  finding  the 
proper  course  and  distance  to  drive  a tunnel  between  two  stations  connected 
bv  a survey.  In  outside  tunneling,  the  survey  is  generally  carried  over  the 
surface  in  a straight  line.  In  underground  work  this  is  impossible,  so  that  it 
is  a much  more  difficult  task  to  ascertain  the  distance  and  direction  to  drive, 
from  the  number  of  measurements  to  be  made  in  connection  with  the  two 
stations,  but  if  the  work  is  accurately  done  it  is  much  more  a feat  than  in 
outside  work.  To  include  all  the  elements  that  enter  into  such  a calculation, 
we  will  suppose  that  an  underground  slope  is  to  be  run  between  two  beds  of 
coal.  The  distance  between  the  two  ends  must  be  accurately  obtained,  as 
well  as  the  relation  of  the  two  stations  found.  Having  tabled  the  work,  we 
get  the  difference  between  the  sums  of  sines  and  cosines,  as  just  described, 
for  the  two  points;  the  quotient  from  dividing  the  first  by  the  second  gives 
us  the  course,  and  from  the  last  rule  the  horizontal  distance  is  found.  The 
levels  give  us  the  difference  in  elevation,  and  from  these  data  we  get  the 
slope  per  hundred,  and  the  distance  measured  on  that  slope.  All  of  the  work 
is  done  in  the  mine  and  while  the  transit  is  setting  up  at  one  of  the  end 
stations,  so  that  before  leaving  the  mine,  we  can  give  the  course,  pitch,  and 
distance  of  the  tunnel  and  set  the  first  station  for  lining  in  the  center.  The 
more  important  the  work,  the  greater  need  of  accuracy.  In  one  case  a 
1,000'  chain  was  constructed  to  measure  the  distance  between  two  shafts 
that  were  to  be  connected  by  work  driven  from  both  ends,  and  much 
of  the  outside  work  was  done  on  the  ice  of  the  Susquehanna  River,  and  a 
transit  reading  to  5"  was  used.  The  work  closed  vertically  and  laterally 
within  an  inch. 

Calculation  of  Areas.— In  connection  with  the  mapping  of  the  part  newly 
worked,  the  engineer  of  the  company  sometimes  calculates  the  area 
excavated  since  the  last  posting,  and  estimates  the  royalties  accruing  to  the 
various  parties  whose  lands  are  leased. 

This  method,  at  best,  is  liable  to  grave  errors,  and  requires  a number  of 
accurate  cross-sections  of  the  bed  to  determine  its  composition,  as  well  as 


78 


SURVEYING . 


numerous  determinations  of  the  specific  gravity  to  determine  its  weight. 
The  old  method  of  estimating  workable  coal  in  a property  allowed  1,000  tons 
per  acre  per  foot  of  thickness  of  the  bed.  To  obtain  this  amount,  the  roof 
must  be  good,  the  pillars  of  medium  size,  and  the  bed  near  the  surface; 
or  the  surface  must  be  so  valueless  that  the  pillars  can  be -‘drawn”  or 
“robbed.”  As  beds  increase  in  depth,  if  the  surface  be  valuable,  the  ratio 
of  pillars  to  stall  must  increase  or  the  greater  pressure  will  cause  the  mine  to 
cave  in  It  has  been  found  that,  when  the  surface  is  to  be  kept  up  and  the 
workings  are  to  be  carefully  driven,  but  850  tons  per  acre  per  foot  of  thick- 
ness can  be  used  in  calculation,  under  the  present  system  of  mining.  Efforts 
are  constantly  being  made  to  increase  this  amount,  with  a possible  chance 
of  success  , „ ,,  . 

To  estimate  the  amount  of  coal  excavated  from  any  property,  the  best 
method  is  to  institute  an  account  of  all  cars  of  coal  taken  out  from  the  work- 
ings under  that  property.  As  soon  as  the  measurements  on  the  mine  tracing 
show  that  a gangway  or  room  has  crossed  the  property  line,  the  oflice  is 
notified,  and  all  cars  coming  from  those  places  are  credited  to  that  property. 
This  is  the  only  absolutely  accurate  method  of  computation.  The  total 
number  of  cars  of  coal  run  through  the  breaker  is  known,  with  the  total 
weight  of  prepared  coal.  The  ratio  of  the  cars  coming  from  a given  property 
to  the  total  number  of  cars  is  taken  as  the  ratio  between  the  total  prepared 
coal  and  the  coal  sold  from  that  property. 


RAILROAD  CURVES. 

These  are  arcs  of  circles,  and  are  divided  into  simple,  compound,  and 
reverse  curves.  A simple  curve  has  but  one  radius,  a compound  one  is  con- 
tinuous and  has  two  or  more  radii,  and  a 
reverse  one  is  also  continuous  but  com- 
posed of  arcs  described  in  opposite  direc- 
tions. 

Curves  are  designated  by  the  number 
of  degrees  in  the  central  angle,  which  is 
subtended  by  an  arc  whose  chord  is  100  ft. 
long.  Thus,  if  the  angle  BOG , Fig.  1,  is 
10°  and  B G is  100  ft.  long,  B G H C is  a 10° 
curve. 

The  angle  FE  C,  formed  by  the  pro- 
longation of  two  adjacent  straight  por- 
tions of  a railroad,  or  tangents , as  they  are 
technically  called,  is  termed  an  intersec - 
tion  angle. 

The  deflection  angle  of  a curve  is  the 
angle  formed  at  any  point  of  the  curve 
between  a tangent  and  a chord  of  100  ft., 
and  is  therefore  one-half  the  size  of  the 
y degree  of  the  curve.  If  the  chord  B G is 

100  ft.,  the\angle  EBG  is  the  deflection  angle  of  the  curve  BGHC,  and  is 
one-half  the  angle  B O G.  . n . 

When  the  deflection  angle  D is  given,  the  radius  of  the  curve,  R,  is 
found  by  the  formula 

sin  D 


The  curve  used  to  connect  two  tangents  is  determined  mainly  by  the  form 
of  the  country.  When  this  is  decided,  the  point  of  beginning,  called  the 
P.  C.  (point  of  curve),  and  the  point  where  the  curve  ends,  called  the  P.  T. 
(point  of  tangent),  must  be  located.  Both  these  points  are  the  same  distance 
from  the  point  of  intersection  of  the  tangents,  called  the  P.  I.  ( point  of  inter- 
section). This  distance  is  called  the  tangent  distance  of  a curve,  and  is  found 
by  the  formula 

7=  R tan  h l 


in  which  7=  tangent  distance; 

R = radius  of  curve; 

T = intersection  angle. 

Having  set  the  tangent  points  B and  C\  Fig.  1,  in  order  to  locate  points  on 
the  curve,  set  up  the  transit  at  B , the  P.  C.  Set  the  vernier  at  zero,  and  sight 
to  E,  the  P.  I.  Suppose  B to  be  a full  station  on  the  tangent,  and  that  it  has 


RAILROAD  CURVES. 


79 


been  decided  to  set  stakes  at  each  100  ft.  Let  the  central  angle  BOG , meas- 
ured by  the  100-ft.  chord  B G,  be  10°;  then,  the  deflection  angle  E B G,  having 
its  vertex  B in  the  circumference,  and  being  subtended  by  the  chord  B G, 
will  equal  £ B G G,  or  5°.  Turn  an  angle  of  5°  from  B,  which  in  this  case  will 
be  to  the  right,  measure  100  ft.  from  B,  aud  drive  a stake  at  G.  Turn  off  an 
additional  angle  of  5°,  making  10°  from  zero,  and  at  another  100  ft.  measured 
from  6r,  and  drive  a stake  at  H.  Continue  this  process  until  20°,  or  one-half 
the  intersection  angle,  has  been  turned  off.  This  last  deflection  will  bring 
the  lbrechainman  to  the  point  of  tangency  C,  or  the  P.  T. 

When  the  P.  C.  comes  between  two  stations  it  is  called  a substation,  and 
the  chord  between  it  and  the  next  station  on  the  curve  is  called  a subchord. 
Had  the  P.  C.  been  a substation,  say  32  ft.  beyond  a regular  station,  the 
deflection  angle  for  the  measuring  distance  of  100  — 32  = 68  ft.  would  be 
found  in  this  manner:  The  deflection  for  100  ft.  is  5°  — 300';  hence,  for  1 ft. 


Fig.  2. 


it  is  = 3',  and  for  68  ft.  it  is  3 X 68  = 204'  = 3°  24'.  This  is  turned  off 
100 

and  a stake  set  in  line  68  ft.  from  the  transit.  Other  stations  are  then  located 
as  above,  by  turning  off  an  additional  5°  each  time. 

Rules  for'Measuring  the  Radius  of  a Curve.— Stretch  a string,  say  20  ft.  long,  or 
longer  if  the  curve  is  not  a sharp  one,  across  the 
curve  corresponding  to  the  line  from  A to  C,  in 
Fig.  2.  Then  measure  from  B the  center  of  the 
line  A C,  and  at  right  angles  with  it,  to  the  rail  at 
D.  Multiply  the  distance  A to  B,  or  one-half  the 
length  of  the  string,  in  inches,  by  itself;  measure 
the  distance  D to  B in  inches,  and  multiply  it  by 
itself.  Add  these  two  products,  and  divide  the  sum 
by  twice  the  distance  from  B to  D,  measured  exactly  in  inches  and  fractional 
parts  of  inches.  This  will  give  the  radius  of  the  curve  in  inches. 

It  may  be  more  convenient  to  use  a straightedge  instead  of  a string.  Care 
must  be  taken  to  have  the  ends  of  the  string  or  straightedge  touch  the  same 
part  of  the  rail  as  is  taken  in  measuring  the  distance  from  the  center.  If  the 
string  touches  the  bottom  of  the  rail  flange  at  each  end,  and  the  center 
measurement  is  made  to  the  rail  head,  the  result  will  not  be  correct. 

In  practice,  it  will  be  found  best  to  make  trials  on  different  parts  of  the 
curve,  to  allow  for  irregularities. 

Example. — Let  AC  be  a 20-ft.  string;  half  the  distance,  or  A B , is  then 
10  ft.,  or  120  in.  Suppose  B D is  found  on  measurement  to  be  3 in.  Then  120 
multiplied  by  120  is  14,400,  and  3 multiplied  by  3 is  9;  14,400  added  to  9 is 
14,409,  which,  divided  by  twice  3,  or  6,  equals  2,401i  in.,  or  200  ft.  1£  in.,  which 
is  the  radius  of  the  curve. 

The  formula  is  thus  stated, 

A B*  + B D* 

2 B D = R- 


Or,  applied  to  the  above  example, 

1002  Q 

o\7q  = 2>401*  in-  = 200  ft*  in- 

2 X o 

To  Find  the  Radius  of  a Circular  Railroad  Curve,  the  Straight  Portions  of  a Road 
Being  Given.— If  Q I and  PD,  Fig.  3,  are  the  straight  portions  that  are  to  be 
connected,  the  radius  of  the  curve  ID  may  be  found  as  follows: 

Produce  Q I and  P D until  they  meet  and  form  the  angle  T.  Bisect  the 
angle  Q TP  by  the  line  T C.  From  the  point  on  either  line  from  which  the 
curve  is  to  begin,  in  this  instance  making  the  point  I the  point  of  curve,  erect 
the  line  I C perpendicular  to  Q T,  and  the  point  where  this  joins  the  line  T C, 
or  C , is  the  center  of  the  curve,  and  the  line  I C is  the  radius.  To  find  the 
end  of  the  curve,  or  point  of  tangent,  as  D,  draw  a line  from  C,  perpendicular 
to  TP.  The  line  CD  will  also  be  a radius  of  the  circle  of  which  I D is  the 
arc,  and  the  point  D will  be  the  point  of  tangent. 

To  Find  the  Radii  of  Compound  Curves  to  Join  Two  Straight  Portions  or  Road. 
This  kind  of  curve  is  adopted  where  the  railroad  is  required  to  pass  through 
given  points,  as  C. , D,  P,  P,  Fig.  3 ( b ),  or  to  avoid  obstructions. 

Compound  railroad  curves  are  composed  of  straight  lines  and  circular 
arcs,  and  have  common  normals,  O H,  O P,  P I.  Q J , K R.  and  therefore  com- 
mon tangents  where  the  arcs  are  joined.  The  normals  are  perpendicular  to 
the  straight  portions  of  the  road  also;  OH  is  perpendicular  to  A B E F is 
perpendicular  to  QJ  and  K R. 


80 


SURVEYING. 


To  find  the  radii  0 B,  C Q,  Fig.  3 (c),  to  connect  two  straight  lines  of  rail- 
road,  AB,  D E,  the  road  has  to  pass  from  the  point  B,  through  the  point  C , 
and  to  touch  the  straight  road  E F at  any  point  D. 

Join  B and  C,  make  the  angle  B CO  = 0 B C,  which  is  supposed  to  he 
given,  equal  90°  — TB  C.  Draw  B 0 perpendicular  to  AB,  then  OB  = CO , 
and  is  the  radius  of  the  arc  B C. 

With  OB  as  radius,  describe  the  arc  B C;  draw  C F perpendicular  to  C Q, 
and  produce  DE  to  meet  it  in  F;  make  DF  = CF\  and  draw  D Q perpen- 
dicular to  E F , to  meet  C Q in  Q.  Then  CQ  -=  Q D,  and  the  radii  0 B and 
0 D are  determined. 

Practical  Method  of  Laying  Out  Sharp  Curves  in  a Mine.— Curves  m a mine  are 

usually  so  sharp  that  they  are  designated  as  curves  of  so  many  feet  radius, 

instead  of  as  curves  of  so  many  degrees. 

Suppose  that  it  is  required  to  connect  the  two  headings  A and  B,  Fig.  4(a), 
which  are  perpendicular  to  each  other,  with  a curve  of  60  ft.  radius.  Pre- 
pare the  device  shown  in  Fig.  4 (6),  by  taking  three  small  wires  or  inelastic 
strings  f g,  gh,  and  g k,  each  10  ft.  long,  and  connecting  one  end  of  each  to 
a small  ring,  and  the  other  end  of  two  to  the  ends  of  a piece  y.00'?  ^3. 
long.  Form  a neat  loop  at  the  end  / of  the  string#/.  To  use  this  device, 
lay  off  on  the  center  line  of  the  heading  B,  c d and  d e equal  to  60  ft.  and 
3 10  ft.,  respectively.  Place  the  loop  / of  the 

device  described  over  a small  wire  peg  driven 
in  at  e,  and  the  ring  g over  a similar  peg  at  d. 
Take  hold  of  the  stick  h k,  pull  the  strings  g h 
and  g k taut,  and  place  the  center  mark  on  h k 
on  the  center  line  of  the  heading  B.  Drive  a 
small  peg  in  at  m,  located  by  the  point  k,  which 
is  on  the  curve.  Move  the  device  forward, 
place  the  loop  / over  the  peg  at  d,  the  ring  g 
over  the  peg  at  m,  and  take  hold  of  the  stick 
h k and  pull  until  the  strings  g h and  g k are 


Fig.  4. 


taut,  and  the  strings  f g and  g h are  in  a straight  line.  The  point  A:  will  fall 
on  the  curve  at  n,  which  mark  by  driving  in  a peg.  To  locate  other 
points,  proceed  exactly  as  in  the  last  step.  The  distance  c d in  any  case 
is  found  by  the  formula  c d = R tan  £ J,  in  which  R is  the  radius  of  the 
curve,  and  I the  intersection  angle  of  the  center  lines  of  the  headings. 


HINTS  TO  BEGINNERS. 

Abuse  of  Instruments.— Surveying  instruments  of  value  and  precision  are 
not  made  of  cast  iron,  as  one  would  think  from  the  way  they  are  frequently 
handled.  Underground  work  is  transacted  in  places  dark,  dirty,  and  con- 
fined, so  that  extra  care  must  be  observed  to  prevent  accidental  knocks  that 
damage  the  instrument  even  if  they  do  not  destroy  its  accuracy. 


STADIA  MEASUREMENTS. 


81 


As  it  frequently  happens  that  long  distances  must  be  traversed  under- 
ground in  going  between  the  shaft  or  slope  and  the  workings  to  be  surveyed, 
the  transit  and  level  should  be  carried  so  as  to  obviate  all  accidents.  They 
should  never  be  attached  to  the  tripod  and  carried  on  the  shoulder,  and,  if 
the  route  to  be  passed  over  is  up  or  down  a slope  or  working  place,  the 
person  carrying  the  instrument  should  be  the  last  to  descend  and  the  first  to 
ascend,  so  that  loose  stones  or  dirt  that  may  be  dislodged  will  not  affect  or 
endanger  the  instrument  or  trip  the  carrier. 

Be  sure  that  the  tripod  head  is  tightly  screwed  on  to  the  tripod.  The 
writer  remembers  a case  where  the  transitman  and  himself,  when  new  to 
the  work,  spent  over  an  hour  in  endeavoring  to  obtain  two  readings  of  an 
angle  that  would  agree.  The  variations— from  8'  to  2°— were  caused  by  the 
slight  movement  of  an  old  instrument  with  too  much  “ lost  motion,”  and  a 
loose  tripod  head. 

A great  many  engineers  prefer  kerosene  to  fish  oil  for  their  lamps.  Kero- 
sene never  drops  upon  your  book  to  make  an  unsightly  smear,  and  perhaps 
obliterate  part  of  your  notes.  A kerosene  lamp  is  hotter  and,  with  the 
glazed  mine  hat,  is  more  apt  to  produce  headaches.  The  writer,  during  the 
latter  part  of  his  underground  work,  wore  a straw  hat,  had  a piece  of  thin 
sheet  brass  riveted  to  its  front  with  a hole  in  the  top  for  the  lamp  hook.  To 
the  lamp  was  brazed  a narrow  cross  strip  of  the  same  metal,  and  the  strip 
ends,  bent  back  upon  themselves,  were  slid  down  the  sides  of  the  plate  on 
the  hat  and  kept  the  lamp  from  swaying.  With  such  an  arrangement  it  is 
not  necessary  to  remove  the  lamp  to  read  the  vernier,  and  when  the  lamp 
is  used,  for  other  purposes,  the  hat  can  be  removed  with  the  lamp  fastened  tcb 
it.  This  arrangement  keeps  the  hands  free  from  lamp  smoke  or  oil,  and  a 
cleaner  note  book  is  the  result. 

When  there  is  an  antipathy  to  a lamp  upon  the  head,  and  when,  with  a 
long,  wooden  handle,  one  or  both  hands  are  free  in  going  about  the  work, 
a larger  lamp  is  used  of  “torch”  pattern,  employed  by  wheel  testers  or 
engineers  in  railroad  practice.  Kerosene  can  be  burned  in  this.  The  handle 
can  be  tucked  under  the  left  arm  while  taking  side  notes.  Such  a lamp  is 
convenient  in  finding  old  stations  in  a high  place,  when  there  is  no  firedamp. 

For  plumbing  wet  shafts,  kerosene  resists  the  extinguishing  power  of 
water  better  than  fish  oil,  and  is  less  readily  blown  out  by  a strong  ventilating 
current.  It  makes  more  smoke,  and,  in  tight  headings,  or  mines  with  poor 
ventilation,  with  a large  party,  fouls  the  air  much  more  readily  than  fish  oil. 
Sometimes  a mixture  of  the  two  is  burnt  in  very  drafty  places,  where  it  is 
ham  to  maintain  a light.  Kerosene  is  burned  in  the  plummet  lamp  unless 
it  is  used  with  the  “ safety  ” attachment.  Sweet  oil,  or  any  oil  burning 
without  smoke,  must  then  be  used.  Smoke  clogs  the  openings  in  the  gauze, 
restricts  the  entry  and  escape  of  gases,  and,  especially  if  the  gauze  be  damp 
with  oil,  may  ignite  and  communicate  the  flame  from  within  to  the  outside 
body  of  gas. 

White  lead  or  Dutch  white  (white  lead  and  sulphate  of  baryta  in  equal 
parts)  is  best  for  painting  stations.  Zinc  white  has  been  tried  with  less 
success.  The  mixture  should  not  contain  too  much  linseed  oil— especially 
in  wet  places— or  it  will  run  and  destroy  the  witness. 


THEORY  OF  STADIA  MEASUREMENTS. 

By  Arthur  Winslow.* 

Late  Assistant  Geologist,  Second  Geological  Survey  of  Pennsylvania,  State 
Geologist  of  Missouri. 

The  fundamental  principle  on  which  stadia  measurements  are  based  is 
the  geometrical  one  that  the  lengths  of  parallel  lines  subtending  an  angle  are 
proportional  to  their  distances  from  its  apex.  Thus  if,  in  Fig.  1 (a),  a represents 
the  length  of  a line  subtending  an  angle  at  a distance  d from  its  apex,  and  a' 
the  length  of  a line,  parallel  to,  and  twice  the  length  of,  a subtending  the 
same  angle  at  a distance  d'  from  its  apex,  then  d'  will  equal  2d. 


* Mr.  Winslow’s  calculations  and  tables  have  been  proved  practically  correct  by  the  several 
corps  of  the  Second  Geological  Survey  of  Pennsylvania.  The  corps  in  the  anthracite  regions,  under 
directions  of  Mr.  Frank  A.  Hill,  geologist  in  charge,  took  over  30,000  stadia  sights,  and  better 
results  were  obtained  when  tie  surveys  were  made  than  in  previous  work  in  which  distances 

were  chained. 


82 


SUR  VEYINO. 


This  is,  in  a general  way,  the  underlying  principle  of  stadia  work;  the 
nature  of  the  instruments  used,  however,  introduces  several  modifications, 
and  these  will  be  best  understood  by  a consideration  of  the  conditions  under 
which  such  measurements  are  generally  made. 

There  are  placed  in  the  telescopes  of  most  instruments  fitted  for  stadia 
work,  either  two  horizontal  wires  (usually  adjustable),  or  a glass  with  two 
etched  horizontal  lines  at  the  position  of  the  cross-wires  and  equidistant 
from  the  center  wire.  A self-reading  stadia  rod  is  further  provided,  gradu- 
ated according  to  the  units  of  measurements  used.  In  a horizontal  sight 

with  such  a telescope  and  rod , 
the  positions  of  the  stadia  wires 
are  projected  upon  the  rod,  and 
intercept  a distance  which,  in 
Fig.  1 (b),  is  represented  by  a. 

In  point  of  fact,  there  is 
formed,  at  the  position  of  the 
stadia  wires,  a small  conjugate 
image  of  the  rod  that  the  wires 
intersect  at  points  b and  c, 
which  are,  respectively,  the 
foci  of  the  points  B and  C on 
the  rod.  If,  for  the  sake  of 
simplicity,  the  object  glass  be 
considered  a simple  biconvex 
iens,  then,  -by  a principle  of 
optics,  the  rays  from  any  point 
of  an  object  converge  to  a focus  at  such  a position  that  a straight  line,  called 
a secondary  axis,  connecting  the  point  with  its  image,  passes  through  the 
center  of  'the  lens.  This  point  of  intersection  of  the  secondary  axes  is 
called  the  optical  center.  Hence,  it  follows  that  lines  such  as  c C and  b B 
in  Fig  1(b)  drawn  from  the  stadia  wires  through  the  center  of  the  object 
glass  will  intersect  the  rod  at  points  corresponding  to  those  that  the  wires 
cut  on  the  image  of  the  rod.  From  this  follows  the  proportion: 

d _ a 

~v  ”T- 

d = j-  a,  (1) 

where  d = distance  of  rod  from  center  of  objective;  . 

p ==  distance  of  stadia  wires  from  center  of  objective; 
a = distance  intercepted  on  rod  by  stadia  wires; 

I = distance  of  stadia  wires  apart. 

If  p remained  the  same  for  all  lengths  of  sight,  then  y-  could  be  made  a 


Fig.  1. 


desirable  constant  and  d would  be  directly  proportional  to  a.  Unfortunately, 
however  for  the  simplicity  of  such  measurements,  p (the  focal  length)  varies 
with  the  length  of  the  sight,  increasing  as  the  distance  diminishes  and  vice 
versa.  Thus,  the  proportionality  between  d and  a is  variable.  I he  object, 
then,  is  to  determine  exactly  what  function  a is  of  d and  to  express  the  rela- 
tion in  some  convenient  formula. 

The  following  is  the  general  formula  for  biconvex  lenses: 

i + ? = 7:  (2) 

f is  the  principal  focal  length  of  the  lens,  and  p and  p'  are  the  focal  distances 
of  image  and  object,  and  are,  approximately , the  same  as  p and  d,  respectively, 
in  equation  (1): 

Therefore,  j ^ = y,  approximately, 

d d 


and 


p f L 


a a 


From  (1), 


Whence, 


•**  I ~ f L 
d = -j-  a + /•  (2) 


STADIA  MEASUREMENTS. 


83 


In  this  formula,  it  will  be  noticed  that  as  / and  I remain  constant  for 
sights  of  all  lengths,  the  factor  by  which  a is  to  be  multiplied  is  a constant, 
and  that  d is  thus  equal  to  a constant  times  the  length  of  a,  plus/.  This  for- 
mula would  seem,  then,  to  express  the  relation  desired,  and  it  is  generally 
considered  as  the  fundamental  one  for  stadia  measurements.  As  above 

stated,  however,  the  equation  ~ = — is  only  approximately  true,  and 

the  conjunction  of  this  formula  with  (2)  being,  therefore,  not  rigidly  admissi- 
ble, equation  (3)  does  not  express  the  exact  relation.*  The  equation  express- 
ing the  true  relation,  though  differing  from  (3)  in  value,  agrees  with  it  in 

form,  and  also  in  that  the  expression  corresponding  to  --  is  a constant,  .and 
that  the  amount  to  be  added  remains,  practically,  /.  The  constant  corre- 
sponding to  -j  may  be  called  fcf,  and  thus  the  distance  of  the  rod  from  the 

objective  of  the  telescope  is  seen  to  be  equal  to  a constant  times  the  reading 
on  the  rod,  plus  the  principal  focal  length  of  the  objective.  To  obtain  the 
exact  distance  to  the  center  of  the  instrument,  it  is  further  necessary  to  add 
the  distance  of  the  objective  from  that  center  to/;  which  sum  may  be  called  c. 
The  final  expression  for  the  distance,  with  a horizontal  sight,  is  then 

d = k a -f  c.  (4) 

The  necessity  of  adding  c is  somewhat  of  an  encumbrance.  In  the  stadia 
work  of  the  U.  S.  Government  surveys,  an  approximate  method  is  adopted  in 
which  the  total  distance  is  read  directlv  from  the  rod.  For  this  method  the 
rod  is  arbitrarily  graduated,  so  that,  at  the  distance  of  an  average  sight,  the 
same  number  of  units  of  the  graduation  are  intercepted,  between  the  stadia 
wires  on  the  rod,  as  units  of  length  are  contained  in  the  distance.  For  any 
other  distance,  however,  this  proportionality  does  not  remain  the  same;  for, 
according  to  the  preceding  demonstration,  the  reading  on  the  rod  is  propor- 
tional to  its  distance,  not 
from  the  center  of  the  in- 
strument, but  from  a point 
at  a distance  “ c ” in  front 
of  that  center,  so  that, 
when  the  rod  is  moved 
from  the  position  where 
the  reading  expresses  the 
exact  distance,  to  a point 
say  half  that  distance  from 
the  instrument  center,  the 
reading  expresses  a dis- 
tance less  than  half;  and, 
at  a point  double  that  dis- 
tance from  instrument  cen- 
ter, the  distance  expressed 
by  the  reading  is  more 
than  twice  the  distance. 

The  error  for  all  distances 
less  than  the  average  is 
minus,  and  for  greater  dis- 
tances, plus.  The  method 
is,  however,  a close  approx- 
imation, and  excellent  re- 
sults are  obtained  by  its  use. 

Another  method  of  get- 
ting rid  of  the  necessity  of 
adding  the  constant  was 
devised  by  ' Mr.  Porro,  a 
Piedmontese,  who  constructed  an  instrument  in  which  there  was  such  a 
combination  of  lenses  m the  objective  that  the  readings  on  the  rod,  for  all 
lengths  of  sight,  were  exactly  proportional  to  the  distances.:}:  The  instrument 


* This  is  demonstrated  later  on. 

t k is  dependent  on  /,  and  can  therefore  be  made  a convenient  value  in  any  instrument  fitted 
with  adjustable  stadia  wires.  It  is  generally  made  equal  to  100,  so  that  a reading  on  the  rod  of  1' 
corresponds  to  a distance  of  100'  -f  /. 

} A notice  of  this  instrument  will  be  found  in  an  article  by  Mr.  Benjamin  Smith  Lyman, 
entitled  “ Telescope  Measurements  in  Surveying,”  in  “Journal  Franklin  Institute,”  May  and 
June,  1868,  and  a fuller  description  is  contained  in  “ Annales  des  Mines,”  Vol.  XVI,  fourth  series. 


84 


SURVEYING. 


was  however,  bulky  and  difficult  to  construct,  and  never  came  into 

SflS^SlSIiS 

mmmm. 

the  rod.  In  Fig.  2 (&)., 

A B = a = reading  on  rod;  _ . t.  r TT. 

up  = d ==  inclined  distance  = c + GF  = c + k.  CH, 
jfP  — j)  = horizontal  distance  = d cos  n; 
pp  = Q = vertical  distance  = D tan 
n = vertical  angle; 

AG  B = 2m. 

and  the 

sines  of  the  opposite  angles, 

AF  sinm  . 

GUF  = sin  [90°  + \n  — m)Y 


or, 


AF  = G-Fsinm 


cos  ( n — m ) 9 


and 


B F 
GF 


sin  m 


iET[90°  — (w+m)]’ 

1 


or, 


p p = (?  p sin  m 


or 


cos  (n  + m)’ 

iP-(-  JSP  = <?  F7 sin 


cos  ( n — m) ' cos  {n  4-  m). 


a „ T,  CH  1 

.4  F + i?  -F  — a>  an<^  G F — y tan  m 


C II  cos  m 


2 sin  m 

By  substituting  and  reducing  to  a common  denominator, 

C TT  r».os  m f cos  ( n_  + m)  + cos  ( n — rrrf J 
a T “i"  cos  (»+"»»)  cos  (n  — m) 

Reducing  this  according  to  trigonometrical  formulas, 
cos2  cos2  m — sin2  n sin2  m 


CH  = cl 


as 


d = c + ka 


cos  n cos2  m 

d = MF=c  + k.  CH. 

cos2  n cos2  m — sin2  n sin  - m 


cos  n cos2  m 

The  horizontal  distance,  D = d cos  n.  . 2 

F)  = c cos  n + k a cos2  n — kci  sin-  n tan  m. 


IOST4  1-  fcUWD-i*  — . , , .. 

The  third 


very  small  even  for  long  gs^^t0  07'V  TlSeforeiThe  final formula  for 
ffiSTX  “?adir  Aeld%%°cauf,  and  with  Wires  equidistant  from 
the  center  wire,  is  the  following:  cosB  + O*cos,n,  (5) 


STADIA  MEASUREMENTS.  85 


The  vertical  distance  Q is  easily  obtained  from  the  relation:  Q = Dtann. 

.*.  Q = c sin  n + a k cos  n sin  n\ 

or,  Q = c sin  n + a Jc  . (6)* 

With  the  aid  of  formulas  (5)  and  (6),  the  horizontal  and  vertical  distances 
can  be  immediately  calculated  when  the  reading  from  a vertical  rod  and 
the  angle  of  elevation  of  any  sight  are  given.  From  these  formulas  the 
stadia  reduction  tables  following  have  been  calculated.  The  values  of  a A;  cos'"  n 
sin  2 n 

and  a k— - — were  separately  calculated  for  each  2 minutes  up  to  30° 

of  elevation;  but,  as  the  value  of  c sin  n and  c cos  n has  quite  an  inappre- 
ciable variation  for  1°,  it  was  thought  sufficient  to  determine  these  values 
only  for  each  degree.  As  c varies  with  different  instruments,  these  last  two 
expressions  were  calculated  for  three  different  values  of  c,  thus  furnishing 
a ratio  from  which  values  of  c sin  n and  c cos  n can  be  easily  determined 
for  an  instrument  having  any  constant  (c). 

Similar  tables  have  been  computed  by  J.  A.  Ockerson  and  Jared  Teeple, 
of  the  United  States  Lake  Survey.  Their  use  is,  however,  limited,  from  the 
fact  that  the  meter  is  the  unit  of  horizontal  measurement,  while  the  eleva- 
tions are  in  feet.  The  bulk  of  the  tables  furnishes  differences  of  level  for 
stadia  readings  up  to  400  meters,  but  only  up  to  10°  of  elevation.  Supple- 
mentary tables  give  the  elevations  up  to  30°  for  a distance  of  1 meter.  For 
obtaining  horizontal  distances,  reference  has  to  be  made  to  another  table 
which  is  somewhat  an  objectionable  feature,  and  a multiplication  and  a 
subtraction  has  to  be  made  in  order  to  obtain  the  result.  Last,  but  not  least, 
these  tables  are  apparently  only  accurate  when  used  with  an  instrument 
whose  constant  is  .43  meter. 

The  many  advantages  of  stadia  measurements  in  surveying  need  not  be 
dwelt  on  here,  both  because  attention  has  been  repeatedly  called  to  them 
and  because  they  are  self-evident  to  every  engineer.  Neither  will  it  be 
within  the  compass  of  this  article  to  describe  the  various  forms  of  rods  and 
instruments,  or  the  conventionalities  of  stadia  work. 

It  is  seen  that,  in  the  deduced  formula,  the  factor  by  which  the  reading 
on  the  rod  is  multiplied  is  a constant  for  each  instrument.  The  question 
now  arises,  Does  this  remain  the  case  with  a compound  objective  ? 

In  view  of  the  difficulty  of  demonstrating  this  mathematically,  it  was 
decided  to  make  a practical  test  of  this  point  with  a carefully  adjusted 
instrument.  The  readings  were  taken  from  two  targets  set  so  that  the  sight 
should  be  horizontal,  thus  preventing  any  personal  error  or  prejudice  from 
affecting  the  reading.  A distance  of  500  ft.  was  first  measured  off  on  a level 
stretch  of  ground,  and  each  50-ft.  point  accurately  located.  From  one  end 
of  this  line,  three  successive  series  of  stadia  readings  were  then  taken  from 
the  first  50-ft.  and  each  succeeding  100-ft.  mark.  The  following  table  con- 
tains the  results: 


Distances. 

Feet. 

Spaces  Intercepted  on  the  Rod. 

1st  Series. 
Feet. 

2d  Series. 
Feet. 

3d  Series. 
Feet. 

Mean. 

Feet. 

50 

.485 

.4860 

.4855 

.4855 

100 

.985 

.9870 

.9830 

.9850 

200 

1.985 

1.9860 

1.9840 

1.9850 

300 

2.989 

2.9875 

2.9870 

2.9878 

400 

3.983 

3.9800 

3.9890 

3.9840 

500  | 

4.985 

4.9850 

4.9900 

4.9867 

Multiplying  the  mean  of  these  readings  by  100,  and  subtracting  the  result 
from  the  corresponding  distance,  we  obtain  the  following  table: 


*The  above  demonstration  is  substantially  that  given  by  Mr.  George  J.  Specht  in  an  article 
on  Topographical  Surveying  in  “ Van  Nostrand’s  Engineering  Magazine,”  February  1880 
though  enlarged  and  corrected.  ’ 


86 


SURVEYING. 


Distances. 

Feet. 

Mean  of 
Stadia  Readings 
Times  100. 
Feet. 

1 

Differences. 

Feet. 

Variations 
From  Mean. 
Feet. 

50 

100 

200 

300 

400 

500 

48.55 

98.50 

198.50 

298.78 

398.40 

498.67 

1.45 

1.50 

1.50 

1.22 

1.60 

1.33 

| 

+ .02 
+ .07 
+ .07 
— .21 
+ .17 
— .10 

r>  nr  «• 1 AQ 

Stun  of  differences  = 8.60;  mean  of  difference  - 1.43. 

The  variations  between  the  4^ft  Ting  oSy^Tft. &A 

3SS ^SbteSsaaSBraeffleas* 

is  a constant  value  tPwone  having  a compound,  plano-convex 

taken  that  m * settii ig  th< 3 s0  set  that  the  reading,  at  any  dis- 

ment  constant  and  mat  tne  ires  am0unt  of  this  constant. f 

tance,  is  less  tton  tiie  ■ true  d: ish a uy*  h distances  and  elevations 

onlfaVS^^ 

-eragl  height  of  the 

telescope ^^.^S^o^r^ere  this  method  will  be  impracticable,  and 

then^hemolieif  procedure  must  be  left  to  the^ud^^^^^^^ur^eyon  If 

rod,  and  the  difference  between  this  as  the  case  may  be. 

used  in  sighting  to  the  rod  eit  small  that  in  a great  deal  of  stadia 

This  difference  will  ordniarily  be  so  ^ma11  | rod  for  the  angle  of 

work  no  reduction  will  he  nece^ry.  In  sghtog  TO  tgt  always  be  used.  By 

depression  or  elevation,  the  center  h measured  For  theoretical  exact- 
this  means  an  exactly  continuous  line  is e“easure  idistant  fr0m  the 

ness  it  is  necessary  that the  stadia  wires  shoui^ne  d^tance  read  is  for  an 

angle°of  elevatioVdifferin^  from  the  true  one  by  an  amount  proportional  to 

tteSSn«eirghdS 

measurements. . The  common  errors  o cf1‘ffIJXngSa  difference  of  a whole 
Sff,  ”5  of  .noth,,,  on.  .ho»M  „ „ 

#This  applies  to  an  inStrument  witli  m0vable  Sta<na  ™esh'  ^ 
rlass.  In  the  latter  ease,  the  graUnation  of  “•  arJe  not  affected  by  variations  of 

o aimed  as  an  advantage  for  etched  lines  “ ,feyA  serles  0f  tests  made  with  one  of 

srrSigi^s  tS”  stzlk  rrfS^TSmVr^ 

between^hat'produced^n'  theTnXmen.  by  the  snn  of  a hot  summer's  day  and  that  produce  y 
•”?&&  wEER  evMenflJ  proportional  to  the  length  of  sight,  with  a 1,000'  sight  it  would 
amount  to  22.5',  etc. 


stadia  measurements. 


87 


even  footmark,  and  in  the  check,  reading  the  other  one.  This  is  assuming 
the  measurements  to  be  made  by  the  ordinary  method,  and  not  by  the 

approximate  one  of  the  United  States  Engineers.  y 


HORIZONTAL  DISTANCES  AND  DIFFERENCES  OF  LEVEL  FOR 
STADIA  MEASUREMENTS. 

The  formulas  used  in  the  computation  of  the  following  tables  were  those 
given  by  Mr  George  J.  Specht  in  an  article  on  Topographical  Surveying 
published  m Van  Nostrand’s  Engineering  Magazine”  for  February  *]880 
These  formulas  furnish  expressions  for  horizontal  distances  and  differences 
h *°yr.  st7adla  measurements,  with  the  conditions  that  the  stadia  rod 

They  ^ areas  follows”  ^ Stadia  wires  be  e(luidistant  from  the  center  wire. 


= c cos  n + a k cos2  n\ 
= D tan  n — c sin  n 


ak  sin2« 


glass,  plus  focal 


= horizontal  distance; 

= difference  of  level; 

= distance  from  center  of  instrument  to  center  of  obie< 
length  of  object  glass;  J 

a = rea^ngSi^tadia  rwi;^aSS  diVided  by  distanCf  of  stadia  wires  apart; 
n = vertical  angle; 

a k = (genirfhy  WO)  multiplied  by  k' which  is  a constant  for  each  instrument 

table?*.the  vertical  columns  consist  of  two  series  of  numbers  for 
each  degree,  which  series  represent,  respectively,  the  different  values  of 

a k cos2  n and for  every  2 minutes,  when  ak  — 100.  To  obtain  the 

horizontal  distance  or  the  difference  of  level  in  any  case,  the  corresponding 
value  of  c cos  n or  c sin  n must  further  be  added;  and  the  mean  of  each  of 
these  expressions,  for  each  degree,  with  three  of  the  most  common  values  of 
c,  is  given  under  each  column.  va±ucc  ui 

iet  itbe  re(luired  to  find  the  horizontal  distance  and  the 

contra  nt °f  7^VeiTW+nn  = + 6°  18',  a = 570,  and  the  instrument 
constant  c = J5-  In  the > column  headed  6°  opposite  18' in  the  series  for 

thfrefore,  when  a^i 9570°  &S  the  expressi0lJ  for  ak  cos2 n when  ak  = 100; 

m ^ ^akco&n  = 98.80  X 5.70  = 563.16. 

column to^e  S75be  a(Med  ° C°S  ^ which>  in  this  case> is  found  in  the  subjoined 
In  a similar  manner,  the  required  difference  of  level  is 
~ 4.  (+10.91X5.70)  +.08  - +62.27. 

One  multiplication  and  one  addition  must  be  made  in  each  case. 

It  is  to  be  noticed  that,  with  the  smaller  angles,  cos  n in  the  expressions 
c cos  n and  c sin  n may  be  entirely  neglected  without  appreciable  error 
For  values  of  c,  which  differ  from  those  given,  an  approSSate^^tlon 
?woIexpre4otns+  amount  of  dlfferenee,  may  very  easily  be  made  in  these 


88 


STADIA  MEASUREMENTS. 


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ELEMENTS  OF  MECHANICS. 


91 


ELEMENTS  OF  MECHANICS. 

Only  the  elements  of  machines  are  here  treated,  as  all  machinery  how- 
ever complicated,  is  merely  a combination  of  the  six  elementary  forms  viz  • 
the  lever , the  wheel-  and  axle , the  pulley , the  inclined  plane,  the  wedqe  and 
the  screw;  and  these  six  can  be  still  further  reduced  to  the  lever  and  the 
inclined  plane.  They  are  termed  mechanical  powers,  but  they  do  not 
produce  force;  they  are  only  methods  of  applying  and  directing  it 

The  law  of  all  mechanics  is: 

The  power  multiplied  by  the  distance  through  which  it  moves  is  equal  to  the 
weight  multiplied  by  the  distance  through  which  it  moves. 

Thus,  20 ilb.  of  power  moving  through  5 ft.  = 100  lb.  of  weight  moving 
through  1 ft.  In  the  following  discussion  friction  is  not  considered  the 
idea  being  to  give  an  elementary  knowledge  of  the  principles  of  the 
elements  of  mechanics.  * 

Levers.— There  are  three  classes  of  levers.  They  are:  (1)  power  at  one 
end,  weight  at  the  other,  and  fulcrum  between;  (2)  power  at  one  end 
fuicrum  at  the  other,  and  weight  between;  (3)  weight  at  one  end,  fulcrum 
at  the  other,  and  power  between. 

The  handle  of  a blacksmith’s  bellows  is  a lever  of  the  first  class.  The 
hand  is  the  power  and  the  bellows  the  weight,  with  the  pivot  between 
as  the  fulcrum.  A crowbar  as  used  for  prying  down  top  rock  is  a lever  of 
the  second  class.  The  hand  is  the  power,  the  rock  to  be  barred  down 
the  weight,  and  the  point  in  the  roof  against  which  the  bar  presses 
^ the  fulcrum.  The  treadle  of  a grindstone  is  a lever  of  the  third  class. 
The  foot  is  the  power,  the  hinge  at  the  back  of  the  foot  is  the  fulcrum 
and  the  moving  of  the  machinery  is  the  weight.  ’ 

A lever  is  in  equilibrium  when  the  arms  balance  each  other.  The  dis- 
tances through  which  the  power  and  the  weight  move  depend  on  the 
comparative  length  of  the  arms.  Let  L represent  power’s  distance  from 
the  fulcrum  (C),  l the  weight’s  distance,  and  a the  distance  between  power 
and  weight;  then,  if  L is  twice  l,  the  power  will  move  twice  as  far  as  the 
weight.  Substituting  these  terms  in  the  law  of  mechanics,  we  have 


92 


elements  oe  mechanics. 


th e short* arm  of  The  firs!  actfoule  lonTa™  of  the  second, Cd^so^nto 

the  last.  . . fniprnm  be  four  times  the  distance  from  the 

If  the  distance  from  A to  the  fulcrum  d m to  B then  a power  of 

5 lb.  at  A will  lift  20  lb.  at  B. 
If  the  arms  of  the  second  lever 


13  D r-a 

V 

A 

5) 

E 

B 

6 

Fig.  1. 


;ie  aiuJia  ^ 

are  of  the  same  comparative 
length,  the  20-lb.  power  obtained 
at  B will  exert  a pressure  of  80 
lb  on  E\  and  if  the  third  lever 
has  the  same  comparative 

lengths  this.  80  lh.at-E  wiUlift  320  lb.  at  G.  Thus,  ^power  ^ weight 
A will  balance  a weight  of  320  id. 

' EZX.  ¥5.  ;«.  .h.  .r . Th. 

windlass  is  a common  form.  Thepower  is^apphedto  the 

the  handle,  and  the  short  arm  is  the  radius  oi t ine  ax 
Thiis  Tis  the  fulcrum,  Fc  the  long  arm,  and  Fb  the 

S^aiSSJSSSVSS' t.  proportional  » ti.i.  «U1.  « Have 

P :W  : 


Fig.  2. 


Fig.  3. 


r : R.  PR  = Wr. 

Wr  - Wr 

P = TT  R~  P ‘ 

RP  RP 
W~—.  r = ^ 

A train.  Fig.  3,  consists  of  a series  of 
wheels  and  axles  that  act  on  one  another 
on  the  principle  of  a compound  lever. 
The  driver  is  the  wheel  to  which  power 
is  applied  The  driven , or  follower,  is 
the  one  that  receives  m'diorifrointhe 
driver.  The  pinion  is  the  small  gear 
wheel  on  the  axle.  , , , • 

If  the  diameter  of  the  wheel  A is  16 

in  and  of  the  pinion  B 4 m.,  a pull  oi 
1 lb  applied  at  P will  exert  a force  of 
4 lb.  on  the  wheel  C ; if  the  diameter 

of  C is  6 in.,  and  of  D 3 in.,  a force  of  4 lb.  on  C e | fjn°£  will  raise  a 
E.  If  E is  16  in.  in  diameter,  and  F 4 tin.,  a force  o amQunt  ace0rding  to 

weight  of  32  lb  on  F 2,m  Jd  The  wright  will  only  pass  through  A of  the 

law  of  mechanics, 

jyyppr  ^ P R Rr Rf^_ 

P = p R"'  " — rrfr" 

n : n"  : : r'r"  : RR'. 
v : v'  ::  rr'r"  : RR'R". 
n n / n"  = number  of  revolutions; 

’ y v'  = velocity  or  speed  of  rotation; 
r r'  r",  etc.  = radii  of  the  pinions;  F 4 

JB  R'  P",  etc.  = radii  of  the  wheels. 


ELEMENTS  OF  MECHANICS. 


93 


The  Inclined  Plane. — In  Fig-.  5 we  see  that  the  power  must  descend  a dis- 
tance equal  to  A C in  order  to  elevate  the  weight  to  the  height  B C;  hence 
we  have  P X length  of  the  inclined  plane  = WX  the  height  of  the  inclined 
plane,  or  P : W : : height  of  inclined  plane : length  of  inclined  plane;  or, 

p = w _ pi  l 

l h sin  a 

™ !?•  Find  the.  Weight  Required  to  Balance  Any  Weight  on  Any  Inclined  Plane. 

Multiply  the  given  weight  by  the  sine  of  the  angle 
of  inclination. 

Thus,  to  find  the  weight  required  to  balance  a 
loaded  car  weighing  2,000  lb.  on  a plane  pitching 
18°,  we  multiply  2,000  by  the  sine  of  18°,  or  2,000  X 
.3090170  = 618.034  lb. 

Or,  if  the  length  of  the  plane  and  the  vertical 
height  are  given,  multiply  the  load  bv  the  quotient 
of  the  vertical  height  divided  by  the  length. 

Thus,  if  a plane  between  two  levels  is  300  ft. 
long  and  rises  92.7  ft.,  and  the  load  is  2,000  lb.,  the  balancing  weight  is 
found  as  follows:  6 

92  7 

2,000X— = 618+. 

Case  1.— To  find  the  horsepower  required  to  hoist  a given  load  up  an 
inclined  plane  in  a given  time,  use  the  formula 


Fig.  5. 


| Load  (in  lb.)  + weight  of  hoisting  rope  (in  lb.)  J 


( vertical  height 
X < through  which  the 
(load  is  raised  (in  ft.) 


}. 


33.000  X time  of  hoisting  (in  minutes) 

Example.  —Find  the  horsepower  required  to  raise,  in  3 minutes,  a car 

weighing  1 ton  and  containing  1 ton  of  material  up  an  inclined  plane  1,000 
ft.  long  and  pitching  30°,  if  the  rope  weighs  1,500  lb. 

c The  total  load  equals  car  + contents  + rope  = 2,000  + 2,000  + 1,500  = 
5,500  lb. 

The  vertical  height  through  which  the  load  is  hoisted  equals 

1.000  X sin  30°  = 1,000  X .5  = 500  ft. 

• H P = 5,500  X 500  _ 27  7 

. . j-l.  x . 33;000  X 3 

Case  2. — When  the  power  acts  parallel  to  the  base,  use  the  formula 
W x height  of  inclined  plane  = P X length  of  base. 

These  rules  are  theoretically  correct,  but  in  practice  an  allowance  of 
about  30 i<>  must  be  made  for  friction  and  contingencies. 

The  screw  consists  of  an  inclined  plane  wound  around  a cylinder.  The 
inclined  plane  forms  the  thread,  and  the  cylinder,  the  body.  It  works  in  a 
nut  that  is  fitted  with  reverse  threads  to  move  on  the  thread  of  the  screw. 
The  nut  may  run  on  the  screw,  or  the  screw  in  the  nut.  The  power  may  be 
applied  to  either,  as  desired,  by  means  of  a wrench  or  a lever. 

When  the  power  is  applied  at  the  end  of  a lever,  it  describes  a circle  of 
which  the  lever  is  the  radius  r.  The  distance  through  which  the  power  passes 
is  the  circumference  of  the  circle;  and  the  height  to  which  the  weight  is 
lifted  at  each  revolution  of  the  screw  is  the  distance  between  two  of  the 
threads,  called  the  pitch  ( p ).  Therefore  we  have  P X circumference  of 
circle  = W X pitch,  or  P : W : : p : 2 n r. 


Wp 


r P 


The  power  of 


lengthening  the  lever 
distance  between  the 


P : W : 


2 7r  r p 

the  screw  may  be  increased  by 
or  by  diminishing  the 
threads. 

Example. — How  great  a weight  can  be  raised 
by  a force  of  40  lb.  applied  at  the  end  of  a wrench 
14  in.  long,  using  a screw  with  5 threads  per  inch? 
W X  *  * = 40  X 28  X 3.1416. 

W = 17,593  lb. 

The  wedge  usually  consists  of  two  inclined 
planes  placed  back  to  back.  (Fig.  6.)  In  theory, 
the  same  formula  applies  to  the  wedge  as  to  the 
inclined  plane,  Case  2. 
thickness  of  wedge  : length  of  wedge. 


ELEMENTS  OF  MECHANICS . 

Friction,  in  the  other  mechanical  P°^rs,  i^lft^each^ wTh^  wedge 
efficiency;  in  this  it  is  essential,  since,  ou^in  in  the  others  the  powder 

isappl^^  steady*  force;  in  this  it  is  a sudden  blow,  and  is  equal  to  the 

m°Tlie1  pu He y is*shnply™nothCT  v^- pqf a sing^ 

TvllrlW  a™  anydaiseused  to  change  the 

direction  of  toeforce^  ^ _ ty  of  p 

P = w.  V = v‘ m 

Mnuahle  Pullev — A form  of  the  single  pulley, 
Movable  Kuney.  weight,  is  shown  m 

%Lef  ta“his  one  half  of  tlfe  weight  is  sus- 

Srned  by  the  hook,  and  the  other  half  by  the 
a,.-.  ..  laineu  .““r  thp  koWer  is  only  one-half  the 

rw??cth^^ 

^Combinations  of  Pulleys SSTlM 

^weSr  ^Yatacef lto ofweight.  \‘i)  In  Fig.  10,  a power  of  lib.  will  in  the 

8 421  _9_ 


Fig.  7. 


Fig.  8. 


Fig.  12. 

f-ne  ll^re^resents  the  OTdi^ry^a^le^bloc^  used  bymechK 

wtoch  catTbe  calculated  by  the  continuous  rope  is  used,  a 

Rule.— In  any  combination  of  VuiffV^  ™ fh  mnrahie  block  as  many  times 

'ing  the  load,  not  counting  the  free  ma.  has  a tension 

K&5 t&SS.’S-ffwftS r-« r.  a . - of 

voneys,  p = W w = T P. 


Differential  Pulley.— Fig.  13. 


2" 
w = 


2 PR 


Fig.  13. 


FRICTION  AND  LUBRICATION. 


95 


In  all  combinations  of  pulleys,  nearly  one-half  the  effective  force  is  lost 
by  friction. 

Composition  of  Forces. — When  two  forces  act  on  a body  at  different  angles, 
their  result  may  be  obtained  by  the  following  rule: 

Rule.— Through  a point  draw  two  lines  parallel  to  the  directions  of  the  lines  of 
action  of  the  two  forces.  With  any  convenient  scale , measure  off,  from  the  point 
of  intersection,  distances  corresponding  to  the  magnitudes  of  the  respective  forces, 
and  complete  the  parallelogram.  From  the  common  point  of  application,  draw  the 
diagonal  of  the  parallelogram;  this  diagonal  will  he  the  resultant,  and  its  magni- 
tude can  he  measured  with  the  same  scale  that  was  used  to  measure  the  two  forces. 
When  more  than  two  forces  act  on  a body  simultaneously,  find  the  resultant  of 
any  two  of  them  as  above;  then,  by  the  same  method,  combine  this  resultant  with  a 
third  force,  and  this  resultant  with  the  fourth  force , and  so  on. 


FRICTION  AND  LUBRICATION. 

Friction. — Friction  is  the  resistance  to  motion  due  to  the  contact  of 
surfaces.  It  is  of  two  kinds,  sliding  and  rolling.  If  the  surface  of  a body 
could  be  made  perfectly  smooth,  there  would  be  no  friction;  but,  in  spite  of 
the  most  exact  polish,  the  microscope  reveals  minute  projections  and  cavities! 
We  till  these  with  oil  or  grease,  and  thus  diminish  friction.  Since  no  surface 
can  be  made  perfectly  smooth,  some  separation  of  the  two  bodies  must,  in  all 
cases,  take  place  in  order  to  clear  such  projections  as  exist  on  the  surfaces. 
Therefore,  friction  is  always  more  or  less  affected  by  the  amount  of  the 
perpendicular  pressure  that  tends  to  keep  them  together. 

The  ultimate  friction  is  the  greatest  frictional  resistance  that  one  body 
sliding  over  another  is  capable  of  opposing  to  any  sliding  force  when  at  rest. 

The  coefficient  of  friction  is  the  proportion  that  the  ultimate  friction  in  a 
given  case  bears  to  the  perpendicular  pressure.  The  coefficient  of  friction  is 
usually  expressed  in  decimals;  but  sometimes,  as  in  the  case  of  cars  and 
engines,  it  is  expressed  in  pounds  (of  friction)  per  ton. 

The  coefficient  of  friction  equals  the  ultimate  friction  divided  by  the 
perpendicular  pressure,  and  the  ultimate  friction  equals  the  perpendicular 
pressure  multiplied  by  the  coefficient  of  friction.  Thus,  if  we  have  a block 
weighing  100  lb.  standing  on  another  block,  and  it  takes  35  lb.  pressure  to 
slide  it,  the  coefficient  of  friction  = x305^,  or  .35. 


Table  of  Coefficients  of  Friction. 


Materials. 

Smooth,  Clean, 
and  Dry  Plane 
Surfaces. 

Smooth  Plane  Sur- 
faces, Perfectly 
Lubricated  With 
Tallow. 

Oak  on  oak 

.40 

.079 

Wrought  iron  on  oak 

.62 

.085 

Wrought  iron  on  cast  iron 

.19 

.103 

Wrought  iron  on  wrought  iron 

.14 

.082 

"Wrought  iron  on  brass 

.17 

.103 

Cast  iron  on  cast  iron 

.15 

.100 

Cast  iron  on  brass 

.15 

.103 

Steel  on  cast  iron  

.20 

.105 

Steel  on  steel  

.14 

Steel  on  brass 

.15 

.056 

Brass  on  cast  iron - 

.22 

.086 

Brass  on  wrought  iron 

.16 

.081 

Brass  on  brass 

.20 

Oak  on  cast  iron 

.080 

Oak  on  wrought  iron 

.098 

Cast  iron  on  oak 

.078 

Steel  on  wrought  iron 

.093 

The  above  coefficients  are  only  approximate,  for  the  coefficient  will  vary 
with  the  intensity  of  the  pressure  and  the  velocity,  and  also  with  the  condi- 
tions of  the  atmosphere.  But  they  are  correct  enough  for  practical  purposes. 


96 


ELEMENTS  GF  MECHANICS. 


Thp  friction  of  liauids  moving  in  contact  with  solid  bodies  is  independent 
nf  thp  nressure  because  the  forcing  of  the  particles  of  the  fluid  over  the  pro- 

the  area  of  surface  or  contact. 

Coefficients  of  Friction  in  Axles.  _ 


Axle. 


Bell  metal 

Cast  iron 
Wrought  iron 
Wrought  iron 

Cast  iron  

Cast  iron  

Wrought  iron 


Bearing. 

Ordinary 

Lubrication. 

Bell  metal  

.097 

Bell  metal  

.07 

Bell  metal  

.07 

Cast  iron  

.07 

Cast  iron  

.07 

Lignum  vitae 

.10 

Lignum  vitae  

.12 

Lubricated 

Continuously. 


.049 

.05 

.05 

.05 


rnmmmm 

Frictional  Resistance  of  Shafting- 

Let  K = coefficient  of  friction; 

J “ re^hf^^ftSgTnWleys  + the  resultant  stress  of  belts; 

H = horsepower  absorbed; 

D = diameter  of  journal  in  inches; 

E = number  of  revolutions  per  minute. 

Then’  Ordinary  Oiling.  Continuous  Oiling. 

...  _ m R9  v P V D-  .0112  X PX  D\  „ „ 

K = :S»5MXPXi)XP;  .000000339  XPXPXPl 

As  f rough  approximation,  100  ft.  of  shafting,  3 in.  diameter,  making 

Friction,”  under  Vend- 

^Friction  of  Mine  Cers.-The  Metier .of 'mine  ^™s  |0  “U^h  mat^h 

^^tto^heT^e^otdition  ofgthe  track  and  the  lubrication  are 

important  factors  in  determimngthe^  requisites  of  good 

In  this  connection,  we _may,  however  state  some  ol  me  U _n  dry 


ings  should  renewal6  andso  contracted  that,  while  it  may 

^3^"^  ™t  open  by  jarring  or  by  being  acer- 

dentally  struck  by  asPra£  ^tP^nS^f^ilinff  wheels  that  are  improvements 
onM^^^lS^^r^^  undoubtedly  some 

annular  oil  chambers,  and  those  ^th ended  to  a welfiubricated  bearing  is 

SgSS  SK£i££^- «» '«■«> 

Wa\Vithda  view  of  adopting  a sta™da*d ^number6 ofU years^fth  different 
of  WTilkesbarre,  Pa.,  experimented  for  a number  oi  years 


FRICTION  AND  LUBRICATION. 


97 


styles  of  self-lubricating  wheels,  and  as  a result  of  the  experiments  it  adopted 
a wheel  patented  by  its  chief  engineer,  Mr.  Jas.  H.  Bowden. 

Mr.  R.  Van  A.  Norris,  E.  M.,  Assistant  Engineer,  made  a series  of  989  tests 
with  old-style  wheels,  some  of  which  had  patent  removable  bushings,  and 
others  annular  oil  chambers,  and  the  Bowden  wheel.  The  old  wheels  were 
found  to  be  practically  alike  in  regard  to  friction.  All  the  wheels  were  of 
the  loose  outside  type,  16  in.  in  diameter,  mounted  on  2}  in.  steel  axles, 
with  journals  5£  in.  long.  The  axles  passed  loosely  through  solid  cast 
boxes,  bolted  to  the  bottom  sills  of  the  cars,  and  were  not  expected  to 
revolve. 

The  table  of  friction  tests  shows  the  results  obtained  with  both  old-  and 
new-style  wheels,  and  is  of  interest  to  all  colliery  managers,  inasmuch  as 
the  figures  given  for  the  old-style  wheels  alone  are  the  most  complete  in 
existence,  and,  as  stated  before,  they  are  good  averages. 

Tests  were  made  on  the  starting  and  running  friction  of  each  style  of 
wheel,  under  the  conditions  of  empty  and  loaded  cars,  level  and  grade 
track,  curves,  and  tangents.  The  instruments  used  were  a Pennsylvania 
Railroad  spring  dynamometer,  graduated  to  3,000  lb.,  with  a sliding  recorder, 
a hydraulic  gauge  (not  recording)  reading  to  10,000  lb.,  graduated  to  25  lb., 
and  a spring  balance,  capacity  300  lb.,  graduated  to  3 lb.  All  these  were 
tested  and  found  correct  previous  to  the  experiments. 

Most  of  the  observations  on  single  cars  were  made  with  the  300-lb. 
balance.  The  two  types  of  “ old-style  ” wheels  have  been  classed  together  in 
the  table.  Each  car  was  carefully  oiled  before  testing,  and  several  of  each 
type  were  used,  the  results  being  averages  from  the  number  of  trials  shown 
in  the  table. 

In  the  experiments  on  the  slow  start  and  motion,  the  cars  were  started 
very  slowly  by  a block  and  tackle,  and  the  reading  was  taken  at  the  moment 
of  starting.  They  were  then  kept  just  moving  along  the  track  for  a 
considerable  distance,  and  the  average  tractive  force  was  noted,  the  whole 
constituting  one  experiment. 

The  track  selected  for  these  experiments  was  a perfectly  straight  and 
level  piece  of  42  in.  gauge,  about  200  ft.  long,  in  rather  better  condition  than 
the  average  mine  track.  The  cars  were  41£  in.  gauge,  3*  ft.  wheel  base,  10  ft. 
long,  capacity  about  85  cu.  ft.,  with  6-in.  topping. 

To  ascertain  the  tractive  force  required  at  higher  speeds,  trips  of  one,  four, 
and  twenty  cars,  both  empty  and  loaded,  were  attached  to  a mine  locomotive 
and  run  about  a mile  for  each  test,  the  resistance  at  various  points  on  the 
track,  where  its  curve  and  grade  were  known,  being  noted,  care  also  being 
taken  to  run  at  a constant  speed.  Unfortunately,  only  four  of  the  “new- 
style”  cars  were  available  on  the  tracks  where  these  trials  were  made. 

The  remarkably  low  results  for  the  twenty-car  trips  are  attributed  to 
variations  in  the  condition  of  the  track,  and  the  fact  that  the  whole  train 
was  seldom  pulling  directly  on  the  locomotive,  the  cars  moving  by  jerks,  so 
that  correct  observations  were  impracticable.  The  hydraulic  gauge  was  used 
for  these  twenty-car  tests,  and  the  needle  showed  vibrations  from  1 to  4 tons 
and  back.  The  mean  was  taken  as  nearly  as  possible.  The  gauge  was 
rather  too  quickly  sensitive  for  the  work,  and  the  Pennsylvania  Railroad 
dynamometer  was  not  strong  enough  to  stand  the  starting  jerks  and  the 
strain  of  accelerating  speed. 

The  tests  marked  “rope  haul”  were  made  on  an  empty-car  haulage 
system,  about  500  ft.  long,  with  overhead  endless  rope  running  continuously 
at  a speed  of  180  ft.  per  min.,  the  cars  being  attached  to  the  moving  rope  by 
a chain,  a ring  at  the  end  of  which  was  slipped  over  a pin  on  the  side  of  the 
car.  The  increase  of  friction  on  the  heavier  grades  was  due  to  the  rope 
pulling  at  a greater  angle  across  the  car.  Correction  was  not  made  for  this 
angularity  at  the  time,  and  the  rope  has  since  been  rearranged,  so  that  the 
correction  cannot  now  be  made.  There  were  not  enough  curve  experi- 
ments to  permit  the  deduction  of  any  general  formula  for  the  resistance 
of  these  cars  on  curves. 

The  experiments  on  grade  agree  fairly  well  with  those  on  a level,  the 
rather  higher  values  obtained  being  probably  due  more  to  the  greater  effort 
required  in  moving  them,  and  the  consequent  jerkiness  of  the  motion,  than 
to  any  real  increase  in  resistance.  As  the  experiments  on  all  styles  of 
wheels  were  made  in  an  exactly  similar  manner,  the  comparative  value 
of  the  results  is  believed  to  be  nearly  correct,  the  probable  error  in  each  set  of 
experiments,  as  computed  by  the  method  of  least  squares,  varying  from  about 
4$  for  slow  start  and  motion  to  12$  for  the  rapid  motion  and  twenty-car  trips. 


Summary  of  Friction  Tests  on  Susquehanna 


98 


ELEMENTS  OF  MECHANICS. 


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Summary  of  Friction  Tests  on  Susquehanna  Coal  Co.’s  Mine  Cars,  April,  1889— ( Continued). 


FRICTION  AND  LUBRICATION. 


99 


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Total  number  of  tests 


100 


ELEMENTS  OF  MECHANICS. 


Lubrication.— There  is  probably  no  factor  that  has  a more  direct  bearing 
on  the  cost  of  production  per  ton  of  coal  and  ores  than  the  lubrication  o_ 
mine  machinery  and  yet  it  is  doubtful  if  there  is  another  item  connected 
with  t^e  operation  of  a mine  less  understood  by  owners,  their  managers,  and 

e"fteiraSpfantsaIre'equipped  with  boilers  of  the  highest  known  efficiency; 
®team  P- stpam  will  heat  the  feedwater  for 


heaters  are  used  that,  by  utilizing 
boilers  to  the  highest  point.  Mor 


• waste  steam,  will  heat  the  feedwater  for 
iern  engines  that  will  develop  a horsepower 
^^S^o^fsteama^e  installed;  bends,  instead  of  elbows,  are 
placed in  steam^ndexhaust  pipes,  so  that  the  friction  and  back  pressure 
mav  be  deduced  to  a minimum  In  a word,  everything  is  done  in  the  equip- 
ment of  a plant  to  secure  economy  in  its  operation.  After  all  this  is  done, 
freauently  a long  step  is  taken  in  the  opposite  direction  by  the  use  of  an  oil 
unsuited  to  the  existing  conditions,  and  those  m charge  of  the  plant  are  led 
to  believe  that  the  lubrication  is  all  that  could  be  desired,  simply  because 
the  ermines  and  machinery  run  quietly  and  the  temperature  of  the  bearings 
^e^not^t^co^^^hirmingly  high.  The  office  of  a lubricant  is  not  merely  to 
setfure^h^re^lt^but,  primarily,  to  reduce  friction  and  wear  to  a nnnimum; 
fnd  an  oil  that  will  do  this  is  the  best  oil  to  use,  no  matter  what  the  price 

PeXv?eahzeythee  great  loss  in  power  due  to  the  friction  of  wearing  parts. 
r>np  nf  the  greatest  living  authorities  on  lubrication  writes. 

° “ It  ma v^probably  he  fairly  estimated  that  one-half  the  power  expended 
in  the  ^vJrSe  case  whether  in  mill,  mine,  or  workshop,  is  wasted  on  lost 
work  being  consumed  in  overcoming  the  friction  of  lubricated  surfaces. 

He  addsgthat Treduction  of  504  in  the  work  lost  by  friction  has  often  been 

SeeAseodneyof  m\“Sin°sta“h^ing  the  loss  that  will  occur  by  the  use  of 
inforinr  Oihripunts  attention  is  called  to  two  flour  mills  located  m one  ot  the 
Middle1  S^ate^OneoTthe  plants  was  equipped  with  a condensmpngme 

and  valves  found  to  be  properly  adjusted  and  the  engine  working  within 
Itfribuf edToR?ierabofltrsS°buT ^ 

“ c"ey’ " 

“ to. inferior  lubrica- 

Among  tne  expeiibeh  ^ k power  produced  in  excess  of  that 

iiisll 

(9)6  W°^randTaVn§fXchXrTwhich  is  constantly  doing  more  work  per 
^"idiere^^l^^ai^ele^S^o^danger^that^ought  to  r®c.e'vetse^9^Pj2“g^r 

WUMm 

^it^m^t^ffieulMrfsm'article  of  this  character,  to  do  much  more  than 


FRICTION  AND  LUBRICATION. 


101 


point  out  the  danger  due  to  the  use  of  inferior  lubricants,  leaving  it  to  the 
purchaser  himself  to  determine  as  to  the  intrinsic  worth  of  the  lubricants 
offered  to  him.  In  making  his  selection  he  would  do  well  to  consult  with 
and  heed  the  advice  of  some  highly  responsible  manufacturer  of  lubricants 
who  has  given  to  the  question,  in  all  its  phases,  the  most  careful  study,  and 
who  would  most  probably  have  the  benefit  of  a wide  experience  in  the  applica- 
tion as  well  as  the  manufacture  of  lubricants.  Some  buyers  have,  to  then 
ultimate  regret,  adopted,  as  a method  of  determining  the  merits  of  lubri- 
cants, a schedule  of  laboratory  tests.  Such  a method  is  not  only  useless,  but 
it  is  misleading  to  any  one  other  than  a manufacturer  of  lubricants,  who 
makes  use  of  it  merely  as  a means  of  insuring  uniformity  in  his  manu- 
factured products,  and  not  as  a measure  whereby  to  judge  their  practical 
value.  Indeed,  many  oils  can  be  very  properly  described  by  practically  the 
same  schedule  of  tests,  and  yet  are  widely  apart  when  their  utility  for  a 
given  service  is  considered.  . . 

As  a general  guide  in  purchasing  cylinder  oil  for  mine  lubrication,  it 
might  be  said  that  a dark-colored  oil  is  of  greater  value,  as  a rule,  than  one 
that  has  been  filtered  to  a red  or  light  amber  color,  as  the  process  of  filtration 
necessarily  takes  from  the  oil  a considerable  percentage  of  its  lubricating 
value,  and  at  the  same  time  the  process  is  an  expensive  one.  In  short,  if  a 
light-colored  oil  is  insisted  upon,  a high  price  must  be  paid  for  an  inferior 
lubricant.  As  a word  of  caution,  however,  it  would  be  well  to  add  right 
here  that  irresponsible  manufacturers  frequently  take  advantage  of  the  fact 
that  the  most  efficient  and  best  known  cylinder  oils  are  dark-colored,  and 
endeavor,  with  more  or  less  success,  to  market  as  “cylinder  oil”  products 
absolutely  unsuited  to  the  lubrication  of  steam  cylinders,  and  that  would 
consequently  be  expensive  could  they  be  procured  without  cost. 

For  the  lubrication  of  engine  bearings,  where  modern  appliances  for 
feeding  are  used,  an  engine  oil  of  a free  running  nature  is  best,  as  it  more 
quickly  reaches  the  parts  requiring  lubrication  than  an  oil  of  a more  sluggish 
nature.  It,  of  course,  must  not  be  an  oil  susceptible  to  temperature  changes, 
but  must  be  capable  of  performing  the  service  required  of  it  under  the  most 
severe  conditions,  where  an  oil  of  less  “ backbone  ” would  fail.  Such  an  oil 
would  also  be  suitable  for  the  lubrication  of  dynamos,  and  should  also  give 
satisfaction  where  used  in  lubricating  the  cylinders  of  air  compressors. 
Where  the  machinery  is  of  an  old  type  and  loose-jointed,  or  when  the  bear- 
ings are  open  and  the  oil  is  applied  directly  to  them  by  means  of  an  oiler, 
an  engine  oil  of  a more  sluggish,  or  viscid,  nature  is  best. 

Perhaps  of  equal  importance  to  the  lubrication  of  power  machinery 
must  be  considered  the  lubrication  of  the  axles  of  mine  cars.  This  is 
important,  first,  because  of  the  fact  that  perhaps  three-fourths  of  the  oil 
used  about  a coal  mine  is  used  for  this  purpose,  and,  secondly,  because  there 
is  really  a marked  difference  in  the  quality  and,  therefore,  in  the  efficiency 
of  lubricants  used  for  this  purpose.  Fully  nine-tenths  of  the  prominent 
railroads  of  this  country  are  today  using  car-axle  oil,  costing  perhaps  as 
much  per  gallon  as  much  of  the  so-called  cylinder  oil  that  is  used  in  coal 
mines,  they  having  discovered,  by  exhaustive  experiments,  that  the  increased 
efficiency  gained  bv  using  an  oil  of  such  quality  many  times  offsets  the 
difference  in  the  cost  per  gallon  and  enables  them  to  secure  a greater  mile- 
age without  any  increase  in  their  power  or  other  fixed  charges.  This,  we  are 
certain,  would  apply  just  as  forcibly  to  the  lubrication  of  coal  cars,  no 
matter  whether  the ‘power  is  derived  from  “long-eared  mules”  or  electric 
motors,  and  we  believe  this  feature  of  lubrication  of  mine  equipment  should 
receive  more  careful  attention  than  it  does  receive,  as  a rule. 

There  is  a considerable  amount  of  waste  in  the  lubrication  of  mine  cars. 
This  waste  is  hard  to  avoid,  and,  naturally,  makes  the  buyer  hesitate  before 
adopting  the  use  of  a car  oil  that  costs  very  much  per  gallon;  but  we  believe 
it  can  be  demonstrated,  even  in  the  face  of  this  waste,  that  the  increased 
efficiency  secured  by  the  use  of  a high-grade  car  oil  would  warrant  its  use. 
Such  waste  is  pretty  hard  to  correct  in  mines  where  the  old-fashioned  style 
of  car  axles  is  still  in  use,  and  where  the  oil  is  applied  through  an  ordinary 
spout  oil  can  into  the  axle  box,  and  allowed  to  drip  off  the  axles  and  on  to 
the  ground.  When  axles  are  equipped  in  the  same  manner  as  those  of 
freight  cars,  or  where  cars  are  equipped  with  one  of  the  several  different 
stylefc  of  patent  car  wheels  and  axles  that  are  coming  into  use  quite 
extensively,  it  is  possible  to  regulate  the  feeding  of  the  oil  to  the  axles,  so  as 
to  reduce  the  waste  to  a minimum.  One  of  these  patent  car  wheels,  which 
is  perhaps  better  known  than  any  other,  is  constructed  with  a hollow  hub 


102 


STRENGTH  OF  MATERIALS. 


that  acts  as  a reservoir  tor  the  oil,  the  oil  passing  from  this  reservoir  through 
small  holes  onto  a telt  washer.  which  it  must  saturate,  and  by  which  n is 
applied  to  the  axles.  Such  wheels  require  a limpid  oil.  as  a heavy^  sluggish 
oil  would  not  so  readilv  saturate  the  felt  washer  referred  to.  A tight  cap  is 
adjusted  to  the  end  of  the  axle,  to  prevent  waste  of  oil.  These  wheels  will 
run  quite  a length  of  time  without  reoiling  after  the  reservoir  is  once  filled. 

Of  course,  it  costs  something  to  equip  mine  cars  with  these  patent  axles, 
but  we  are  convinced  that  such  an  outlay  would  result  in  more  economical 
operation,  particularly  if  at  the  same  time  the  very  best  quality  of  car  oil 
obtainable  is  used. 


BEST  LUBRICANTS  FOR  DIFFERENT  PU  RPOSES  (TH  U RSTON). 

Low  temperatures,  as  in  rock  drills 
driven  by  compressed  air 

Very  great  pressures,  slow  speed 

Heavy  pressures,  with  slow  speed 

Heavy  pressures  and  high  speed 

Light  pressures  and  high  speed  

Ordinarv  machinery - 

{ oils. 

Steam  cylinders  - - - j Heavy  mineral  oils.  lard,  tallow. 

( Clarified  sperm,  neat’s  foot,  por- 
Watches  and  other  delicate  mechanism.  < poise,  olive,  and  light  mineral 

( lubricating  oils. 

For  mixture  with  mineral  oils,  sperm  is  best;  lard  is  much  used;  olive 
and  cottonseed  are  good.  

STRENGTH  AND  WEIGHT  OF  MATERIALS 


Light  mineral  lubricating  oils. 

Graphite,  soapstone,  and  other 
solid  lubricants. 

The  above,  and  lard,  tallow,  and 
other  gTeases. 

Sperm  oil.  castor  oil,  and  heavy 
mineral  oils. 

Sperm,  refined  petroleum,  olive, 
rape,  cottonseed. 

Lard  oil.  tallow  oil.  heavy  mineral 
oils,  and  the  heavier  vegetable 


WOODEN  BEAMS. 

To  Find  the  Quiescent  Breaking  Load  of  a Horizontal  Square  or  Rectangular  Beam 
Supported  at  Both  Ends  and  Loaded  at  the  Middle. -Multiply  the  br^dth  in 

inches  bv  the  square  of  depth  in  inches,  divide  the  product  by  distance  in 
feet  between  the  supports,  and  multiply  the  quotient  by  the  constant  given 
in  the  table  on  the  next  page.  Take  safe  working  load  one-third  of  break- 

ingTo°Find  the  Quiescent  Breaking  Load  of  a Horizontal  Cylindrical  Beam.— Divide 
the  cube  of  the  diameter  in  inches  by  the  distance  between  the  supports  in 

feet,  and  multiplv  the  quotient  by  the  constant.  . . . , 

When  the  load  is  uniformly  distributed  on  the  beam,  the  results  obtained 
by  the  above  rules  should  be  doubled.  n . . , , . 

Example  1. — Find  the  quiescent  breaking  load  and  safe  working  load  oi 
a yellow-pine  collar  8 in.  square.  12  ft.  between  legs. 

Breaking  load  = 8 X 500  — 21,333  lb.  for  seasoned,  and  10,666  lb.  for 

^Saf^working  load  = 7.111  lb.  for  seasoned,  and  3,556  lb.  for  green  timber. 

Example  2.— Find  the  quiescent  breaking  load,  and  the  safe  working 
load  of  a hemlock  collar  10  in.  diameter,  7 ft,  between  legs. 

103  . , OO, /1-i 

Breaking  load  = ^ X 236  = 33,714  lb.  for  seasoned  timber,  and 

= 16,857  lb.  for  green  timber. 

03  71 4 , 33,714  11.238 

Safe  working  load  = — = 11,238  lb.  for  seasoned,  and  - 6 or  —j- 

= 5.619  lb.  for  green  timber.  _ _ , , . 

To  Find  the  Load  a Rectangular  Collar  Will  Support  When  Its  Depth  Is  Increased. 

When  the  length  and  width  remain  constant,  the  load  vanes  as  the  square  ot 
the  depth. 


IRON  AND  STEEL  BEAMS. 


103 


Example  —A  rectangular  collar  10  in  deep  supports  15,000  lb.  What  will 
it  support  if  its  depth  Ans. 

Havin*r  the  Length  and  Diameter  of  a Collar,  to  Find  the  Diameter  of  a Longer  Collar 
to  Support  the  Same  Weight.— For  the  same  load,  the  strength  of  collars  vanes 
as  the  cubes  of  their  diameters,  and  inversely  as  their  lengths.  . 

Example  —If  a collar  6 ft.  long  and  8 in.  diameter  supports  a certain 
weight,  what  must  be  the  diameter  of  a collar  12  ft.  long  to  support  the  same 
weight?  ■ 0. 

if  6 : f 12  : : 8 in.  : 10+  m.  Ans. 

Having  the  Loads  of  Two  Beams  of  Equal  Length  and  the  Diameter  of  One,  to 
Find  the^Diameter  Of  the  Other. — When  the  lengths  are  equal,  the  diameters 
vary  as  the  cube  roots  of  the  loads,  or  the  cubes  of  the  diameters  vary  as  the 

^Example  1.— A beam  11  in.  in  diameter  supports  a load  of  32,160  lb.  What 
will  be  the  diameter  of  another  beam  the  same  length,  to  support  a load 

of  19,440  lb.?  

if  32,160  : if 19,440  : : 11 : 9.  Ans. 

Example  2.— A beam  8 in.  in  diameter  will  support  a load  of  10,240  lb, 
What  load  will  a beam  the  same  length  and  7 m m diameter  support? 
vv  83 : 73 : : 10,240  : 6,860.  Ans. 

Table  of  Constants. 

Calculated  for  seasoned  timber.  For  green  timber,  take  one-half  of  these 
constants.  Safe  working  load  is  one-third  of  breaking  load. 


Woods. 


Ash,  white 

Ash,  swamp 

Ash,  black 

Balsam,  Canada 
Beech,  white 

Beech,  red 

Birch,  black 

Birch,  yellow  ... 

Cedar,  white 

Chestnut  

Elm 

Elm,  rock 

Hemlock  

Hickory  

Ironwood  


Square  or 
Rectan- 
gular. 

Round. 

Woods. 

Square  or 
Rectan- 
gular. 

Round 

650 

383 

Locust  

600 

353 

400 

236 

Lignum  vitae 

650 

383 

300 

177 

Larch 

400 

236 

350 

206 

Maple 

550 

324 

450 

265 

Oak,  red  or  black ... 

550 

324 

550 

324 

Oak,  white 

600 

353 

450 

265 

Oak,  live 

600 

353 

450 

266 

Pine,  white 

450 

265 

250 

147 

Pine,  yellow  

500 

295 

450 

265 

Pine,  pitch 

550 

324 

350 

206 

Poplar  

550 

324 

600 

353 

Spruce  ■' 

450 

265 

400 

236 

Sycamore 

500 

295 

650 

383 

Willow  

350 

206 

600 

353 

1 

To  Find  the  Diameter  of  a Collar  When  the  Weight  Increases  in  Proportion  to  the 
Length  —Find  the  required  diameter  to  support  the  same  weight  as  the  short 
collar.  Then  the  length  of  the  short  collar  is  to  the  length  of  the  long  one 
as  the  diameter  found  to  support  the  original  weight  is  to  the  required 

Example. — If  a collar  6 ft.  long,  8 in.  in  diameter,  supports  a certain  weight, 
what  must  be  the  diameter  of  a collar  12  ft.  long  to  support  twice  the  weignt  ? 

1 : 2 : : — : 4^,  or  1 : 2 : : 2 X 83 : ( )3, 

6 


or 


12 

fl:if2  ::8f2  :(  ) ==  12.7.  Ans. 


IRON  AND  STEEL  BEAMS. 

Constants  for  use  in  calculating  strength  of  iron  and  steel  beams: 

Cast  iron  

Wrought  iron  *  1 * 

Steel  5 000 


Safe  Loads  Uniformly  Distributed  for  Standard  and  Special  I Beams. 

( Tons  of  2,000  Pounds. ) 


104 


STRENGTH  OF  MATERIALS. 


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c3rO 


PILLARS  OR  PROPS. 


105 


Sard  steel  will  break  the  same  as  cast  iron.  # Soft  steel  will  bend  like 
wrought  iron.  The  elastic  limit  of  wrought  iron  is  reached  at  about  2,200  lb. 
a o it  dop«  not  break,  we  use  the  limit  of  elasticity.  . , 

Tn  FinH  thp  Quiescent  Breaking  Load  of  a Horizontal  Square  or  Rectangular 

lron  or  S ee  Be?m  SuC  r,ed  at  Both  En<ls  and  Loaded  at  tie  Middle.-Multiply 

iff?  snuareof  its  depth  in  inches  by  its  breadth  in  inches;  multiply  this  result 
by6 th^?onstant  for  the  material  used,  and  divide  by  the  length  in  feet 
between  the  supports.  For  the  neat  load,  subtract  one-half  the  weight  of 

thebe  Quiescent  Breaking  Load  of  a Cylindrical  Iron  or  Steel  Beam. 

Find  the  breaking  load  of  a square  beam  the  sides  of  which  are  equal  to  the 

d'a^fe  waking6 loatUn  each  of  th™preceding  cases  is  one-third  of  the  breaking 
load.  If  the  load  is  equally  distributed  over  the  beam,  it  will  be  twice  as 
great.  

PILLARS  OR  PROPS. 

To  Find  the  Crushing  Load  of  Either  Square  or  Rectangular  Wooden } 

ProDS.— Call  one  side8 of  the  square  or  the  least  side  of  the  rectangle  the 
breadth.  Divide  the  square  of  the  length  in  inches  by  the  square  of  the 
breadth'  in  inches  multiply  the  quotient  by  .004,  add  1 to  the  product,  and 
divide  the  constant  in  the  following  table  by  the  result  Then  multiply 
this  quotient  by  the  number  of  square  inches  m the  end  of  the  prop. 

Constant  . , 

Or,  breaking  load  m lb.  = -r» — : ; ~~  X 0 a> 


( fx-°“)+1 

when  l = length  in  inches,  b = breadth  in  inches,  and  d = depth  in  inches. 

Crushing  Loads  of  Well-Seasoned  American  Woods. 


Wood. 


Ash  

Beech 

Birch  

Cedar,  red 

Cedar,  white 

Chestnut  

Hemlock 

Hickory 

Linden 

Locust,  black,  yellow 
Locust,  honey 
Maple,  broad-leafed 
Oregon 


Crushing 
Load.  Lb. 
per  Sq.  In. 


6,800 

7.000 

8.000 
6.000 
4,400 

5.300 

5.300 
8,000 

5.000 
9.800 

7.000 

5.300 


Wood. 


Crushing 
Load.  Lb. 
per.  Sq.  In. 


Maple,  sugar,  black 

Maple,  white,  red 

Oak,  white,  red,  black 

Oak,  scrub,  basket  

Oak,  chestnut,  live 

Oak,  pin  - 

Pine,  white 

Pine,  pitch 

Pine,  Georgia 

Poplar  

Spruce,  black 

Spruce,  white 

Willow 


8,000 

6,800 

7.000 

6.000 

7.500 

6.500 

5.400 
5,000 

8.500 
5,000 
5,700 

4.500 

4.400 


For  green  timber,  take  one-half  of  the  constants  or  crushing  strength. 
Safe  working  load  equals  one-third  of  crushing  load.  ■ , -rvr,c+ 

Example8— What  is  the  breaking  load  of  a well-seasoned  hemlock  post 

10  in.  by  8 in.  and  12  ft.  long? 

5,300+  [l  + (^TX  -004)]  = 2,308.4  lb.  per  sq.  in.  of  area.  2,308.4  X 80 

= Tcf  Find 'the  Breaking  Load  of  a Cylindrical  Wooden 

load  of  a square  prop  whose  ends  are  equal  m area  to  those  oi  me  cym 

drical  one  and  proceed  according  to  foregoing  rule.  . . 

Example.— What  is  the  safe  working  load  for  a hemlock  mine  prop  10  m. 

diaTheearea  of  the^nd  of  the  prop  = 78.54  sq.  in.  A square  of  equal  area 
will  have  sides  equal  to  1/  78.54  = 8.86+  in. 

Then,  5,300  + [l  + X .004)]  = 3,058.3  lb.  per  each  sq.  In.  of  area. 


106 


STRENGTH  OF  MATERIALS. 


And  3,058.3  X 78.54  = 240,198  lb.  This  is  the  crushing  strength  of  a similar 
prop  of  seasoned  timber,  but,  as  mine  timber  is  used  in  its  green  state,  we 
take  one-half  of  240,198  lb.,  or  120,099  lb.,  as  the  crushing  load  of  the  prop  in 
question.  Then,  the  safe  working  load  is  one-third  of  this,  or  40,033  lb. 

The  strength  of  similar  props  varies  as  the  cubes  of  their  diameters,  and 
inversely  as  their  lengths. 

Safe  Loads,  in  Tons  of  2,000  Pounds,  for  Hollow  Cylindrical  Cast-Iron 

Columns. 


(The  Carnegie  Steel  Co .,  Limited.) 


Outside  Diam. 
Inches. 

Thickness  of 
Metal. 

Length  of  Columns  in  Ft. 

Sectional  Area. 
Inches. 

Weight  in  Lb.  of 
Columns  per 
Ft.  of  Length. 

8 

10 

12 

14 

16  | 

18 

20 

22 

24 

Tons. 

Tons. 

Tons. 

Tons. 

1 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

6 

£ 

26.2 

23.0 

20.1 

17.5 

15.2 

13.2 

11.5 

8.6 

26.95 

6 

f 

37.5 

33.0 

28.8 

25.0 

21.7 

18.9 

16.5 

12.4 

38.59 

6 

7 

42.7 

37.6 

32.8 

28.5 

24.7 

21.5 

18.8 

14.1 

43.96 

6 

1 

47.6 

41.9 

36.5 

3i.8 

27.6 

24.0 

21.0 

15.7 

49.01 

6 

1| 

52.2 

46.0 

40.1 

34.8 

30.2 

26.3 

23.0 

17.2 

53.76 

7 

f 

47.7 

43.1 

38.5 

34.3 

30.4 

26.9 

23.9 

21.2 

18.9 

14.7 

45.96 

7 

l 

61.1 

55.2 

49.3 

43.8 

38.9 

34.4 

30.6 

27.1 

24.2 

18.9 

58.90 

7 

1} 

67.2 

60.8 

54.3 

48.3 

42.8 

37.9 

33.7 

29.9 

26.7 

20.8 

64.77 

8 

2 

57.9 

53.3 

48.6 

44.1 

39.7 

35.8 

32.2 

28.9 

26.1 

17.1 

53.29 

8 

l 

74.6 

68.7 

62.5 

56.7 

51.1 

46.0 

41.4 

37.3 

33.6 

22.0 

68.64 

8 

1£ 

89.9 

82.8 

75.5 

68.4 

61.7 

55.5 

49.9 

44.9 

40.5 

26.5 

82.71 

9 

f 

68.1 

63.6 

58.9 

54.2 

49.6 

45.2 

41.2 

37.5 

34.1 

19.4 

60.65 

9 

l 

88.0 

82.3 

76.2 

70.0 

64.1 

58.4 

53.2 

48.4 

44.1 

25.1 

78.40 

9 

H 

106.6 

99.6 

92.2 

84.8 

77.6 

70.8 

64.4 

58.7 

53.4 

30.4 

94.94 

9 

U 

123.8 

115.7 

107.1 

98.5 

90.1 

82.2 

74.8 

68.1 

62.0 

35.3 

110.26 

9 

H 

139.6 

130.5 

120.8 

111.1 

101.6 

92.7 

84.4 

76.8 

69.9 

39.9 

124.36 

10 

1 

101.4 

95.9 

89.8 

83.6 

. 77.4 

71.5 

65.8 

60.5 

55.5 

28.3 

88.23 

10 

H 

123.3 

116.5 

109.1 

101.6 

94.1 

86.8 

79.9 

73.4 

67.5 

34.4 

107.23 

10 

1£ 

143.7 

135.8 

127.3 

118.5 

109.7 

101.2 

93.2 

85.6 

78.7 

40.1 

124.99 

10 

If 

162.7 

153.8 

144.1 

134.1 

124.2 

114.6 

105.5 

97.0 

89.1 

45.4 

141.65 

11 

1 

114.8 

109.4 

103.5 

97.3 

91.0 

84.8 

80.2 

73.1 

67.7 

31.4 

98.03 

11 

H 

139.9 

133.3 

126.1 

118.6 

110.9 

103.3 

97.8 

89.4, 

82.5 

38.3 

119.46 

11 

U 

163.5 

155.9 

147.5 

138.6 

128.7 

120.8 

114.3 

104.1 

96.4 

44.8 

139.68 

11 

1$ 

185.7 

177.1 

167.5 

157.5 

147.3 

137.2 

129.8 

118.3 

109.5 

50.9 

158.68 

11 

2 

206.6 

196.9 

186.3 

175.1 

163.8 

152.6 

144.4 

131.5 

121.8 

56.6 

176.44 

12 

1 

128.0 

122.9 

117.2 

111.0 

104.7 

98.4 

92.2 

86.1 

80.4 

34.6 

107.51 

12 

1£ 

156.4 

150.1 

143.1 

135.7 

127.9 

120.2 

112.6 

105.2 

98.2 

42.2 

131.41 

12 

li 

183.3 

175.9 

167.7 

159.0 

149.9 

140.9 

132.0 

123.3 

115.1 

49.5 

154.10 

12 

1$ 

208.7 

200.4 

191.0 

181.1 

170.7 

160.4 

150.3 

140.5 

131.1 

56.4 

175.53 

12 

2 

232.7 

223.4 

213.0 

201.9 

190.4 

178.9 

167.6 

156.6 

146.1 

62.8 

195.75 

13 

1 

141.2 

136.3 

130.7 

124.7 

118.5 

112.1 

105.8 

99.5 

93.5 

37.7 

117.53 

13 

li 

172.8 

166.8 

160.0 

152.7 

145.0 

137.2 

129.4 

121.8 

114.4 

46.1 

143.86 

13 

1£ 

203.0 

195.9 

187.9 

179.3 

170.3 

161.1 

152.0 

143.1 

134.3 

54.2 

168.98 

13 

W 

231.6 

223.6 

214.5 

204.7 

194.4 

183.9 

173.5 

163.3 

153.3 

61.9 

192.88 

13 

2 

258.9 

249.9 

239.7 

228.7 

217.3 

205.5 

193.9 

182.5 

171.3 

69.1 

2x5.56 

14 

1 

154.3 

149.6 

144.3 

138.5 

132.3 

125.9 

119.5 

113.1 

106.8 

40.8 

127.6C 

14 

1£ 

189.2 

183.4 

176.9 

169.7 

162.2 

154.4 

146.5 

138.6 

131.0 

50.1 

156.31 

14 

1£ 

222.6 

215.8 

208.1 

199.7 

190.8 

181.7 

172.3 

163.1 

154.1 

58.9 

183.67 

14 

If 

254.4 

246.7 

237.9 

228.3 

218.1 

207.6 

197.0 

186.5 

176.2 

67.4 

21C.0G 

14 

2 

284.8 

276.2 

266.4 

255.6 

244.2 

232.4 

220.6 

208.8 

197.2 

75.4 

235.12 

15 

1 

167.4 

162.9 

157.8 

152.1 

146.0 

139.7 

133.3 

126.8 

120.4 

44.0 

137.28 

15 

1£ 

205.5 

200.0 

193.7 

186.7 

179.3 

171.5 

163.6 

155.7 

147.9 

54.0 

168.48 

15 

1£ 

242.1 

235.7 

228.2 

220.0 

211.2 

202.1 

192.8 

183.5 

174.2 

63.6 

198.74 

15 

If 

277.2 

269.8 

261.3 

251.9 

241.9 

231.4 

220.7 

210.1 

199.5 

72.9 

227.45 

15 

2 

310.8 

302.5 

293.0 

282.5 

271.2 

259.5 

247.5 

235.5 

223.6 

1 81.7 

254.90 

j 

SPECIFIC  GRA  VITY. 


107 


Minimum  Safe-Bearing  Values  of  Masonry  Materials. 


Materials. 


Tons  per  Sq.  Ft. 


Granite,  capstone 

Squared  masonry 

Sandstone,  capstone 

Squared  masonry 

Rubble,  laid  in  lime  mortar 

Rubble,  laid  in  cement  mortar 

Limestone,  capstone 

Squared  masonry 

Rubble,  laid  in  lime  mortar 

Rubble,  laid  in  cement  mortar  

Bricks,  hard,  laid  in  lime  mortar 

Hard,  laid  in  Portland  cement  mortar  

Hard,  laid  in  Rosendale  cement  mortar  ... 
Concrete,  1 Portland,  2 sand,  5 broken  stone 


50 

25 

25 

12 

5 

10 

36 

18 

5 

10 

7 

14 

10 

10 


SPECIFIC  GRAVITY,  WEIGHT,  AND  PROPERTIES  OF  MATERIALS,  ETC. 

The  specific  gravity  of  a body  is  the  ratio  of  its  weight  to  the  weight  of 
an  equal  balk  of  pure  water,  at  a standard  temperature  (62°  F.  = 16.670°  C.). 

Some  experimenters  have  used  60°  F.  as  the  standard  temperature,  others 
32°  and  still  others,  39.1°.  To  reduce  a specific  gravity,  referred  to  water 
at  39  1°  F.,  to  the  standard  of  water  at  62°  F.,  multiply  by  1.00112. 

Given  specific  gravity  referred  to  water  at  62°  F.,  multiply  by  62.355  to 
find  the  weight  of  a cubic  foot  of  the  substance.  Given  weight  per  cubic 
foot,  to  find  specific  gravity,  multiply  by  0.016037.  . . _ 

Given  specific  gravity,  to  find  the  weight  per  cubic  inch,  multiply  by 

0. 036085. nd  ^ Specific  Gravity  of  a Solid  Heavier  Than  Water.— Weigh  the  body 
both  in  air  and  in  water,  and  divide  the  weight  in  air  by  the  difference  of 
the  weights  in  air  and  water. 

Example.— A piece  of  coal  weighs,  say,  480  grains.  Loss  of  weight 
when  weighed  in  water,  398  grains. 


1,000. 


1.206,  specific  gravity  of  the  coal  compared  with  water  at 


As  a cubic  foot  of  water  weighs,  approximately,  1,000  oz.,  the  weight  of  a 
cubic  foot  of  any  substance  can  be  found  by  multiplying  its  specific  gravity 

by To°°Fi'nd  the  Specific  Gravity  of  a Solid  Lighter  Than  Water.— Attach  to  it 
another  body  heavy  enough  to  sink  it;  weigh  severally  the  compound  mass 
and  the  heavier  body  in  water,  divide  the  weight  of  the  body  in  air  by  the 
weight  of  the  body  in  air  plus  the  weight  of  the  sinker  in  water  minus  the 
combined  weight  of  the  sinker  and  body  in  water. 

To  Find  the  Specific  Gravity  of  a Fluid.— Weigh  both  in  and  out  of  the  fluid 
a solid  (insoluble)  of  known  specific  gravity,  and  divide  the  product  of  the 
weight  lost  in  the  fluid  and  the  specific  gravity  of  the  solid  by  the  weight  of 

th¥he  weight  of  a cubic  foot  of  water  at  a temperature  of  62°  is  about 
1 000  oz.  avoirdupois,  and  the  specific  gravity  of  a body,  water  being  1,000, 
shows  the  weight  of  a cubic  foot  of  that  body  in  ounces  avoirdupois. 
Then,  if  the  magnitude  of  the  body  be  known,  its  weight  can  be  com- 
puted; or,  if  its  weight  be  known,  its  magnitude  can  be  calculated,  provided 
we  know  its  specific  gravity;  or,  of  the  magnitude,  weight,  and  specific 
gravity,  any  two  being  known,  the  third  may  be  found. 

To  Find  the  Magnitude  of  a Body  in  Cubic  Feet  From  its  Weight.— Divide  the 
weight  of  the  body  in  ounces  by  1,000  times  the  specific  gravity  of  the  body. 

To  Find  the  Weight  of  a Body  in  Ounces  From  Its  Magnitude.— Divide  the 
weight  of  the  body  in  ounces  by  the  specific  gravity  of  the  substance  mul- 
tiplied by  1,000.  . , , .,  . ,,  . 

Note— The  specific  gravitv  of  any  substance  is  equal  to  its  weight  in 
grams  per  cubic  centimeter.  (See  table  of  metric  weights  and  measures.) 


108 


WEIGHT  OF  MATERIALS . 
Specific  Gravity  of  Substances- 


Substance. 


Air,  atmospheric;  at  60°  F.  under  pressure  of  1 at- 
mosphere, or  14.7  lb.  per  sq.  in. 

Alcohol,  pure  

Alcohol,  of  commerce 

Aluminum 

Anthracite*  coal - 

Asphaltum 

Brass,  cast  

Brass,  rolled  - 

Bronze,  gun  metal " 

Brick,  best  pressed 

Brick,  common  hard 

Carbonic-acid  gas 

Clay,  dry,  in  lumps,  loose 

Clay,  potters’,  dry ...  - 

Coke, f loose,  of  good  coal 

Coal,  bituminous  % 

Coal,  bituminous,  broken  loose . 

Coal,  bituminous,  moderately  shaken 

Copper,  cast 

Copper,  rolled 

Earth,  common  ioam,  perfectly  dry,  loose 

Earth,  common  loam,  perfectly  dry,  shaken ■■■•" 

Earth,  common  loam, perfectly  dry  , moderately  packed 

Earth,  common  loam,  slightly  moist,  loose  

Earth,  common  loam,  more  moist,  loose 

Earth,  common  loam,  more  moist,  shaken 

Earth,  common  loam,  more  moist,  packed 

Earth,  common  loam,  as  a soft  flowing  mud 

Earth,  common  loam,  as  a soft  mud  packed 

Gold,  cast,  pure  or  24  carat 

Gravel  

Gutta  percha 

Gypsum  (plaster  of  Pans) 

Gypsum,  in  irregular  lumps 

Gypsum,  ground,  loose 

Gypsum,  ground,  well  shaken 

Gvnsum,  calcined,  loose 

Hydrogen  gas,  14£  times  lighter  than  air  and  lb  times 

lighter  than  oxygen 

Ice - 

Iron,  cast 

Iron,  rolled  bars 

Iron,  sheet 

Iron,  wrought  

Lead  - 

Lime,  q uick - - • - - - • ■ — • ■ - v ■ - • • • * vr  • 

Lime,  quick,  ground,  loose,  per  struck  bushel,  66  lb. 


Mercury,  at  32°  F. 

Mercury,  at  60°  F 

Mercury,  at  212°  F ■ ■ ;- 

Nitrogen  gas,  & part  lighter  than  air 
Oils,  whale,  olive  


Average 
Specific  ^ 
Gravity.  ( 

Average 
Weight  per 
Du.  Ft.  Lb. 

.00123 

.0765 

.793 

49.43 

.834 

52.1 

2.66 

166.0 

1.5 

93.5 

1.4 

, 87.3 

8.1 

504.0 

8.4 

524.0 

8.5 

529.0 

150.0 

125.0 

.00187 

.1167 

63.0 

1.9 

119.0 

27.5 

1.35 

84.0 

50.0 

54.0 

8.7 

542.0 

8.9 

555.0 

.25 

15.6 

76.0 

87.0 

95.0 

78.0 

80.0 

90.0 

96.0 
108.0 
115.0 

19.26 

1,204.0 

98.0 

.98 

61.1 

2.27 

141.6 

82.0 

56.0 

64.0 

56.0 

.92 

7.21 

7.65 

7.77 

11.38 
1.5 

13.62 

13.58 

13.38 

.92 


.00527 

57.4 

450.0 

480.0 

485.0 

485.0 
709.6 

95.0 

53.0 

849.0 

846.0 

836.0 
.0744 

57.3 


* Anthracite  increases  about  75  per  cent,  in  bulk  when  broken  to  any  market  size.  A ton 

’“n'A^e^SeTSoolw&sfrom  35  to  42  lb,  A «ou  occupies « M» M -« ; «• 

1 1 heaped  bushel,  loose,  weighs  about  74  lb.,  and  a ton  occupies  from  43  to  48  o.  ft.  Bttumt 
nous  coal,  when  broken,  occupies  75  per  cent,  more  space  than  in  the  solid. 


L 


- 


SPECIFIC  GRAVITY. 

Specific  Gravity  of  Substances— (Contin ued). 


109 


Substance. 


Oxygen  gas,  part  heavier  than  air 

Petroieum  

Powder - 

Rosin 

Silver 

Slate  

Steel  

Sulphur  — »—*••• 

Tallow  

cast  

Water,  purej  rain  or  distilled,  at  32°  F.,  Barom.  30 in. 
Water,  pure,  rain  or  distilled,  at  62°  F.,  Barom.  30  in. 
Water,  pure,  rain  or  distilled,  at  212°  F.,  Barom.  30  in. 

Water,  sea,  average - 

Zinc  


Average 

Specific 

Gravity. 

Average 
Weight  per 
Cu.  Ft.  Lb. 

.00136 

.0846 

.878 

54.8 

1.5-1.85 

105.0 

1.1 

68.6 

10.5 

655.0 

2.8 

175.0 

7.85 

490.0 

2.0 

125.0 

.94 

58.6 

7.35 

459.0 

62.417 

1.00 

62.355 

59.7 

1.028 

64.08 

7.00 

437.5 

The  following  table  gives  the  specific  gravities  of  various  coals: 


Name  of  Coal. 

Sp.  Gr. 

Weight  of  a 
Cu.  Ft.  Lb. 

Weight  of  a 
Cu.Yd.  Tons. 

Newcastle  Hartley,  England 

1.29 

80.6 

.972 

Wigan,  4 ft.,  England 

1.20 

75.0 

.914 

Portland,  England 

1.30 

81.2 

.978 

Anthracite,  Wales 

1.39 

86.9 

1.047 

Eglington,  Scotland 

1.25 

78.1 

.941 

Anthracite,  Irish 

1.59 

99.4 

1.193 

Anthracite,  Pennsylvania 

1.55 

96.9 

1.167 

Bituminous,  Pennsylvania 

1.40 

87.5 

. 1.054 

Block  coal,  Indiana 

1.27 

79.4 

.956 

SPECIFIC  GRAVITY  AND  WEIGHT  OF  PREPARED  ANTHRACITE  COAL. 

To  Mr.  Irving  A.  Stearns,  General  Superintendent  of  the  Pennsylvania 
Railroad  Co.’s  Coal  Department,  we  are  indebted  for  the  following  sum- 
mary of  tests  made  by  the  mining  engineers  of  the  company. 

In  a series  of  tests  to  ascertain  the  specific  gravity  of  the  coal  from  differ- 
ent seams  worked  by  the  company,  it  was  found  that  the  average  specific 
gravity  was  1.4784,  and  the  average  weight  per  cubic  foot  was  92.50  lb.  This 
was  calculated  for  space  filled  at  breaker  without  settling.  Add  5 °jo  for 
packed  spaces  of  large  heaps. 

Weight  per  Cubic  Foot  of  Susquehanna  Coal  Co.’s  White  Ash  Anthra- 
cite Coal. 


Size. 

Size  of  Mesh. 

Weight  peri 
Cu.  Ft.  1 
Pounds.  1 

> 

Cu.Ft.  Froml 

Over. 

Through. 

Cu.  Ft.  Solid. 

Lump 

Broken 

4£"  to  9 " 
2f"  to  2f ' 

3i"  to  4i" 

57 

53 

1.614 
, 1.755 

Egg 

11"  to  2|" 

2f"  to  2£" 

52 

1.769 

Large  stove 

H"  to  H" 

1 *"  to  2i" 

51* 

1.787 

Small  stove 

1 " to  H" 

H"  to  H" 

5H 

1.795 

Chestnut 

I"  to  V' 

1 " to  li" 

51  I 

| 1.804 

Pea 

I"  to  f" 

£"to 

50* 

1.813 

No.  1 buckwheat 

xV'to  f" 

f"  to 

•50* 

1.813 

.No.  2 buckwheat 

TV'to  §" 

50* 

1.813 

110 


WEIGHT  OF  MATERIALS. 


LINE  SHAFTING. 

Shafting1  is  usually  made  cylindrically  true,  either  by  a special  rolling 
process,  when  it  is  known  as  cold-rolled  shafting  oi  it  is  turned  u|p  m a 
machine  called  a lathe.  In  the  latter  case,  it  is  called  bright  shafting.  What 
is  known  as  black  shafting  is  simply  bar  iron  rolled  by  the  ordinary  process 
and  turned  where  it  receives  the  couplings  pulleys,  bearings  etc 

Bright  turned  shafting  varies  m diameter  by  4 m.  up  to  about  32  in.  m 
diameter;  above  this  diameter  the  shafting  varies  by  2 in-  Tiie  actual 
diameter  of  a bright  shaft  is  less  than  the  commercial  diameter  it 

being  designated  from  the  diameter  of  the  ordinary  round  bar  iron,  from 
whfch  it  is  turned.  Thus,  a length  of  what  is  called  3"  bright  shafting  is 

°n^Cold-roiied  shutting  is  designated  by  its  commercial  diameter;  thus,  a 
leneth  of  what  is  called  3"  shafting  is  3 in.  in  diameter. 

Cold-rolled  iron  is  considerably  stronger  than  ordinary  turned  wrought 
iron*  the  increased  strength  being  due  to  the  process  of  rolling,  which  seems 
to°  compreffi  tho  metal  and  so  make  it  denser-not  merely  skin  deep,  but 
practically  throughout  the  whole  diameter. 

STRENGTH  OF  SHAFTING. 

D = diameter  of  shaft; 

jt  = revolutions  per  minute; 

H = horsepower  transmitted; 

C = constant  given  in  table. 

Constants  foe,  Line  Shafting. 

in  the  accompanying  table  the  bearings  are  WPOsed  to  » 

excessive  bending;  also, 
in  the  third  vertical  col- 
umn, an  average  num- 
ber and  weight  of  pulleys 
and  power  given  off  is 
assumed. 

In  determining  the 
constants  given  in  the 
accompanying  table,  al- 


No Pulleys 

Pulleys 

Material  of  Shaft. 

Between 

Between 

Bearings. 

Bearings. 

Steel  or  cold-rolled  iron 

65 

85 

Wrought  iron 

Cast  iron - 

70 

9C 

95 

120 

ii 


D3  X R 


1)  = 


s 1C  X H 

M R 


R = 


CXH 

H * 


Shafts  are  subject  to  forces  that  produce  stresses  of  two  kmds-transverse 
and  torsional.  When  the  machines  to  bedriven  are  below  the  shaft,  there 
is  a transverse  stress  on  the  shaft,  due  to  the  weight  of  the  shaft  itself, ■ 
nullev  and  tension  of  the  belt.  Sometimes  the  power  is  taken  off  horizon 
tally  on  one  side,  in  which  case  the  tension  of  the  belt 
transverse  stress,  while  the  weight  of  the  pulley  acts  with  the 
shaft  to  produce  a vertical  transverse  stress.  When  the  machinery  to  oe 
driven  is  placed  on  the  floor  above  the  shaft,  the  tension  of  the  belt  produces 
a transverse  stress  in  opposite  direction  to  that  due  to  the  weight  of  the 

S^^The  torsional  strength  of  shafts,  or  their  resistance  to  breaking  by.  twisting, 
is  nronortional  to  the  cube  of  their  diameter.  Their  stiffness  or  resistance  to 
bending  is  proportional  to  the  fourth  power  of  their  diameters,  ^d  inversely 
proportional  to  the  cube  of  the  lengths  of  their  spans.  No  simple 
formula  can  be  given  that  will  sately  apply  to  engine  and  other  shafting 
that  is  subjected  to  the  bending  stresses  produced  by  overhung  cranks,  the 
weight  of  heavy  flywheels,  the  poll  of  large  helts  or  to  ^evere^shocks  p - 
duced  by  the  intermittent  action  of  the  power  or  load.  The  emulations  101 
such  shafts  should  always  be  based  on  the  special  conditions  h 

In  the  following  table  is  given  the  maximum  distance  between  the  bear 
ings  of  some  continuous  shafts  that  are  used  for the  d^iwavs 

Pulleys  from  which  considerable  power  is  to  be  taken  should  always 

be  Fen^hsof  shafts  composing  a line  of  shaft- 

ing  may  be  proportional  to  the  quantity  of  power  delivered  by 

length.  In  this  connection,  the  positions  of  the  various  pulleys  depend 


WEIGHT  OF  CASTINGS. 


Ill 


on  the  distance  between  the  pulley  and  the  bearing,  and  on  the  amount  of 
power  given  off  by  the  pulleys.  Suppose,  for  example,  that  a piece  of  shaft- 
ing delivers  a certain  amount  of  _____ 

power;  then,  it  is  obvious  that  the 
shaft  will  deflect  or  bend  less  if  the 
pulley  transmitting  that  power  be 
placed  close  to  a hanger  or  bear- 
ing, than  if  it  be  placed  midway 
between  the  two  hangers  or  bear- 
ings. It  is  impossible  to  give  any 
rule  for  the  proper  distance  of  bear- 
ings that  could  be  used  univer- 
sally, as  in  some  cases  the  require- 
ments demand  that  the  bearings 
be  nearer  together  than  in  others. 

If  the  work  done  by  a line  of  shaft- 
ing is  distributed  quite  equally 
along  its  entire  length,  and  the 
power  can  be  applied  near  the 
middle,  the  strength  of  the  shaft 
need  be  only  half  as  great  as  would 

be  required  if  the  power  were  applied  at  one  end  of  the  shaft. 


Diameter 
of  Shaft. 
Inches. 

Distance  Between  Bearings. 
Feet. 

Wrought-Iron 

Shaft. 

Steel  Shaft. 

2 

11 

11.50 

3 

13 

13.75 

4 

15 

15.75 

5 

17 

18.25 

6 

19 

20.00 

7 

21 

22.25 

8 

23 

24.00 

9 

25 

26.00 

WEIGHT  OF  CASTINGS. 


To  Find  the  Approximate  Weight  of  a Casting.— For  iron,  multiply  the  weight 
of  the  pattern  by  20.  Copper  is  £ heavier;  lead,  f heavier;  brass,  £ heavier; 
and  zinc  is  T%7<y  as  heavy.  _ 


Thickness 

or 

Diameter. 

Inches. 

Weight  of 
a Square 
Foot. 
Pounds. 

Weight  of  a 
Square  Bar 
1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 
1 Ft.  Long. 
Pounds. 

Thickness 

or 

Diameter. 

Inches. 

Weight  of 
a Square 
Foot. 
Pounds. 

Weight  of  a 
Square  Bar 
1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 
1 Ft.  Long. 
Pounds. 

i 

9.375 

.195 

.154 

4£ 

168.7 

63.33 

49.71 

| 

14.06 

.440 

.346 

4| 

173.4 

66.86 

52.52 

8 

£ 

18.75 

. .781 

.610 

4f 

178.1 

70.52 

55.39 

£ 

23.44 

1.221 

.959 

4£ 

182.8 

74.27 

58.34 

£ 

28.12 

1.758 

1.381 

5 

187.5 

78.12 

61.37 

7. 

32.81 

2.393 

1.880 

5£ 

196.9 

86.14 

67.65 

I8 

37.50 

3.125 

2.455 

5£ 

206.2 

94.54 

74.26 

42.19 

3.955 

3.107 

51 

215.6 

103.3 

81.16 

i| 

46.87 

4.883 

3.835 

6 

225.0 

112.5 

88.36 

if 

51.57 

5.909 

4.640 

6£ 

234.4 

122.1 

95.89 

n 

56.26 

7.033 

5.523 

6£ 

243.8 

132.0 

103.7 

if 

60.94 

8.253 

6.484 

253.1 

142.4 

111.9 

if 

65.63 

9.572 

7.518 

7 

262.5 

153.2 

120.2 

i| 

70.32 

10.99 

8.630 

7* 

271.9 

164.2 

129.0 

2 

75.01 

12.50 

9.821 

7£ 

281.3 

175.8 

138.1 

2 £ 

79.70 

14.11 

11.09 

72 

290.7 

187.7 

147.4 

84.40 

15.83 

12.43 

8 

300.0 

200.1 

157.0 

2f 

89.07 

17.63 

13.85 

8i 

309.4 

212.7 

167.0 

2| 

93.75 

19.54 

15.34 

8£ 

318.8 

225.8 

177.3 

2£ 

98.44 

21.54 

16.56 

82 

328.2 

239.3 

187.9 

2f 

103.2 

23.64 

18.56 

9 

337.4 

253.1 

198.8 

2 £ 

107.8 

25.84 

20.29 

92 

346.8 

267.4 

210.0 

3 

112.6 

28.13 

22.10 

k 

356.2 

282.1 

221.5 

3£ 

117.3 

30.52 

23.97 

92 

365.6 

297.0 

233.3 

31 

121.8 

33.01 

25.93 

10 

375.0 

312.5 

245.5 

3f 

126.5 

35.60 

27.95 

102 

384.4 

328.4 

257.8 

3i 

131.2 

38.28 

30.07 

102 

393.7 

344.5 

270.6 

3| 

135.9 

41.07 

32.25 

102 

403.1 

361.2 

283.7 

31 

140.6 

43.95 

34.51 

11 

412.5 

378.2 

297.0 

31 

145.3 

46.93 

36.85 

112 

421.9 

395.5 

310.6 

4 

150.0 

50.01 

39.27 

1H 

431.2 

413.3 

324.6 

41 

154.7 

53.18 

41.77 

112 

440.6 

431.4 

338.8 

41 

. 41 

159.3 

164.0 

56.46 

59.82 

44.33 

46.99 

12 

450.0 

450.0 

353.4 

112 


WEIGHT  OF  MATERIALS. 


WEIGHTS  OF  SHEETS  AND  PLATES  OF  STEEL,  WROUGHT  IRON, 
COPPER,  AND  BRASS. 

( Cambria  Steel  Co.) 

American,  or  Brown  & Sharpe,  Gauge. 


No. 

of 

Gauge. 

Thickness. 

Inch. 

Weight  Per  Square  Foot. 

Steel. 

Iron. 

Copper. 

Brass. 

0000 

.460000 

18.7680 

18.4000 

20.8380 

19.6880 

000 

.409642 

16.7134 

16.3857 

18.5568 

17.5327 

00 

.364796 

14.8837 

14.5918 

16.5253 

15.6133 

0 

.324861 

13.2543 

12.9944 

14.7162 

13.9041 

1 

.289297 

11.8033 

11.5719 

13.1052 

12.3819 

2 

.257627 

10.5112 

10.3051 

11.6705 

11.0264 

3 

.229423 

9.3605 

9.1769 

10.3929 

9.8193 

4 

.204307 

8.3357 

8.1723 

9.2551 

8.7443 

5 

.181940 

7.4232 

7.2776 

8.2419 

7.7870 

6 

.162023 

6.6105 

6.4809 

7.3396 

6.9346 

7 

.144285 

5.8868 

5.7714 

6.5361 

6.1754 

8 

.128490 

5.2424 

5.1396 

5.8206 

5.4994 

9 

.114423 

4.6685 

4.5769 

5.1834 

4.8973 

10 

.101897 

4.1574 

4.0759 

4.6159 

4.3612 

11 

.090742 

3.7023 

3.6297 

4.1106 

3.8838 

12 

.080808 

3.2970 

3.2323 

3.6606 

3.4586 

13 

.071962 

2.9360 

2.8785 

3.2599 

3.0800 

14 

.064084 

2.6146 

2.5634 

2.9030 

2.7428 

15 

.057068 

2.3284 

2.2827 

2.5852 

2.4425 

16 

.050821 

2.0735 

2.0328 

2.3022 

2.1751 

17 

.045257 

1.8465 

1.8103 

2.0501 

1.9370 

18 

.040303 

1.6444 

1.6121 

1.8257 

1.7250 

19 

.035890 

1.4643 

1.4356 

1.6258 

1.5361 

20 

.031961 

1.3040 

1.2784 

1.4478 

1.3679 

21 

.028462 

1.1612 

1.1385 

1.2893 

1.2182 

22 

.025346 

1.0341 

1.0138 

1.1482 

1.0848 

23 

.022572 

92094 

90288 

1.0225 

.96608 

24 

.020101 

82012 

80404 

.91058 

.86032 

25 

.017900 

.73032 

.71600 

.81087 

.76612 

26 

.015941 

.65039 

.63764 

.72213 

.68227 

27 

.014195 

.57916 

.56780 

.64303 

.60755 

28 

.012641 

.51575 

,50564 

.57264 

.54103 

29 

.011257 

.45929 

.45028 

.50994 

.48180 

30 

.010025 

.40902 

.40100 

.45413 

.42907 

31 

.008928 

.36426 

.35712 

.40444 

.38212 

32 

.007950 

.32436 

.31800 

.36014 

.34026 

33 

.007080 

.28886 

.28320 

.32072 

.30302 

34 

.006305 

.25724 

.25220 

.28562 

.26985 

35 

.005615 

.22909 

.22460 

.25436 

.24032 

36 

.005000 

.20400 

.20000 

.22650 

.21400 

37 

.004453 

.18168 

.17812 

.20172 

.19059 

38 

.003965 

,16177 

.15860 

.17961 

.16970 

39 

.003531 

.14406 

1 .14124 

.15995 

.15113 

40 

.003144 

1 

.12828 

.12576 

.14242 

.13456 

CAST-IRON  PIPE. 


113 


WEIGHT  OF  CAST-IRON  PIPE  PER  FOOT  IN  POUNDS. 

These  weights  are  for  plain  pipe.  For  hautbov  pipe,  add  8 in.  in  length 
for  each  joint.  For  copper,  add  for  lead,  for  welded  iron,  T?. 


Diam- 
eter of 
Bore. 
Inches. 

Thickness  of  Pipe. 

Inches. 

i 

4 

3. 

8 

a 

8 

f 

•7 

8 

1 

H 

H 

If 

lk 

If 

2 

1 

3.07 

5.07 

7.38 

li 

3.69 

6.00 

8.61 

li 

4.30 

6.92 

9.84 

If 

4.92 

7.84 

11.10 

2 

5.53 

8.76 

12.30 

16.2 

2£ 

6.15 

9.69 

13.50 

17.7 

2£ 

6.76 

10.60 

14.80 

19.2 

24.0 

2* 

7.37 

11.50 

16.00 

20.8 

25.9 

3 

7.98 

12.50 

17.20 

22.3 

27.7 

33.4 

3i 

9.21 

14.30 

19.70 

25.4 

31.4 

37.7 

4 

10.30 

16.10 

22.20 

28.5 

35.1 

42.0 

4£ 

11.70 

18.00 

24.60 

31.5 

38.8 

46.3 

5 

12.90 

19.80 

27.10 

34.6 

42.5 

50.6 

5i 

14.20 

21.70 

29.50 

37.7 

46.1 

54.9 

6 

15.40 

23.50 

32.00 

40.8 

49.8 

59.2 

68.9 

84.4 

6£ 

16.60 

25.40 

34.50 

43.8 

53.5 

63.5 

73.8 

7 

17.80 

27.20 

36.90 

46.9 

57.2 

67.8 

78.7 

89.4 

7£ 

19.10 

29.10 

39.40 

50.0 

60.9 

72.1 

83.7 

95.5 

108 

127 

8 

20.30 

30.90 

41.80 

53.1 

64.6 

76.4 

88.6 

101.0 

114 

148 

8£ 

21.50 

32.80 

44.30 

56.1 

68.3 

80.7 

93.5 

107.0 

120 

134 

9 

22.80 

34.60 

46.80 

59.2 

72.0 

85.1 

98.4 

112.0 

126 

140 

155 

9£ 

24.00 

36.40 

49.20 

62.3 

75.7 

89.3 

103.0 

118.0 

132 

147 

163 

202 

10 

25.10 

38.30 

51.70 

65.3 

79.4 

93.6 

108.0 

123.0 

138 

164 

170 

11 

27.60 

42.00 

56.60 

71.5 

86.7 

102.0 

118.0 

134.0 

151 

168 

185 

220 

275 

12 

30.00 

45.70 

61.50 

77.7 

94.1 

111.0 

128.0 

145.0 

163 

181 

199 

237 

13 

32.50 

49.40 

66.40 

83.8 

102.0 

120.0 

138.0 

156.0 

175 

195 

214 

254 

294 

14 

35.00 

53.10 

71.40 

89.4 

109.0 

128.0 

148.0 

168.0 

188 

208 

229 

271 

314 

15 

37.40 

56.70 

76.30 

96.1 

116.0 

137.0 

158.0 

179.0 

200 

222 

244 

289 

334 

16 

39.10 

60.40 

81.20 

102.0 

124.0 

145.0 

167.0 

190.0 

212 

235 

258 

306 

353 

17 

42.30 

64.10 

86.10 

108.0 

131.0 

154.0 

177.0 

201.0 

225 

249 

273 

323 

373 

18 

44.80 

67.80 

91.00 

115.0 

139.0 

163.0 

187.0 

212.0 

237 

262 

288 

340 

393 

19 

47.30 

71.50 

96.00 

121.0 

146.0 

171.0 

197.0 

223.0 

249 

276 

303 

357 

412 

20 

49.70 

75.20 

101.00 

127.0 

153.0 

180.0 

207.0 

234.0 

261 

289 

317 

375 

432 

21 

52.20 

78.90 

106.00 

133.0 

161.0 

188.0 

217.0 

245.0 

274 

303 

332 

392 

452 

22 

54.60 

• 82.60 

111.00 

139.0 

168.0 

196.0 

227.0 

256.0 

286 

316 

347 

409 

471 

23 

57.10 

' 86.30 

116.00 

145.0 

175.0 

206.0 

236.0 

267.0 

298 

330 

362 

426 

491 

24 

59.60 

i 89.90 

121.00 

1 152.0 

183.0 

214.0 

246.0 

278.0 

311 

343 

375 

444 

511 

25 

62.00 

i 93.60 

126.00 

1 158.0 

190.0 

223.0 

256.0 

' 289.0 

323 

357 

391 

461 

531 

26 

64.50 

i 97.30 

' 131.00 

1 164.0 

198.0 

231.0 

266.0 

i 300.0 

' 335 

370 

406 

478 

550 

27 

66.90 

1 101.00 

1 135.00 

1 170.0 

• 205.0 

240.0 

' 276.0 

i 311.0 

i 348 

384 

421 

495 

570 

28 

69.40 

1 105.00 

1 140.00 

1 176.0 

i 212.0 

249.0 

1 286.0 

i 323.0 

i 360 

397 

436 

512 

590 

29 

71.80 

1 109.00 

1 145.00 

1 182.0 

i 220.0 

i 257.0 

i 295.0 

> 334.0 

i 372 

411 

450 

530 

609 

30 

74.2C 

> 112.00 

1 150.00 

1 188.0 

l 227.0 

i 266.0 

i| 305.0 

1 345.0 

l 384 

424 

465 

| 547 

| 629 

DIAMETER-  AND  NUMBER  OF  WOOD  SCREWS. 


Formulas  for  Wood  Screws. 

No. 

Diameter. 

No. 

Diameter. 

No.* 

Diameter. 

N = 

number 

0 

.056 

11 

.201 

22 

.347 

I)  =- 

diameter 

1 

.069 

12 

.215 

23 

.361 

D - 

{NX  -01325)  + .056 

2 

.082 

13 

.228 

24 

,374 

D - .056 

3 

.096 

14 

.241 

25 

.387 

N — 

.01325 

4 

5 

.109 

.122 

15 

16 

.255 

.268 

26 

27 

401 

414 

6 

.135 

17 

281 

28 

427 

7 

.149 

18 

.293 

29 

440 

8 

.162 

19 

,308 

30 

453 

9 

.175 

20 

.321 

10 

.188 

21 

.334 

114 


WEIGHT  OF  MATERIALS. 


WEIGHT  OF  WROUGHT  IRON. 

The  following  table  is  for  wrought  iron.  Multiply  by  .95  for  weight  of  cast 
iron;  by  1.02  for  steel;  by  1.16  for  copper;  by  1.09  for  brass;  by  1.48  for  lead. 


Thickness 

or 

Diameter. 

Inches. 

Weight 
of  a 

Square  Foot. 
Pounds. 

Weight  of  a 
Square  Bar 
1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 
1 Ft.  Long. 
Pounds. 

Thickness 

or 

Diameter. 

Inches. 

Weight  . 
of  a 

Square  Foot. 
Pounds. 

Weight  of  a 
Square  Bar 
1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 
1 Ft.  Long. 
Pounds. 

5.052 

.0526 

.0414 

4f 

176.8 

64.47 

50.63 

1 

10.10 

.2105 

.1653 

4k 

181.9 

68.20 

53.57 

| 

15.16 

.4736 

.3720 

4f 

186.9 

72.05 

56.59 

20.21 

.8420 

.6613 

4f 

192.0 

75.99 

59.69 

| 

25.26 

1.316 

1.033 

4f 

•197.0 

80.05 

62.87 

f 

30.31 

1.895 

1.488 

5 

202.1 

84.20 

66.13 

7_ 

35.37 

2.579 

2.025 

5f 

212.2 

92.83 

72.91 

l6 

40.42 

3.368 

2.645 

5f 

222.3 

101.9 

80.02 

lj 

45.47 

4.263 

3.348 

5f 

232.4 

111.4 

87.46 

It 

50.52 

5.263 

4.133 

6 

242.5 

121.3 

95.23 

If 

55.57 

6.368 

5.001 

6f 

252.6 

131.6 

103.3 

1£ 

60.63 

7.578 

5.952 

6i 

262.7 

142.3 

111.8 

If 

65.68 

8.893 

6.985 

6f 

272.8 

153.5 

120.5 

If 

70.73 

10.31 

8.101 

7 

282.9 

165.0 

129.6 

If 

75.78 

11.84 

9.300 

7j 

293.0 

177.0 

139.0 

2 

80.83 

13.47 

10.58 

7i 

303.1 

189.5 

148.8 

2£ 

85.89 

15.21 

11.95 

7f 

313.2 

202.3 

158.9 

2f 

90.94 

17.05 

13.39 

8 

323.3 

215.6 

169.3 

2f 

95.99 

19.00 

14.92 

8i 

333.4 

229.3 

180.1 

2\ 

101.0 

21.05 

16.53 

8£ 

343.5 

243.4 

191.1 

2f 

106.1 

23.21 

18.23 

8f 

353.6 

247.9 

202.5 

2f 

111.2 

25.47 

20.01 

9 

363.8 

272.8 

214.3 

2f 

116.2 

27.84 

21.87 

9| 

373.9 

288.2 

226.3 

3 

121.3 

30.31 

23.81 

9f 

384.0 

304.0 

238.7 

3f 

126.3 

32.89 

25.83 

9f 

394.1 

320.2 

251.5 

3f 

131.4 

35.57 

27.94 

10 

404.2 

336.8 

264.5 

3f 

136.4 

38.37 

30.13 

m 

414.3 

353.9 

277.9 

3f 

141.5 

41.26 

32.41 

10k 

424.4 

371.3 

291.6 

3| 

146.5 

44.26 

34.76 

lOf 

434.5 

389.2 

305.7 

3f 

151.6 

47.37 

37.20 

ii 

444.6 

407.5 

320.1 

3f 

156.6 

50.57 

39.72 

ni 

454.7 

426.3 

334.8 

4 

161.7 

53.89 

42.33 

lii 

464.8 

445.4 

349.8 

41 

166.7 

57.31 

45.01 

iif 

474.9 

465.0 

365.2 

41 

171.8 

60.84 

47.78 

12 

485.0 

485.0 

380.9 

Spikes  and  Nails. 


Starn 

Length. 

lard  Steel-Wire  1 
Common. 

ST ails. 

Finishing. 

Steel-Wire  Spikes. 

Common  Iron  Nails. 

Sizes. 

In. 

Diam. 

No.  per 

Diam. 

No.  per 

Length. 

Diam. 

No.  per 

Size* 

Length. 

No.  per 

In. 

Lb. 

In. 

Lb. 

In. 

In. 

Lb. 

In. 

Lb. 

2d 

1 

.0524 

1,060 

.0453 

1,558 

3 

.1620 

41 

2d 

1 

800 

3d 

li 

.0588 

640 

.0508 

913 

3i 

.1819 

• 30 

3d 

li 

400 

4d 

li 

.0720 

380 

.0508 

761 

4 

.2043 

23 

4d 

li 

300 

5d 

If 

.0764 

275 

.0571 

500 

4i 

.2294 

17 

5d 

If 

200 

6d 

2 

.0808 

210 

.0641 

350 

5 

.2576 

13 

6d 

2 

150 

7d 

2i 

.0858 

160 

.0641 

315 

5i 

.2893 

11 

7d 

2i 

120 

8d 

2i 

.0935 

115 

.0720 

214 

6 

.2893 

10 

8d 

2i 

85 

9d 

2f 

.0963 

93 

.0720 

195 

6i 

.2249 

7i 

9d 

2f 

75 

lOd 

3 

.1082 

77 

.0808 

137 

7 

.2249 

7 

lOd 

3 

60 

12d 

3f 

.1144 

60 

.0808 

127 

8 

.3648 

5 

12d 

3i 

50 

16d 

3i 

.1285 

48 

.0907 

90 

9 

.3648 

4i 

16d 

3i 

40 

20d 

4 

.1620 

31 

.1019 

62 

20d 

4 

20 

30d 

4i 

.1819 

22 

30d 

4i 

16 

40d 

5 

.2043 

17 

40d 

5 

14: 

50d 

5i 

.2294 

13 

50d 

5i 

11 

60d 

6 

.2576 

11 

60d 

6 

8 

WROUGHT  IRON. 


115 


Weight,  in  Pounds,  of  1 Lineal  Foot  of  Wrought  Iron— Flat. 


Multiply  by  .95  for  weight  of  cast  iron;  by  1.02  for  weight  of  steel;  by  1.16 
for  copper;  by  1.09  for  brass;  by  1.48  for  lead. 


Size. 

Inches, 

Weight. 

Pounds. 

Size. 

Inches. 

Weight. 

Pounds. 

Size. 

Inches. 

Weight. 

Pounds. 

1 X* 

0.85 

5£Xt 

6.65 

4 XI 

8.45 

ttx  £ 

1.06 

5£  X 1 

6.97 

4£  X 1 

8.98 

U X J 

1.27 

5f  X I 

7.29 

4£  X 1 

9.51 

if  X £ 

1.48 

6X| 

7.60 

4f  X I 

10.03 

2 X £ 

1.69 

5 XI 

10.56 

2£  X £ 

1.90 

i X£ 

1.69 

5£  X 1 

11.09 

2s  X 4 

2.11 

*-4  X 1 

2.11 

5£  X I 

11.62 

2f  X | 

2.32 

-*£j  X ? 

2.53 

5f  XI 

12.15 

3 X£ 

2.53 

If  Xi 

2.96 

6 XI 

12.67 

3£  X £ 

2.75 

2 Xi  ! 

! 3.38 

3£  X £ 

2.96 

2£  X 1 | 

-5.80 

1 Xf 

2.53 

3f  X £ 

3.17 

2£X£ 

4-22 

1£  X f 

3.17 

4 X£ 

3.38 

2f  X £ 

4.65 

1£  X f 

3.80 

4£X£ 

3.59 

3 X£ 

5.07 

If  Xf 

4.44 

4£  X £ 

3.80 

3£  X £ 

5.49 

2 Xf 

5.07 

4f  X £ 

4.01 

3£  X £ 

5.92 

2£Xf 

5.70 

5 X £ 

4.22 

3f  X £ 

6.33 

2£  X f 

6.33 

5£x£ 

4.44 

4 X £ 

6.76 

2f  Xf 

6.97 

X £ 

4.65 

4£  X £ 

7.18 

3 X f 

7.60 

5f  X £ 

4.86  | 

4£  X £ 

7.60 

3£  X f 

8.24 

6 X £ 

5.07 

4f  X £ 

8.03 

3£  X f 

8.87 

5 X £ 

8.45 

3f  X f 

9.51 

1 XI 

1.27 

5£  X £ 

8.87 

4 X f 

10.14 

1£  X | 

1.58 

5£  X £ 

9.30 

4£X  f 

10.77 

1|  X f 

1.90 

5f  X £ 

9.72 

4£  X f 

11.41 

If  XI 

2.22 

6 X £ 

10.14 

4f  Xf 

12.04 

2 XI 

2.53 

5 X f 

12.67 

2£  X ! 

2.85 

1 XI 

2.11 

5£  X f 

13.31 

2i  X 1 

3.17 

l£  X t 

2.64 

5£  X f 

13.94 

2f  XI 

3.49 

1£  X 1 

3.17 

5f  X f 

14.57 

3 XI 

3.80 

If  XI 

‘ 3.70 

6 Xf 

15.21 

3£  X | 

4.12 

2 XI 

4.22 

31X1 

4.44  . 

2£  X ! 

4.75 

11X1 

5.07 

3f  X 1 

4.75 

2£  X 1 

5.28 

2 XI 

6.76 

4 XI 

5.07 

2f  XI 

5.81 

3 XI 

10.14 

4£  X 1 

5.39 

3 XI 

6.33 

4X1 

13.52 

4£  X t 

5.70 

3£  X 1 

6.87 

5 XI 

16.90 

4f  X f 

6.02 

3£  X I 

7.39 

6X1 

20.28 

5 X | 

633 

3f  X I 

7.92 

7.  X 1 

23.66 

Strength  of  Metals  in  Pounds  per  Square  Inch. 


Material. 

Ultimate 

Tensile. 

Ultimate 

Compres- 

sion. 

Ultimate 

Shearing. 

Modulus 

of 

Rupture. 

Modulus 

of 

Elasticity. 

Millions. 

Wrought  iron 

50,000 

44,000 

44,000 

48,000 

27 

Shape  iron 

48,000 

26 

Structural  steel j 

60,000 

65,000 

52,000 

52,000 

60,000 

29 

Cast  iron  

18,000 

81,000 

25,000 

45,000 

12 

Steel,  castings 

70,000 

70,000 

60,000 

70,000 

30 

Brass,  cast 

24,000 

*30,000 

36,000 

20,000 

9 

Bronze,  phosphor 

50,000 

14 

Bronze,  aluminum 

75,000 

120,000 

Aluminum,  commercial 

15,000 

12,000 

12,000 

1 

11 

* Unit  stress  producing  10 $ reduction  in  original  length. 


116 


WEIGHT  OF  MATERIALS. 


Weight  of  Wrought-Iron  Boltheads,  Nuts,  and  Washers. 


Diameter  of 
Bolt. 
Inches. 

Hexagon  Heads 
and  Nuts. 
Per  Pair. 

Square  Heads 
and  Nuts. 
Per  Pair. 

Round  Washers. 
Per  Pair. 

j. 

20  to  a lb. 

16  to  a lb. 

20  to  a lb. 

4 

A 

10  to  a lb. 

8i  to  a lb. 

10  to  a lb. 

i 

5 to  a lb. 

to  a lb. 

5 to  a lb. 

a 

A 

2t  to  a lb. 

2£  to  a lb. 

3 to  a lb. 

8 

3 

2 to  a lb. 

0.56  lb. 

0.63  lb. 

7 

0.77  lb. 

0.88  lb. 

0.77  lb. 

8 

1 

1.251b. 

1.31  lb. 

1.25  lb. 

1! 

1.75  lb. 

2.10  lb. 

1.751b. 

h 

2.13  lb*. 

2.56  lb. 

2.25  lb. 

It 

3.00  lb. 

3.60  lb. 

3.25  lb. 

3.75  lb. 

4.42  lb. 

4.25  lb. 

J-2 

It 

It 

H 

2 

4.75  lb. 

5.70  lb. 

5.25  lb. 

5.75  lb. 

7.00  lb. 

6.50  lb. 

7.27  lb. 

8.72  lb. 

8.00  lb. 

8.75  lb. 

10.50  lb. 

9.60  lb. 

Weight  of  100  Bolts  With  Square  Heads  and  Nuts. 
(The  Carnegie  Steel  Co Limited.) 


! Diameter  of  Bolts. 


_L,engtu 
Under 
Head  to 
Point. 

1 

E 

pi 

— ■ — 

fW 
o'  - 

K 

& 

E 

f" 

Lb. 

Lb. 

1" 

Lb. 

11 

4.0 

7.0 

10.5 

15.2 

22.5 

39.5 

63.0 

1A 

4.4 

7.5 

11.3 

16.3 

23.8 

41.6 

66.0 

-Lf 

o 

4.8 

8.0 

12.0 

17.4 

25.2 

43.8 

69.0 

109.0 

163 

u 

9A 

5.2 

8.5 

12.8 

18.5 

26.5 

45.8 

72.0 

113.3 

169 

91 

o*5 

9.0 

13.5 

19.6 

27.8 

48.0 

75.0 

117.5 

174 

93 

5.8 

9.5 

14.3 

20.7 

29.1 

50.1 

78.0 

121.8 

180 

*4 

Q 

6.3 

10.0 

15.0 

21.8 

30.5 

52.3 

81.0 

126.0 

185 

O 

Qi 

7.0 

n.o 

16.5 

24.0 

33.1 

56.5 

87.0 

134.3 

196 

O3 

A 

7.8 

12.0 

18.0 

26.2 

35.8 

60.8 

93.1 

142.5 

207 

8.5 

13.0 

19.5 

28.4 

38.4 

65.0 

99.1 

151.0 

218 

a 

9.3 

14.0 

21.0 

30.6 

41.1 

69.3 

105.2 

159.6 

229 

0 

10.0 

15.0 

22.5 

32.8 

43.7 

73.5 

111.3 

168.0 

240 

oa 

A 

10.8 

16.0 

24.0 

35.0 

46.4 

77.8 

117.3 

176.6 

251 

u 

Ai 

25.5 

37.2 

49.0 

82.0 

123.4 

185.0 

262 

Da 

7 

27.0 

39.4 

51.7 

86.3 

129.4 

193.7 

273 

1 

71 

28.5 

41.6 

54.3 

90.5 

135.0 

202.0 

284 

* a 
Q 

30.0 

43.8 

59.6 

94.8 

141.5 

210.7 

295 

O 

Q 

46.0 

64.9 

103.3 

153.6 

227.8 

317 

V 

in 

48.2 

70.2 

111.8 

165.7 

224.8 

339 

1U 

1 1 

50.4 

75.5 

120.3 

177.8 

261.9 

360 

11 
1 0 

52.6 

80.8 

128.8 

189.9 

278.9 

382 

14 

1 Q 

86.1 

137.3 

202.0 

296.0 

404 

lo 

1 A 

. 

91.4 

145.8 

214.1 

313.0 

426 

14 

1 K 

96.7 

154.3 

226.2 

330.1 

448 

lo 

1 A 

102.0 

162.8 

238.3 

347.1 

470 

16 
1 *1 

107.3 

171.0 

250.4 

364.2 

492 

17 

1 0 

112.6 

179.5 

262.6 

381.2 

514 

18 
1 n 

117.9 

188.0 

274.7 

398.3 

536 

iy 

20 

123.2 

206.5 

286.8 

415.3 

558 

Per  Inch 

1.4 

2.1 

3.1 

4.2 

5.5 

8.5 

12.3 

16.7 

21.8 

Addit’  al. 

— 

rrr-J 

RAILROAD  IRON. 


117 


IRON  REQUIRED  FOR  ONE  MILE  OF  TRACK. 

Tons  of  Iron. 


Rule. — To  find  the  number  of  tons  of  rails  to  the  mile , divide  the  weight  per  yard 
by  7,  and  multiply  by  11.  Thus,  for  56-pound  rail,  divide  56  by  7 equal  8 , multi- 
plied by  11  equal  88  tons,  for  1 mile  of  single  track. 


. Weight  of 
Rail  per  Yard. 
Pounds. 

Tons  per  Mile. 

Weight  of 
Rail  per  Yard. 
Pounds. 

Tons  per  Mile. 

Tons. 

Pounds. 

Tons. 

Pounds. 

12 

18 

1,920 

45 

70 

1,600 

.14 

22 

48 

75 

960 

16 

25 

320 

50 

78 

1,280 

18 

28 

640 

52 

81 

1,600 

20 

31 

960 

56 

88 

22 

34 

1,280 

57 

89 

1,280 

25 

39 

640 

60 

94 

640 

26 

40 

1,920 

62 

97 

960 

27 

42 

960 

64 

100 

1,280 

28 

44 

65 

102 

* 320 

30 

47 

320 

68 

106 

1,920 

33 

51 

1,920 

70 

110 

35 

55 

72 

113 

320 

40 

62 

1,920 

76 

119 

960 

Number  of  Rails,  Splices,  and  Bolts  per  Mile  of  Track. 


Length  of 
Rail.  Feet. 

No.  of  Rails 
per  Mile. 

No.  of  Splices. 

No.  of  Bolts, 
4 to  Each 
Joint. 

No.  of  Bolts, 
6 to  Each 
Joint. 

18 

586 

1,168 

2,336 

3,504 

20 

528 

1,056 

2,112 

3,168 

21 

503 

1,006 

2,012 

3,018 

22 

480 

960 

1,920 

2,880 

24 

440 

880 

1,760 

2,640 

25 

422 

844 

1,688 

2,532 

26 

406 

812 

1,624 

2,436 

27 

391 

782 

1,564 

2,346 

28 

377 

754 

1,508 

2,262 

30 

352 

704 

1,408 

2,112 

Railroad  Spikes  per  Mile  of  Track. 


Size  Measured 
Under  Head. 

Average  No. 
per  Keg 
of  200  Lb. 

Ties  2 Ft.  Between  Centers, 
4 Spikes  to  a Tie. 

Rails  Used. 
Pounds  per 

Inches. 

Pounds. 

Kegs. 

Yard. 

X t9b 

375 

5,870 

291 

45  to  70 

5 X & 

400 

5,170 

26 

40  to  56 

5 X* 

450 

4,660 

231 

35  to  40 

44X4 

530 

3,960 

20 

28  to  35 

4 X4 

600 

3,520 

17f 

24  to  35 

HWS 

XX 

680 

720 

' 3,110 
2,910 

154 

14| 

1 

i 20  to  30 

34  X ts 
4X1 

900 

1,000 

2,350 

2,090 

11 

104 

t 16  to  25 

34  Xf 
3 X§ 

1,190 

1,240 

1,780 

1,710 

9 

84 

j-  16  to  20 

24  X 1 

1,342 

1,575 

74 

12  to  16 

118 


WIRE  ROPES . 


WIRE  ROPES. 

Wire  rot>es  for  mine  use  are  made  of  either  iron  or  steel,  and  are  geuer- 
allv  round  Flat  wire  ropes  are  sometimes  used,  but  the  round  rope  is  the 
favorite  for  many  reL>n^  and  is  generally . used  in  American  practice, 
excentina  in  some  of  the  deep  metal  mines  having  small  compartment  shafts. 

6X  Taner^ooes  are  sometimes  used,  the  idea  being  to  produce  a rope  of  um- 
fv-.T'n-i  Erpriffth  that  is  to  have  it  less  strong  and  of  less  diameter  at  the  cage 
foTSt£e?f  is  leTs^and  greater  in  strength  and  diameter- at  the 

djum^end? vd^re^he8 lc^d^^is^^eatSt.  The  theory  is  correct . and  some 
weight  of  rope  is  saved;  but  practically  there  is  not  much  ^ 

is  doubtful  whether  taper  ropes  will  ever  be  generally  used.  The  loug- 
established  conviction  that  the  best  of  all  ropes  for  colliery  use  is  a round 
one  made  of  steel  or  iron  has  never  been  overcome  and  probably  ne\er 

WllSfeei  rones  are  in  most  respects  superior  to  iron  ropes,  and  are  therefore 
crninimr  in  fa?or  lvervTear.  The  principal  advantage  of  a steel  rope  is  that 
fr  has  ! greater  stre iigt h th  a n an  iron  rope  of  equal  diameter;  consequently 
it  ^can  be  made  lighter  and  can  pass  around  pulleys  and  drums  with  less 

^Mfenfng’ tof  dmm  therefs  often  a grievous  error  made.  Men 
who  will  not  Stink  of  passing  a rope  around  a pulley  of  too  small  diameter 
will  insert  it  in  the  drum  rim  in  such  a way 
as  to  make  a very  sharp  curve,  and  make  a 
weak  point  in  the  rope  that  would  not  other- 
wise exist.  In  the  accompanying  cut  va) 
shows  the  right  and  (6)  the  wrong  way  of 
passing  the  rope  through  the  drum  rim. 

The  securing  of  the  rope  to  the  drum  or  --i 

the  drum  shaftly  several  Soils  around 

around  either  the  drum  or  the ; shaft ? a pull  ^ 

^Sn^^^^e^s^of^ur^lu^l^cases^auSe^margiif'be^veeu^th'Jb^^ 

loaded'fs  unduly  W 

wrnmmm 

i?1 sns  W 

thTroPe'shoul,l  not  be  changed  from  a large  dn,m  to 

sumebub 

mmmmmsrn 

«mn“cb^e&idtoexmU  wear  for  short  distances  at  intervals 


WIRE  ROPES. 


119 


along  the  rope.  In  the  ordinary  lay,  Fig.  (a),  the  wires  are  twisted  in 
the  opposite  direction  to  the  strands.  This  method  prevents  the  rope  from 
untwisting  when  in  use,  and  the  wires  from  unraveling  when  they  are  worn 
through  or  broken  at  the  surface.  In  the  Lang  lay,  Fig.  (6),  the  wires 
are  twisted  in  the  same  direction  as  the  strands,  thus  giving  each  wire  a 
greater  wearing  surface,  while  the  rope  is  smoother  and  will  wear  longer 
After  the  wires  begin  to  break,  unraveling  becomes  troublesome,  and  it  is 
more  difficult  to  splice  a Lang  lay  rope  than  an  ordinary  lay  one.  Hoisting 
ropes,  especially  those  used  to  raise  and  lower  men,  should  not  be  spliced 
The  locked  wire  rope,  a cross-section  of  which  is  shown  in  Fig.  (c)  consists 
of  wires  of  special  cross-section  formed  in  concentric  layers.  The  lav  of 
the  inner  wires  is  opposite  to  that  of  the  outer  ones,  and  somewhat  longer. 
This  prevents  untwisting,  and  brings  the  greater  stress  upon  the  outside 


layer,  which  is  supposed  to  give  way  first.  The  inside  layer,  although  inac- 
cessible, and  therefore  cannot  be  inspected  or  oiled,  can  be  relied  upon 
until  the  external  portion  of  the  rope  wears  out.  This  form  of  rope  has  a 
smooth  cylindrical  surface,  but  it  is  not  so  flexible  as  the  other  forms,  and  is 
most  suitable  for  haulage  purposes  or  bucket  transportation.  The  life  of  a 
steel  rope  depends  largely  on  the  conditions  to  which  it  is  subjected,  and  the 
care  it  receives.  At  some  mines  the  ropes  must  be  changed  every  six 
months,  while  at  others  the  ropes  last  for  one  year  and  longer.  Where  the 
rope  enters  the  socket  by  which  it  is  attached  to  the  cage  is  perhaps  the 
place  where  signs  of  weakness  will  first  appear.  This  point  should  be  fre- 
quently inspected,  and  a new  connection  made  every  two  or  three  months 
by  cutting  a few  feet  off  the  end  and  paying  it  out  from  the  drum  end. 


WEIGHTS  AND  STRENGTHS  OF  WIRE  ROPES. 

Flat  Ropes, 


( Trenton  Iron  Co .,  Trenton , N.J.) 


Size.  Inches. 

Approximate 
Weight  per  Foot. 
Pounds. 

Breaking  Stress. 
(Approximate.)  Pounds. 

Iron. 

Cast  Steel. 

2 X| 

1.35 

20,000 

40,000 

2|X| 

1.70 

25,000 

50,000 

3X1 

2.05 

30,000 

60,000 

3|  X I 

2.40 

35,000 

70,000 

4 XI 

2.75 

40,000 

80,000 

5 X | 

3.45 

50,000 

100,000 

6 X | 

4.15 

60,000 

120,000 

3X1 

2.40 

37,500 

75,000 

3|X  | 

2.S5 

43,750 

87,500 

4 XI 

3.30 

50,000 

100,000 

5 X I 

4.20 

62,500 

125,000 

6 Xi 

5.10 

75,000 

150,000 

7 XI 

6.00 

87,500 

175,000 

8 XI 

6.90 

100,000 

200,000 

L safe  working  load  allow  from  one-fifth  to  one-seventh  of  the  break 

ing  stress. 

120 


WIRE  ROPES. 


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WIRE  ROPES. 


121 


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5.80 

4.80 
4.00 
3.20 

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The  wire-rope  table  given  on  pages 
120  and  121  is  a rearrangement  of  the 
standard  tables  published  in  the  cata- 
logues of  most  of  the  American  manu- 
facturers of  wire  rope. 

The  proper  working  load  given  in 
this  table  is  one-fifth  of  the  ap- 
proximate breaking  stress,  that  is, 
a factor  of  safety  of  5 is  used,  and 
when  the  values  given  in  this  table 
are  used  this  factor  is  supposed  to 
allow  for  the  bending  stress.  The 
sizes  of  sheaves  or  drums  given  in 
this  fable  are  largely  empirical,  but 
they  are  based  on  a long  experience 
in  the  use  of  wire  ropes,  and  in  most 
cases  represent  the  minimum  diam- 
eter recommended  by  the  rope  makers. 
The  factor  of  safety  of  5 assumes  ordi- 
nary conditions  of  working;  where 
the  conditions  are  extraordinary,  and 
particularly  in  cases  where  men  are 
to  be  hoisted,  a larger  factor  than  5 is 
used,  varying  from  5 to  10.  Many  ele- 
vator specifications  require  a factor  of 
10  to  be  used.  When  any  factor  but 
5 is  used,  the  proper  working  load  is 
obtained  by  dividing  the  approxi- 
mate breaking  stress  by  the  factor  of 
safety  assumed,  or,  if  we  know  the 
load  to  be  lifted  and  multiplv  this 
by  the  assumed  factor,  we  obtain  a 
certain  value,  and  by  comparing 
this  with  the  values  given  in  the 
table  for  the  approximate  breaking 
stress  we  can  determine  the  size  of 
rope,  and  the  minimum  diameter  of 
sheave  to  use. 

For  example,  suppose  it  is  desired 
to  determine  the  size  of  rope  needed 
to  hoist  a load  of  8 tons  through  a 
height  of  300  feet.  Multiplying  8 by  5, 
we  have  40  tons,  and  from  the  table 
we  find  that  the  approximate  breaking 
strength  of  a lf-inch,  crucible-steel 
hoisting  rope  is  42  tons.  Such  a rope 
weighs  2 pounds  per  foot;  hence,  the 
weight  of  the  rope  is  300  X 2 = 600 
pounds,  or  .3  of  a ton,  and  the  total 
load  on  the  rope  is  therefore  8.3  tons. 
8.3  X 5 = 41.5,  which  is  less  than  the 
approximate  breaking  stress  for  the 
given  rope.  The  proper  size  of  sheave 
or  drum  for  this  rope  is  given  by  the 
table  as  4|  feet. 

Galvanized  wire  is  sometimes  used 
in  the  manufacture  of  rope  to  prevent 
corrosion  of  the  iron  or  steel  of  the 
wire.  Galvanizing  accomplishes  this 
in  the  case  of  standing  ropes  but  is 
not  effective  for  running  ropes,  in 
which  the  friction  of  the  rope  against 
sheaves  or  drums  soon  wears  off  a por- 
tion of  the  zinc,  and  with  both  zinc 
and  iron  exposed  and  in  contact  with 
water,  corrosion  proceeds  more  rapidly 
than  it  would  if  the  zinc  were  not 
present. 


122 


WIRE  ROPES. 


flattened-strand  rope. 


Fig 


r x Fig.  2.  FlG-  3* 

able  saving  in  the  wear  of  pulleys  and  sheaves. 

Patent  Flattened-Strand  Rope. 

( From,  A.  Leschen  & Sons  Rope  Co.,  St.  Louis , Mo.) 


© 

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7.06 

6.28 

5.49 

5.10 

4.71 

4.32 

3.92 

3.53 

3.14 

2.74 

2.35 

1.96 

1.57 


Swedish  Iron, 


■;  l 


14 

14 

l 


8.50 

6.50 
5.00 
4.33 
3.71 
3.17 

2.50 
2.15 
1.70 
1.25 

.96 

.67 

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Crucible 
Cast  Steel. 


15.0 

13.2 

10.8 

9.0 

8.0 
6.8 

5.6 

4.2 
3.4 

2.6 
1.8 

1.2 

.8 


3.92 

2.40 

27.0 

5.4 

104 

54. 

3.53 

2.00 

22.5 

4.5 

94 

45. 

3.14 

1.64 

18.0 

3.6 

84 

36. 

2.75 

1.20 

13.5 

2.7 

74 

27. 

2.35 

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10.0 

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1.96 

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1.57 

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176.0 

140.0 
109  9 

94.0 

81.0 

69.0 

56.0 

47.0 

38.0 

29.0 

21.0 

15.0 

9.5 


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35.2 
28.0 
21.8 
18.8 

16.2 
13.8 
11.2 

9.4 

7.6 

5.8 
4.2 
3.0 

1.9 


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5.4 

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1.8 

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260 

211 

168 

124 

84 

67 

56 

404 

32 

224 

134 


74 

64 

54 

5 

44 

34 

24 

2 


80 

64 

53 

38 

30 

21 

13 


52.0 

42.2 
33.6 

24.8 

16.8 
13.4 

11.2 
8.1 

6.4 

4.5 
2.7 


16.0 

12.8 

10.6 

7.6 
6.0 
4.2 

2.6 


&£&.  Jilc*  Pmr^,  n ca,  ^ ““  dr““3  »*  ^ 

as  ordinary  ^ire  rope,  thus  making  unnecessary  any  change  in  plant. 


WIRE  ROPES. 


122a 


MINES  AND  MINERALS. 


mb 


WIPE  ROPES. 


SUSPENSION  CABLEWAYS. 

\ suspension  eablewav  is  a hoisting  and  conveying  device  using  a sus- 
pended cable  for  a traekwav.  There  are  two  types : the  inclined,  or  semi- 
gravitv.  Fig  1.  and  the  horizontal.  Fig.  2.  page  122a.  . 0 

The  inclined  cableway  consists  of  a cable  inclined  20°  to  22°  to  the 
horizontal,  and  passing  over  a cast-iron  addle  B on  top  of  a tower  or 
frame  A It  is  anchored  bv  logs  D buried  about  5 feet  underground,  or  from 
iron  plu<*s  secured  in  the'  rock,  when  the  rock  is  near  the  surface.  The 
trolley  carriage  G runs  down  the  incline  of  the  cableway  by  gravity  until  it 

reaches  a stop.  A hoisting  rope  E operated 
by  a winding  drum  F leads  over  a sheave 
puller  e , thence  to  a pulley  in  the  carriage  G, 
thence  to  a fall  block  if,  upwards  again  to  a 
second  pulley  in  the  carriage,  and  downwards 
again  to  the  fall  block.  Winding  in  the  rope 
heists  the  fall  block  to  the  carriage,  the  car- 
riage remaining  at  the  lower  stop.  W hen  the 
fall  block  collides  with  the  carriage,  both  the 
carriage  and  the  fall  block  are  pulled  up 
the  incline  cable,  and  when  the  carriage 
arrives  at  the  head-tower,  a gate,  or  hook.  O is 
lowered  to  hold  it  in  place.  The  fall  block  is 
then  lowered  and  the  load  discharged.  The 
eneine  F has  usually  a 10"  X 12"  double  cylin- 
der and  a single  friction  drum  37  inches  in 
diameter.  „ _ - 

An  endless  rope  H takes  several  turns 
around  the  sheave  J to  prevent  it  from  slip- 
ping. and  both  ends  are  passed  over  sheaves  h 
at  the  top  of  the  derrick,  one  end  being 
secured  to  the  front  of  the  carriage,  while 
the  other  end  is  taken  through  the  carriage 
and  around  the  return  sheave  I and  fastened 
to  the  rear  end  of  the  carriage  G.  The  end- 
less-rop*e  wheel  J is  provided  with  a band 
brake,  which,  when  applied,  holds  the  car- 
riage securelv  at  any  point  on  the  cable. 

All  ropes  pass  through  the  supporting 
trolleys  A',  which  are  connected  by  a chain  L. 
These'  trolleys  follow  the  carriage  by  gravity, 
and  the  chain  may  or  may  not  be  fast  to  the 
carriage.  , . . 

Instead  of  chain-connected  trolleys,  patent 
button-stop,  fall-rope  carriers,  which  are 
lighter,  mav  be  used.  These  are  spaced 
along  an  auxiliary  rope  on  which  buttons  are 
screwed  The  carriers  are  picked  up  by  a 
horn  on  the  front  of  the  carriage.  These  are 
said  to  be  cheaper  for  operation  than  the 
chain  trolleys.  . _ .. 

The  length  of  the  span  for  inclined  cable- 
wavs  varies  from  200  to  1.200  feet.  The  main 
rope  is  from  It  to  2£  inches  in  diameter,  the 
hoisting  rope  from  f to  # inch,  and  the  end- 
less rope  and  £ inch.  The  rope  mostly  used 
is  dx  strands,  nineteen  wires  to  the  strand, 
crucible  cast  steel.  The  hoisting  rope  lasts 
from  1 vear  to  2 vears.  and  the  main  cable  from  5 years  to  10  years.  These 
eablewav?  are  widely  used  about  slate  quarries  in  Eastern  Pennsylvania, 
where  the  operating*  expense  for  each  cable,  where  two  or  more  are  con- 
nected with  one  boiler,  is  about  §5  per  day  of  10  hours.  This  includes  the 
engineer  <team.  and  maintenance  of  the  cableway.  -v. 

The  horizontal  cableway  requires  a double  friction  drum  and  r^ersible 
link-motion  engine.  It  may  be  operated  at  any  inclination  of  the  carrying 
cable  and  either  from  the  high  or  low  point  of  the  support,  though,  if  posa" 
bfe.  it  should  be  from  the  higher  end.  The  endless,  ot  tractaoiu 
attached  to  one  of  the  drums  of  the  engine  and  the  engineer  thus^has  com 
pU^  control  of  the  carriage ; hence,  because  of  its  greater  applicability,  this 


WIRE  ROPES , 


122c 


system  is  supplanting  the  inclined,  although  the  inclined  costs  one-fourth 
less  for  installation.  The  method  of  operation  is  similar  to  the  inclined. 
The  amount  of  rope  required  is  the  same  in  each  system.  A horizontal 
cableway  of  the  Hamilton  Coal  Co.,  near  Tarentum,  Pa.,  has  a span  of  2,200 
feet.  The  stationary  rope  is  2,500  feet  long  and  2£  inches  in  diameter.  The 
hoisting  rope  is  4,500  feet  long  and  £ inch  in  diameter.  The  head-tower  is  80 
feet  high,  the  tail-tower  is  100  feet,  and  the  rope  deflects  80  feet.  The  skip 
used  holds  3 tons  of  coal  and  makes  10  trips  per  hour.  Five  men  operate  the 
plant  and  it  takes  2 tons  of  coal  for  the  engine.  Based  on  a capacity  of 
100  tons  per  day,  the  cost  of  carrying  the  coal  is  13  cents  per  ton.  For  a 
cableway  . of  average  length,  1,000-1,500  feet,  the  cost  of  operation  should  not 
be  one-half  the  above  cost.  A cableway  2,140  feet  long  was  used  in  con- 
structing the  dam  at  the  power  plant  at  Glens  Falls,  N.  Y. 

One  or  both  towers  of  a cableway  may  be  mounted  on  wheels  capable  of 
moving  on  a track  at  right  angles  to  the  cable  and  the  cableway  then  made 
to  cover  a wide  territory. 


WIRE-ROPE  TRAMWAYS. 

A tramway,  in  America,  is  a cableway  of  the  horizontal  type  consisting 
of  a number  of  spans.  In  England,  the  term  cableway  includes  tramways. 


Single  Tramways. — Single  wire-rope  tramways  have  a single  moving  rope, 
which  serves  to  support  and  advance  the  load  at  one  and  the  same  time, 
Fig.  3.  This  rope  passes  over  suitable  sheaves  at  the  intermediate  supports, 
and  the  load  is  carried  in  buckets  suspended  from  it  by  gooseneck  or 
i straight  hangers.  The  hangers  are  usually  attached  to  the  cable  by  means 
of  a clip,  which  is  either  inserted  in  the  center  of  the  cable  or  strapped  to  it. 
The  carriers  are  often  loaded  and  unloaded  while  in  motion,  the  loading 
being  accomplished  by  a traveling  mechanical  hopper  and  the  unloading  by 
a drop  bottom  to  the  bucket.  If  the  line  is  level,  or  the  grade  light,  the 
hangers  are  provided  with  box  heads  filled  with  wood  or  leather  and  rub- 
ber, which  rest  on  the  rope;  the  rubber  or  wood  providing  sufficient  friction 
to  prevent  the  hanger’s  slipping.  With  this  system,  long  spans  are  evi- 
dently out  of  the  question,  because  with  a long  span  the  angle  of  the 
rope  in  the  vertical  plane,  at  the  supports,  becomes  so  great  that  the  friction 
will  not  hold  the  box  head.  For  all  practical  purposes,  grades  exceeding 
1 : 4 are  to  be  avoided;  and  for  steeper  grades,  to  prevent  slipping,  a clamp  or 
a elip  inserted  in  the  rope  is  used  to  fasten  the  hanger  to  the  rope. 

The  single  moving-rope  tramways  carry  loads  not  exceeding  200  pounds. 
The  speed  of  the  rope  for  the  variety  in  which  the  hangers  are  fastened  to 
the  rope  may  be  as  high  as  450  feet  per  minute,  and  for  one  in  which  the 
hanger  is  loose,  200  feet  per  minute.  The  single  moving-rope  tramway  has 
a capacity  up  to  200  tons  per  day,  and  may  be  built,  say,  H to  2 miles  long. 

Double  Tramways. — The  more  satisfactory  and  substantial  kind  of  wire- 
rope  tramways  has  one  or  more  fixed  ropes  which  constitute  the  permanent 


122d 


WIRE  HOPES. 


- 


wav  and  an  endless  traction  rope.  The  loaded  carrier  travels  outwards  on 
one  fixed  cable  and  returns  by  a parallel  one  suspended  from  the  opposite 
side  of  the  same  supports.  The  terminals  have  suitable  appliances  for  load- 


ing and  unloading  the  buckets,  either  by  hand  or  automatically. 

The  intermediate  supports  are  built  of  wood  or  steel  framing,  with  sad- 
dles of  cast  iron  a.  Fig.  4,  in  which  the  fixed  cables  b rest  The  traction 
rope  c is  supported  (in  the  absence  of  a bucket)  by  the  rollers  d,  set  con- 
veniently on  the  supports.  The  load  is  carried  in  buckets  e,  or  other  con- 
trivances suitable  for  the  purpose,  which  are  suspended  from  a trolley  /, 
which  runs  on  the  fixed  cables,  the  wheels  of  which  are  large  enough  to 
pass  over  the  rope  couplings,  and  also  to  clear  the  saddles.  Grips  g attach 
the  carriers  to  the  traction  rope.  These  grips  may  be  operated  by  hand  or 

^T  hi  s i n dU  > f tramway  is  capable  of  carrying  individual  loads  up  to  1,400 
or  1,500  pounds,  not  including  the  weights  of  the  bucket  and  hanger  itself. 
The  speed  of  traction  rope  may  be  from  150  to  350  feet  per  minute.  The 
capacity  is  from  200  to  1,000  tons  per  day  of  10  hours.  These  figures  represent 
good,  safe  practice,  but  they  are  not,  of  course,  inflexible. 

The  maximum  length  of  line  which  may  be  built  in  one  section  varies 
largely  with  conditions  of  load,  spacing  of  supports,  contour  of  ground,  etc. 
Wire-rope  tramwavs  work  under  great  difficulties,  and  probablv  2*  to  4 miles 
is  the  economical  iimit.  This  has  been  exceeded,  but  the  trouble  is  that  for 
a much  greater  distance  the  friction  becomes  too  great  for  economical  work- 
ing of  the  traction  rope.  This  does  not,  however,  limit  the  length  of  tram- 
wav  which  may  be  built,  as  the  power  station  may  be  located  at  a convenient 
intermediate  point,  dividing  the  line  into  sections.  Several  intermediate 
power  stations  may  be  used,  and  the  length  of  the  line  greatly  increased 
above  the  limit  given.  A tramway  at  Grand  Encampment,  Wyoming,  is  16 
miles  long  and  carries  40  tons  of  ore  per  hour. 


TRANSMISSION  OF  POWER  BY  WIRE  ROPES. 

The  term  transmission,  as  here  used,  applies  simply  to  the  modification  of 
belt  driving,  using  grooved  wheels  or  sheaves  at  each  end  of  the  line,  lhe 
power  is  applied  to  one  sheave  and  taken  off  from  the  other  . 

The  friction  between  rope  and  sheaves  depends  directly  on  the  weight 
and  tension  of  the  rope  and  on  the  nature  of  the  surfaces  in  contact.  This 
pressure  is  better  obtained  by  using  a large,  heavy  rope  at  a low  tension  than 
by  using  a smaller  rope  at  a high  tension.  . ^ - 

The  deflection  or  sag  of  the  rope,  between  the  sheaves,  is  the  same  for 
both  upper  and  lower  parts  of  the  rope  when  the  transmission  is  not  running 
and  should  be,  according  to  John  A.  Roebling’s  Sons  Co.,  equal  to  about  one- 
thirty-sixth  of  the  span.  The  deflection  may  be  calculated  by  the  formula 
from  the  Trenton  Iron  Co.: 

. w s2 
h _ 8 1 * 

in  which  h = the  deflection  in  feet; 

w = weight  of  the  rope  per  foot,  in  pounds; 

8 — span,  in  feet; 
t = tension,  in  pounds. 

When  driving  from  the  under  side,  this  part  of  the  rope  will  be  tightened 
and  its  deflection  decreased,  while  the  upper  part  of  the  rope  becomes  slack- 
ened and  its  deflection  increased.  Under  proper  conditions  the  deflection  ot 
the  lower  rope  should  be  about  one-fiftieth,  and  that  of  the  upper  about  one- 
twenty- fifth  of  the  span.  The  difference  in  the  tensions  of  the  two  parts 
of  the  rope  is  the  effective  pull  of  the  driving  sheaves,  enabling  power  to  be 
transmitted. 

Transmission  ropes  are  subject  to  three  stresses,  viz.:  ..  * 

(1)  The  direct  tension,  due  to  the  power  transmitted,  plus  the  friction  ana 
weight  of  the  rope;  (2)  the  bending  stress,  due  to  the  bending  of  the  rope 
around  the  sheaves;  (3)  the  centrifugal  tension,  due  to  the  centrifugal  force 

in  the  rapidly  running  rope.  . . •,  _ Mr  wm 

The  following  data  on  stresses  m transmission  ropes  are  given  by  Mr.  V\  m. 
Hewitt,  of  the  Trenton  Iron  Co.  . . . , 

In  transmitting  power  by  wire  rope,  working  tension  should  not  exceed 


WIRE  ROPES. 


122e 


1 


the  difference  between  the  maximum  safe  stress  and  the  bending  stress. 
It  may  be  greater,  therefore,  as  the  bending  stress  is  less,  but  to  avoid  slipping 
a certain  ratio  must  exist  between  the  tensions  in  taut  and  slack  portions  of 
the  rope  when  running,  which  is  determined  by  the  formula 

T=  Sefm; 

in  which  T = tension  in  the  taut  portion  of  the  rope; 

S = tension  in  the  slack  portion; 

e = base  of  the  Naperian  system  of  logarithms  — 2.7182818; 
n = number  of  half  laps  of  rope  about  sheaves  or  drums  at  either 
end  of  line; 

7r  = 3.1416; 

f = coefficient  of  friction  depending  on  the  kind  of  filling  in  the 
grooves  of  the  sheaves,  or  character  of  the  material  on 
which  the  rope  tracks. 

The  useful  effort  of  transmitting  force  is  the  difference  between  the  tension 
of  the  taut  and  slack  portions  of  the  rope.  T — S = & (efn^  — 1),  and  to 
obtain  this,  the  initial  tension,  or  tension  when  the  rope  is  at  rest,  must  be 
one-half  the  sum  of  the  two  tensions. 

e fn  7T  _L  1 

TP  S = + i)  = __r^_  (T-S). 


The  following  are  some  of  the  values  of / : 

Dry  rope  on  a grooved  iron  drum 120 

Wet  'rope  on  a grooved  iron  drum 085 

Greasy  rope  on  a grooved  iron  drum 070 

Dry  rope  on  wood-filled  sheaves 235 

Wet  rope  on  wood-filled  sheaves .170 

Greasy  rope  on  wood-filled  sheaves  140 

Dry  rope  on  rubber  and  leather  filling 495 

Wet  rope  on  rubber  and  leather  filling 400 

Greasy  rope  on  rubber  and  leather  filling 205 


e f n TT  -. — i 


above  values  of/,  for  one  up  to  six  half  laps  of  the  rope,  are  as  follows: 

Values  of  efm*. 


f = 


n = Number  of  Half  Laps  About  Sheaves  or  Drums  at  Either 
End  of  Line. 


1 

2 

3 

4 

5 

6 

.070 

1.246 

1.552 

1.934 

2.410 

3.003 

3.741 

.085 

1.306 

1.706 

2.228 

2.910 

3.801 

4.964 

.100 

1.369 

1.875 

2.566 

3.514 

4.810 

6.586 

.120 

1.458 

2.125 

3.099 

4.518 

6.586 

9.602 

.130 

1.504 

2.263 

3.405 

5.122 

7.706 

11.593 

.140 

1.552 

2.410 

3.741 

5.808 

9.017 

13.998 

.150 

1.602 

2.566 

4.111 

6.586 

10.551 

16.902 

.170 

1.706 

2.910 

4.964 

8.467 

14.445 

24.641 

.200 

1.875 

3.514 

6.586 

12.346 

23.140 

43.376 

.205 

1.904 

3.626 

6.904 

13.146 

25.031 

47.663 

.235 

2.092 

4.378 

9.160 

19.166 

40.100 

* 83.902 

.250 

2.193 

4.810 

10.551 

23.140 

50.637 

111.318 

.265 

2.299 

5.286 

12.153 

27.941 

64.239 

147  693 

.300 

2.566 

6.586 

16.902 

43.376 

111.318 

285.680 

.350 

3.001 

9.017 

27.077 

81.307 

244.152 

733.145 

.400 

3.514 

12.346 

43.376  * 

152.405 

535.488 

1,849.140 

.410 

3.626 

13.146 

47.663 

172.814 

626.577 

2,271.775 

.450 

4.111 

16.902 

69.487 

285.680 

1,174.480 

4,828.510 

.495 

4.716 

22.425 

106.194 

502.881 

2,381.400 

.500 

4.810 

23.140 

111.318 

535.488 

2,575.940 

A 


122f 


WIRE  ROPES. 


Values  of 


ef  n 7T  + l 
e t n 7T  _ 1* 


/ = 


n = Number  of  Half  Laps  About  Sheaves  or  Drums  at  Either 
End  of  Line. 


1 

2 

3 

4 

5 

6 

.070 

9.130 

4.623 

3.141 

2.418 

1.999 

1.729 

.085 

7.536 

3.833 

2.629 

2.047 

1.714 

1.505 

.100 

6.420 

3.287 

2.280 

1.795 

1.525 

1.358 

.120 

5.345 

2.777 

1.953 

1.570 

1.358 

1.232 

.130 

4.968 

2.584 

1.832 

1.485 

1.298 

1.189 

.140 

4.623 

2.418 

1.729 

1.416 

1.249 

1.154 

.150 

4.322 

2.280 

1.643 

1.358 

1.209 

1.126 

.170 

3.833 

2.047 

1.505 

1.268 

1.149 

1.085 

.200 

3.287 

1.795 

1.358 

1.176 

1.090 

1.047 

.205 

3.212 

1.762 

1.338 

1.165 

1.083 

1.043 

.235 

2.831 

1.592 

1.245 

1.110 

1.051 

1.024 

.250 

2.676 

1.525 

1.209 

1.090 

1.010 

1.018 

.265 

2.539  • 

1.467 

1.179 

1.072 

1.032 

1.014 

.300 

2.280 

1.358 

1.126 

1.047 

1.018 

1.007 

.350 

2.000 

1.249 

1.077 

1.025 

1.008 

1.003 

.400 

1.795 

1.176 

1.047 

1.013 

1.004 

1.001 

.410 

1.765 

1.164 

L043 

1.012 

1.003 

1.001 

.450 

1.643 

1.126 

1.029 

1.007 

1.002 

1.000 

.495 

1.538 

1.093 

3 .019 

1.004 

1.001 

1.000 

.500 

1.525 

1.090 

1.018 

1.004 

1.001 

1.000 

For  a given  diameter  of  sheave,  and  a variable  diameter  of  wire,  a ratio 
exists  between  these  diameters  corresponding  to  a maximum  working 
tension.  This  ratio  results,  approximately,  in  a working  tension  of  one- 
third  and  bending  stress  of  two-thirds  of  the  maximum  safe  tension,  which 
is  from  one-third  to  two-fifths  of  the  ultimate  stress,  and  practically  deter- 
mines the  minimum  diameter  of  sheave  for  any  rope.  The  ratio  for  any 
size  of  wire  varies  slightly,  according  to  the  number  of  wires  composing  the 
rope,  and  in  terms  of  rope  diameter  is, 

For  7-wire  rope 

For  12-wire  rope  - 

For  19-wire  rope  * 

from  which  we  derive  the  following  table: 


Diam- 
eter of 
Rope. 


T5 

i 


Steel. 


T5 

5 

ft 


7- Wire. 


20 

25 

30 

35 

40 

45 

50 

55 

60 

70 

80 


12- Wire. 


15 

19 

22 

26 

30 

33 

37 

41 

44 

52 

59 


19- Wire. 


12 

15 

18 

21 

24 

27 

30 

32 

35 

41 

47 


40 

50 

60 

70 

80 

90 

100 

110 

120 

140 

160 


Steel 

Iron 

79.6 

160.5 

59.3 

120.0 

47.2 

95.8 

IN  INCHES. 

Iron. 

12-Wire. 

19-Wire. 

30 

24 

38 

30 

45 

36 

53 

42 

60 

48 

68 

54 

75 

60 

83 

66 

90 

72 

105 

84 

120 

96 

WIRE  ROPES. 


122g 


Sheaves. — To  decrease  the  bending  stresses  the  sheaves  for  wire-rope 
transmissions  are  generally  of  as  large  diameter  as  is  practicable  to  give  the 
required  speed  to  the  rope.  Large  sheaves  are  also  advantageous  because 
with  them  the  rope  is  run  at  a high  velocity  allowing  of  a lower  tension, 
and  permitting  a rope  of  smaller  diameter  to  be  used  than  would  be  pos- 
sible with  smaller  sheaves,  provided,  of  course,  that  the  span  is  of  suffi- 
cient length  to  give  the  necessary  weight. 

Sheaves  are  generally  made  of  cast  iron  when  not  exceeding  12  feet  in 
diameter,  and  when  larger  than  this  they  are  usually  built  up  with  wrought- 
iron  arms.  Sheaves,  upon  which  the  rope  is  to  make  but  a single  half-turn, 
are  made  with  V-shaped  grooves  in  their  circumference.  The  bottom  part 
of  the  groove  is  widened  to  receive  the  tilling,  which  consists  of  some  sub- 
stance to  give  a bed  for  the  rope  to  run  on  and  protect  it  from  wear,  and  to 
increase  the  friction  so  that  the  rope  will  not  slip.  This  filling  is  made  of 
blocks  of  wood,  rubber,  and  leather,  or  other  material.  Rubber  and  leather 
have  been  used  separately,  but  blocks  of  rubber  separated  by  pieces  of 
leather  have  been  found  to  give  the  best  results. 

Power  Transmitted. — The  horsepower  transmitted  is  equal  to  the  resistance 
overcome  (the  effective  null),  in  pounds,  multiplied  by  the  speed  of  the 
rope,  in  feet  per  minute,  and  divided  by  33,000,  that  is  (formula  from  John  A. 
Roebling’s  Sons  Co.), 

T V 

H=w,m' 

in  which  H = horsepower  transmitted; 

T = difference  in  tension  between  the  driving  and  driven  sides  of 
the  rope; 

V = speed  of  the  rope,  in  feet  per  minute. 

In  applying  this  formula,  V is  either  given  or  assumed.  T is  equal  to 
the  weight  of  the  rope  suspended  between  the  sheaves  multiplied  by  three 
(for  the  proportion  of  deflection  stated). 

To  transmit  a given  horsepower,  the  speed  of  the  rope  may  be  increased 
and  the  tension  (effective  pull)  correspondingly  decreased,  and  a smaller 
rope  may  be  used  provided  other  considerations  will  allow  it. 

For  determining  the  horsepower  that  can  be  transmitted  over  a given 
transmission,  the  following  formula  is  given  by  the  Trenton  Iron  Co.: 
H=[cd 2 - .000006  ( W + g'  + g")]  s ; 
in  which  H — horsepower  that  can  be  transmitted; 

c = constant  depending  on  material  of  rope,  the  filling  in  the 
grooves  of  the  sheaves,  and  the  number  of  half  laps  about 
the  sheaves  or  drums  at  either  end  of  the  line; 
d = diameter  of  rope,  in  inches; 

W — weight  of  rope,  in  pounds; 

' gf  = weight  of  terminal  sheaves  and  shafts; 

g"  = weight  of  intermediate  sheaves  and  shafts. 

The  following  table  gives  the  value  of  c for  ropes  on  different  materials: 

VALUE  OF  C FOR  ROPES  ON  DIFFERENT  MATERIALS. 


c — for 
Steel  Rope  on 

Number  of  Half  Laps  About  Sheaves  or  Drums  at 
Either  End  of  Line. 

1 

2 

3 

4 

5 

6 

Iron  

5.6L 

8.81 

10.62 

11.65 

12.16 

12.56 

Wood  

6.70 

9.93 

11.51 

12.26 

12.66 

12.83 

Rubber  and 
Leather  

9.29 

11.95 

12.70 

12.91 

12.97 

13.00 

The  values  of  c for  iron  rope  are  one-half  of  the  above. 

It  is  evident  from  the  above  figures  that  when  more  than  three  laps  are 
made  it  is  immaterial  what  the  surface  is  on  which  the  rope  tracks,  as  far  as 
frictional  adhesion  is  concerned. 


122h 


WIRE  ROPES. 


From  the  foregoing  formula,  assuming  the  sheaves  to  be  of  equal  diameter, 
and  of  a size  not  less  than  the  minimum  diameter  given  in  the  table,  we 
deduce  the  following: 

HORSEPOWER  CAPABLE  OF  BEING  TRANSMITTED  BY  A STEEL 
ROPE  MAKING  A SINGLE  LAP  ON  WOOD-FILLED  SHEAVES 


Diam- 
eter of 
Rope 
in 

Inches. 


Velocity  of  Rope  in  Feet  per  Second. 


T6 

i 

T6 

f 

ii 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

4 

8 

13 

17 

21 

25 

28 

32 

37 

40 

7 

13 

20 

26 

33 

40 

44 

51 

57 

62 

10 

19 

28 

38 

47 

56 

64 

73 

80 

89 

13 

26 

38 

51 

63 

75 

88 

99 

109 

121 

17 

34 

51 

67 

83 

99 

115 

130 

144 

159 

22 

43 

65 

86 

106 

128 

147 

167 

184 

203 

27 

53 

79 

104 

130 

155 

179 

203 

225 

247 

32 

63 

95 

126 

157 

186 

217 

245 

38 

76 

103 

150 

186 

223 

52 

104 

156 

206 

68 

135 

| 

202 

The  horsepower  that  may  be  transmitted  by  iron  ropes  is  one-half  of  the 

The  foregoing  table  gives  the  maximum  amount  of  power  capable  of 
being  transmitted  under  the  conditions  stated,  so  that  in  using  wood-lined 
sheaves,  it  is  well  to  make  some  allowance  for  the  stretching  of  the  rope, 
and  to  advocate  somewhat  heavier  equipments  than  the  above  table  would 
give-  that  is,  if  it  is  desired  to  transmit  20  horsepower,  for  instance,  to  put  m 
a plant  that  would  transmit  25  to  30  horsepower,  thus  avoiding  the  necessity 
of  having  to  take  up  a comparatively  small  amount  of  stretch.  On  rubber  and 
leather  filling  however,  the  amount  of  power  capable  of  being  transmitted 
is  considerablv  greater  than  on  wood,  so  that  this  filling  is  generally  used; 
and  in  this  case  no  allowance  need  be  made  for  stretch  as  such  sheaves^  will 
likely  transmit  the  power  given  by  the  table,  under  all  possible  deflections 
of  the  rope. 

Thet 
sheaves, 

rope  makes  but  a single  lap,  or  a half  lap  at  either  end  of  the  line. 


GLOSSARY  OF  ROPE  TERMS. 

Anneaf°d  Wire  Rope.— A wire  rope  made  from  wires  that  have  been  softened 
bvannealing  and  the  tensile  strength  thereby  lowered. 

Bending  Stress.—1 The  stress  produced  in  the  outer  fibers  of  a rope  by  bending 
over  a sheave  or  drum.  , +v. 

Breaking  Strain  Breaking  Strength , Breaking  Stress.—' The  least  load  that 
will  break  a rope.  These  terms  are  used  indiscriminately  to  mean  the 
load  which  will  break  a rope.  The  stress  on  a rope  at  tne  moment  of 
breaking  is  the  breaking  stress , and  the  strain  or  deformation  produced  in 
the  material  bv  this  stress  is  the  breaking  strain. 

Bright  Rope.— Rope  of  any  construction,  whose  wires  have  not  been  gal- 
vanized, tinned,  or  otherwise  coated.  , . o 

Cable-Laid  Rope— A term  applied  to  wire  cables  made  of  several  ropes 
twisted  together,  each  rope  being  composed  of  strands  twisted  together 
without  limitation  as  to  the  number  of  strands  or  direction  of  twist  A 
fiber  cable-laid  rope  is  a rope  having  three  strands  of  hawser-laid  rope, 
twisted  right-handed. 


WIRE  ROPES. 


122i 


Cable —Same  as  cable-laid  rope ; a fiber  cable  consists  of  three  hawsers  laid 
up  left-handed.  . . _ , 

Cast  Steel—  Steel  that  has  been  melted,  cast  into  ingots,  and  rolled  out 

into  bars.  . , * . . 

Clamp—  A device  for  holding  two  pieces  or  parts  of  rope  together  by 
pressure.  , „ 

Clip— a device  similar  to  a clamp  but  smaller  and  for  the  same  purpose. 

Coir. — Coconut-husk  fiber. 

Compound.— A lubricant  applied  to  the  inside  and  outside  of  ropes  pre- 
venting corrosion  and  lessening  abrasion  of  the  rope  when  in  contact 
with  hard  surfaces. 

Core—  The  central  part  of  a rope  forming  a cushion  for  the  strands.  In  wire 
ropes  it  is  sometimes  made  of  wire,  but  usually  it  is  of  hemp,  jute,  or 
some  like  material. 

Coupling. — A device  for  joining  two  rope  ends  without  splicing. 

Crucible  Steel.— A fine  quality  of  steel  made  by  the  crucible  process. 

Drum. — The  part  of  a hoisting  engine  on  which  the  rope  is  wound. 

Elastic  Limit.— The  elastic  limit  is-that  point  at  which  the  deformations  in 
the  material  cease  to  be  proportional  to  the  stresses. 

Elevator  Rope.— A rope  used  to  operate  an  elevator. 

Endless  Rope— A rope  which  moves  in  one  direction,  one  part  of  which 
carries  loaded  cars  from  a mine  at  the  same  time  that  another  part 
brings  the  empties  into  the  mine. 

Fiber—  A single  thread-like  filament. 

Flat  Rope.— A rope  in  which  the  strands  are  woven  or  sewed  together  to 
form  a flat,  braid-like  rope. 

Flattened-Strand  Rope.— A wire  rope  whose  strands  are  flattened  or  oval  and 
which  therefore  presents  an  increased  wearing  surface  over  that  of  the 
ordinary  round-strand  rope. 

Flattened-Strand  Triangular  Rope— A wire  rope  of  the  flattened-strand  con- 
struction in  which  the  strands  are  triangular  in  shape. 

Fleet—  Movement  of  a rope  sideways  in  winding  on  a drum. 

Fleet  Wheel.— A grooved  wheel  or  sheave  that  serves  as  a drum  and  about 
which  one  or  more  coils  of  a haulage  rope  pass. 

Galvanized  Rope.— Rope  made  of  wires  that  have  been  galvanized  or  coated 
with  zinc  to  protect  them  from  corrosion. 

Grip  Wheel.— A wheel,  the  periphery  of  which  is  fitted  with  a series  of 
toggle-jointed,  cast-steel  jaws  that  grip  the  rope  automatically. 

Guy.— A strand  or  rope  used  to  support  a pole,  structure,  derrick,  or  chim- 
ney, etc. 

Haulage  Rope.— A rope  used  for  haulage  purposes. 

Hawser.— A term  applied  to  any  wire  rope  used  for  towing  on  lake  or  sea. 
A fiber  hawser  consists  of  three  strands  laid  up  right-handed. 

Hawser- Laid  Rope  has  three  strands  of  yarn  twisted  left-handed,  the  yarns 
being  laid  up  right-handed.  Synonymous  with  cable-laid  rope  as 
applied  to  wire  ropes. 

Hawser  Wire  Rope.— Galvanized  ropes  of  iron  or  steel  usually  composed  of 
six  strands,  12  wires  each,  principally  used  in  marine  work  for  towing 
purposes. 

Hemp.— A tough,  strong  fiber  obtained  from  the  hemp  plant. 

Hoisting  Rone— A rope  composed  of  a sufficient  number  of  wires  and  strands 
to  insure  flexibility.  Such  ropes  are  used  in  shafts,  elevators,  quarries, 
etc. 

Idler.— A sheave  or  pulley  running  loose  on  a shaft  to  guide  or  support 


Jute.— A fiber  obtained  from  the  inner  bark  of  two  Asiatic  herbs:  Corchorus 

capsularis  and  C.  olitorius. 

Lang-Lay  Rope.— A rope  in  which  the  wires  in  each  strand  are  twisted  in 
the  same  direction  as  the  strands  in  the  rope. 

Lay— A term  indicating  the  direction,  or  length,  of  twist  of  the  wires  and 
strands  in  a rope. 

Live  Load.— A load  which  is  variable  in  distinction  from  a constant  load. 

Load  Stress. — The  stress  produced  by  the  load. 

Locked- Wire  Rope— A rope  with  a smooth  cylindrical  surface,  the  outer 
wires  of  which  are  drawn  to  such  shape  that  each  one  interlocks  with 
the  other  and  the  wires  are  disposed  in  concentric  layers  about  a wire 
core  instead  pf  in  strands.  Particularly  adapted  for  haulage  and  rope- 
transmission  purposes. 


122j 


WIRE  ROPES. 


Manila.— The  fiber  of  Musa  textilis;  Manila  hemp.  „ _ 

Modulus  of  Elasticity. — The  ratio  between  the  amount  of  extension  or  com- 
pression of  a material  and  the  load  producing  this  same  extension  or 
compression.  , . 

Plow  Steel.— & select  grade  of  steel  of  high  tensile  strength.  First  used  in 
rope  for  plowing  fields.  , . . , , ...  , 

Proper  Working  Load.— The  maximum  load  that  a rope  should  be  permitted 
to  support  under  working  conditions.  (See  working  load.) 

Regular-Lay  Rope— A.  rope  in  which  the  wires  in  each  strand  are  twisted  in 
ODposite  direction  to  the  strands  in  the  rope. 

Round-Strand  Rope.— A rope  made  of  round  twisted  strands. 

Running  Rope.— A flexible  rope  that  will  pass  througn  blocks  and  used  for 
hoisting  on  shipboard.  The  term  is  also  often  used  for  any  moving  rope. 

Sheave.— A wheel  or  pulley  around  or  over  which  a rope  passes. 

Shroud  Laid , or  Four-Strand , Rope  has  four  strands  laid  around  a core. 

Sisal— A hemp.  The  fiber  of  the  Agave  Sisalona.  . 

Socket.— A device  fastened  to  the;  end  of  a rope  by  means  of  which  the  rope 
mav  be  attached  to  its  load.  The  socket  may  be  opened  or  closed. 

Splice  —The  joining  of  two  ends  of  rope  by  interweaving  the  strands. 

Step  Socket.— A special  form  of  socket  for  use  on  locked-wire  rope. 

Stirrup—  An  adjustable  bale  of  a socket  _ . 

Stone  Wire.— A term  applied  to  wire  smaller  than  No.  14  put  up  m 12-pound 
coils,  which  are  about  8 inches  inside'  diameter. 

Strand— A term  applied  to  a varying  number  of  wires  or  fibers  twisted 
together.  The  strands  in  turn  are  twisted  together,  forming  a rope. 

Stress. -A  force  or  combination  of  forces  tending  to  change  the  shape  of  a 

Strain.— A chahge  of  shape  produced  in  a body.  (Stress  and  strain  are 
often  used  incorrectly  as  synonymous  terms.) 

Surging.— The  flapping  of  a moving  rope. 

Swedish  Iron.— A soft  and  comparatively  pure  iron. 

Switch  Rope.— A short  length  of  rope  fitted  with  a hook  on  one  end  and  a 
link  on  the  other,  used  for  the  switching  of  freight  cars. 

Tail-Rope—  (1)  The  rope  that  is  used  to  draw  the  empties  back  into  a 
mine  in  a tail-rope  haulage  system.  (2)  A rope  attached  beneath  the 
cage  when  the  cages  are  hoisting  in  balance. 

Taper  Rope. — A rope  which  has  a gradually  diminishing  diameter  frorn  the 
upper  to  the  lower  end.  The  diameter  of  the  rope  is  decreased  by 
1 dropping  one  wire  at  a time  at  regular  intervals.  Both  round  and  flat 
ropes  may  be  made  tapered,  and  such  ropes  are  intended  for  deep-shaft 
hoisting  with  a view  to  proportioning  the  diameter  of  the  rope  to  the 
load  to  be  sustained  at  different  depths. 

Tensile  Strength—  The  stress  required  to  break  a rope  by  pulling  it  in  two. 

Thimble. — An  oval  iron  ring  around  which  a rope  end  is  bent  and  fastened 
to  form  an  eye.  ■ ,,  „ 

Tiller  Rope.— A very  flexible  wire  rope  composed  of  six  small  ropes,  usually 
of  seven-wire  strands  laid  about  a hemp  core.  . 

Tinned  Rope.— Rope  made  of  wires  that  have  been  coated  with  tin  to  protect 
them  from  corrosion . , 

Torsion. — The  process  of  twisting  a wire  thereby  showing  its  ductility. 

Traction  Rope— A rope  used  for  transmitting  the  power  in  a wire-rope  tram- 
way and  to  which  the  buckets  are  attached. 

Transmission  Rope. — A rope  used  for  transmitting  power. 

Traveler.— A truck  rolling  along  a suspended  rope  for  supporting  a load  to 
be  transported.  „ „ . , ^ 

Turnbuckle—  A form  of  coupling  so  threaded  or  swiveled  that  by  turning  it 
the  tension  of  a rope  or  rod  may  be  regulated. 

Ultimate  Tensile  Strength.— Same  as  tensile  strength. 

Universal  Lay—  Another  term  for  lang  lay. 

Whipping.— The  flopping  of  a moving  rope. 

Wire  Gauge.— Standard  sizes  or  diameters  for  wire. 

Wire  Rope— A rope  whose  strands  are  made  of  wires,  twisted  or  woven 
together 

Working  Load.- The  maximum  load  that  a rope  can  carry  under  the  con- 
ditions of  working  without  danger  of  straining.  (Same  as  proper  work- 
ingload.) . 

Wrought  Iron  — A comparatively  pure  and  malleable  iron.  , 

Yarn.—1 Twisted  fiber  of  which  rope  strands  are  made. 


Ife. 


00 

00 

00 

00 

00 

00 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 


rIRE  AND  SHEET-METAL  GAUGES. 

OF  WIRE  AND  SHEET-METAL  GAUGES. 


British 


Wire 
Gauge. 
(Legal 
Standard 
n Great 
Britain.) 
Millim. 


127 

11.78 

10.97 

10.16 

9.45 

8.84 

8.23 

7.62 

7.01 
6.4 
5.89 
5.38 
4.88 
4.47 
4.06 
3.66 
3.26 
2.95 
2.64 
2.34 
2.03 
1.83 

1.63 
1.42 
1.22 

1.01 
.91 
.81 
.71 
.61 
.56 
.51 
.45 
.42 
.38 
.35 
.31 
.29 
.27 
.25 
.23 
.21 
.19 
.17 
.15 
.13 
.12 
.11 
.10 
.09 
.08 
.07 
.06 
.05 
04 
.03 
.025 


Birming- 

ham 

Gauge. 

Inch. 

American 
or  Brown  . 
and 
Sharpe 
Gauge, 
inch. 

Roebling's 

Gauge. 

Inch. 

Trenton 
Iron 
Co.’s 
‘Wire  ! 
Gauge. 
Inch. 

English 

Legal 

Standard. 

Inch. 

.49 

.46 

.500  ( 

.464 

.43 

.45 

.432 

.454 

.46 

.393 

.40 

.4 

.425 

.40964 

.362 

.36 

.372 

.38 

.3648 

.331 

.33 

.348 

.34 

.32486 

.307 

.305 

.324 

.3 

.2893 

.283 

.285 

.3 

.284 

.25763 

.263 

.265 

.276 

.259 

.22942 

.244 

.245 

.252 

.238 

.20431 

.225 

.225 

.232 

.22 

.18194 

.207 

.205 

.212 

.203 

.16202 

.192 

.19 

.192 

.18 

.14428 

.177 

.175 

.176 

.165 

.12849 

.162 

.16 

.16 

.148 

.11443 

.148 

.145 

.144 

.134 

.10189 

.135 

.13 

.128 

.12 

.09074 

.12 

.1175 

.116 

.109 

.08081 

.105 

.105 

.104 

.095 

.07196 

.092 

.0925 

.092 

.083 

.06408 

.08 

.08 

.08 

.072 

.05707 

.072 

.07 

.072 

.065 

.05082 

.063 

.061 

.064 

.058 

.04526 

.054 

.0525 

.056 

.049 

.0403 

.047 

.045 

.048, 

.042 

.03589 

.041 

.04 

.04 

.035 

.03196 

.035 

.035 

.036 

.032 

.02846 

.032 

.031 

.032 

.028 

.02535 

.028 

.028 

.028 

.025 

.02257 

.025 

.025 

.024 

.022 

.0201 

.023 

.0225 

.022 

.02 

.0179 

.02 

.02 

.02 

.018 

.01594 

.018 

.018 

.018 

.016 

.01419 

.017 

.017 

.0164 

.014 

.01264 

.016 

.016 

.0148 

.013 

.01126 

.015 

.015 

.0136 

.012 

.01002 

.014 

.014 

.0124 

.01 

.00893 

.0135 

.013 

.0116 

.009 

.00795 

.013 

.012 

.0108 

.008 

.00708 

.011 

.011 

.01 

.007 

.0063 

.01 

.01 

.0092 

.005 

.00561 

.0095 

.0095 

.0084 

.004 

.005 

.009 

.009 

.0076 

.00445 

.0085 

.0085 

.0068 

.00396 

.008 

.008 

.006 

.00353 

.0075 

.0075 

.0052 

.00314 

.007 

.007 

f 

.0048 
.0044 
.004 
.0036 
.0032 
. .0028 
.0024 
.002 
.0016 
.0012 
.001 

1221 


WIRE  ROPES. 


STRESS  IN  HOISTING 


ROPES  ON  INCLINED  PLANES  OF  VARIOUS 
DEGREES. 

(From  “Wire-Rope  Transportation  “ published  by  Trenton  Iron  Co.) 

The  following  table  is  based  upon  an  allowance  of  40  lb.  per  ton  for 
rolling  friction,  but  there  will  be  an  additional  stress  due  to  the  weight  of 
the  rope  and  inclination  of  the  plane. 


Rise  per 
100  Ft. 
Horizontal. 
Ft. 

Angle 

of 

Inclination. 

Stress  in  Lb. 

per  Ton 
of  2.000  Lb. 

5 

9°  52' 

140 

10 

5°  43' 

240 

15 

8°  32'  1 

336 

20 

11°  lO' 

432 

25 

14°  03' 

527 

30 

16°  42' 

613 

35 

19°  18' 

700 

40 

21°  49' 

782 

45 

24°  14' 

860 

50 

26°  34' 

933 

55 

28°  49' 

1.003 

60 

30°  58' 

1,067 

65 

33°  02' 

1,128 

• 70 

35°  00' 

1.185 

75 

36°  53' 

1,238 

80 

38°  40' 

1.287 

85 

40°  22' 

1.332 

90 

42°  00' 

1.375 

95 

43°  32' 

1.415 

100 

45°  00' 

1.450 

Rise  per 
100  Ft. 
Horizontal. 
Ft. 

Angle 

of 

Inclination. 

i 

Stress  in  Lb. 

per  Ton 
of  2, 000  Lb. 

105 

46°  24'  | 

1,484 

110 

47°  44' 

1.516 

115 

49°  00' 

1,535 

120 

50°  L* 

1,573 

125 

51°  21' 

1.597 

130 

52°  26' 

1.620 

135 

53°  29' 

1,642 

140 

54°  28' 

1.663 

145 

55°  25' 

1.682 

150 

56°  197 

1.699 

155 

57°  11' 

1.715 

160 

58°  00' 

1 1.730 

165 

58°  47' 

1.744 

170 

j 59°  33' 

1,758 

175 

60°  16' 

1,771 

180 

60°  57' 

1.782 

185 

61°  37' 

1.794 

190 

! 62°  15' 

1,804 

195 

62°  52' 

1.813 

200 

63°  27' 

; 1.822 

RELATIVE  EFFECTS  OF  VARIOUS  SIZED  SHEAVES  OR  DRUMS  ON 
THE  LIFE  OF  WIRE  ROPES. 


Aline  officials  and  other  users  of  wire  ropes  have  often  felt  the  want  of  a 
table  or  set  of  tables  that  would  enable  them  to  determine  at  a glance  what 
effect  the  use  of  various  sized  sheaves  would  have  on  various  sized  ropes. 
The  following  tables  have  been  specially  prepared  for  the  Coal  and  Metal 
Aimer's  Poeketbook  bv  Air.  Thomas  E.  Hughes,  of  Pittsburg,  Pa. 


cast-steel  ropes  for  inclines. 

Made  of  6 Strands  of  7 Wires  Each,  Laid  Around  a Hemp  Core. 


Diameters  of  Sheaves  or  Drums  in  Feet,  Showing  Percentages 
Diameter  0f  Life  for  Various  Diameters. 

of  _ = 


Rope. 

Inches. 

100?  j 

90*  * 

80£ 

75£  | 

601 

501 

25* 

11 

16.00 

14.00 

12.00 

11.00 

9.00 

7.00 

4.75 

a8 

li 

14.00 

12.00 

10.00 

8.50 

7-00 

6.00 

1 £2 

•*■8 

11 

12.00 

10.00 

8.00 

7.25 

6.00 

1 5.50 

\ 4.2 d 

I4 

11 

10.00 

8.50 

7.75 

7.00 

6-00  ! 

! 5.00 

; 4.00 

a8 

1 

8.50 

7.75 

6.75 

6.00 

5.00 

4.50 

3.75 

J. 

* 

7.75 

7.00 

6.25 

5.75 

4.50 

3.  /D 

3.25 

8 

3 

7.00 

6.25 

5.50 

5.00 

I 4.25 

3.50 

2.75 

* 

6.Q0 

5.25 

4.50 

4.00 

3-25 

i 3.00 

2.50 

8 

£ 

5.00 

4.50 

4.00 

3.50 

2.75 

j 2.25 

; 1.75 

XOTE  _\ye  do  not  publish  a table  of  iron  ropes  for  inclines  as  the  use  of 
iron  ropes  for  this  purpose  has  been  generally  abandoned,  steel  ropes  being 
far  more  satisfactory  and  economical. 


WIRE  ROPES. 


m 


CAST-STEEL  HOISTING  ROPES. 

Made  of  6 Strands  of  19  Wires  Each,  Laid  Around  a Hemp  Core. 


_ . , Diameters  of  Sheaves  or  Drums  in  Feet,  Showing  Percentages 

Diameter  0f  Life  for  Various  Diameters. 

of 


Hope. 

Inches. 

100/* 

90/ 

80/ 

75/ 

60/ 

50/ 

25/ 

H 

14.00 

12.00  • 

10.00 

8.50 

7.00 

6.00 

4.50 

If 

12.00 

10.00 

8.00 

7.00 

6.00 

5.25 

4.25 

If 

10.00 

8.50 

7.50 

6.75 

5.50 

5.00 

4.00 

If 

9.00 

7.50 

6.50 

5.50 

5.00 

4.50 

3.75 

1 

8.00 

7.00 

6.00 

5.50 

4.50 

4.00 

3.50 

2. 

7.50 

6.75 

5.75 

5.00 

4.25 

3.50 

3.00 

1 

f 

2 

3.' 

8 

5.50 

4.50 

4.00 

3.75 

3.25 

3.00 

2.25 

4.50 

4.00 

3.75 

3.25 

3.00 

2.50 

2.00 

4.00 

3.00 

3.00 

3.00 

2.75 

2.00 

2.25 

2.00 

1.50 

1.50 

IRON  HOISTING  ROPES. 

Made  of  6 Strands  of  19  Wires  Each,  Laid  Around  a Hemp  Core. 


. Diameters  of  Sheaves  or  Drums  in  Feet,  Showing  Percentages 
Diameter  of  Life  for  yari0us  Diameters. 

of  


Rope. 

Inches. 

100/ 

90/ 

80/ 

75/ 

60/ 

50/ 

25/ 

If- 

12.00 

11.00 

9.00 

7.50 

6.00 

5.00 

3.00 

If 

10.00 

9.00 

7.50 

7.00 

5.25 

4.75 

4.00 

If 

9.00 

7.75 

6.50 

5.75 

4.50 

4.00 

3.50 

If 

8.00 

6.75 

5.50 

5.00 

4.25 

3.50 

3.00 

1 

6.75 

6.00 

5.00 

4.75 

4.00 

3.25 

2.75 

z 

6.75 

6.00 

5.00 

4.50 

4.00 

3.00 

2.50 

6 

f 

5.00 

4.75 

4.00 

3.75 

3.00 

2.75 

2.00 

f 

4.50 

3.75 

3.25 

3.00 

2.75 

2.25 

1.75 

3.50 

3.25 

3.00 

2.75 

2.00 

1.50 

1.00 

I 

3.00 

2.00 

1.25 

1.00 

Wire  rope  is  as  pliable  as  new  hemp  rope  of  the  same  strength;  the  former 
will  therefore  run  on  the  same  sized  sheaves  and  pulleys  as  the  latter.  But 
the  greater  the  diameter  of  the  sheaves,  pulleys,  and  drums,  the  longer  wire 
rope  will  last.  In  the  construction  of  machinery  for  wire  rope,  it  will  be 
found  good  economy  to  make  the  drums  and  sheaves  as  large  as  possible. 

The  tables  of  wire-rope  manufacturers  give  “ proper  diameters  of  drum  or 
sheave”  at  from  50  to  65  times  the  rope  diameter;  but  the  expression  would 
more  properly  be  the  “minimum  admissible  diameter.”  For  ordinary  ser- 
vice, by  using  sheaves  and  drums  from  75  to  100  times  the  diameter  of  the 
rope,  the  average  life  of  hoisting  ropes  would  be  materially  lengthened. 
For  rapid  hoisting,  during  which  abnormal  strains  are  most  likely  to  occur, 
or  where  a low  factor  of  safety  is  employed,  a sheave  diameter  of  150  times 
that  of  the  rope  is  to  be  recommended. 

Experience  has  demonstrated  that  the  wear  increases  with  the  speed.  It 
is  therefore  better  to  increase  the  load  than  the  speed.  Wire  rope  is  manu- 
factured either  with  a wire  or  a hemp  center.  The  latter  is  more  pliable 
than  the  former,  and  will  wear  better  where  there  is  short  bending. 

Wire  rope  must  not  be  coiled  or  uncoiled  like  hemp  rope.  When  mounted  on 
a reel,  the  latter  should  be  mounted  on  a spindle  or  flat  turntable  to  pay  off 
the  rope.  When  forwarded  in  a small  coil,  without  reel,  roll  it  over  the 
ground  like  a wheel,  and  run  off  the  rope  in  that  way.  All  untwisting  or 
kinking  must  be  avoided. 


124 


WIRE  ROPES. 


EXTRA  STRAIN  ON  A HOISTING  ROPE  WITH  A FEW  INCHES 

OF  SLACK  CHAIN 


Dynamometer  Tests. 


First  Test 

Empty  cage  lifted  gently  : 

Empty  cage  with  2\  inches  slack  chain 

Empty  cage  with  6 inches  slack  chain : 

Empty  cage  with  12  inches  slack  chain 

Second  Test 

Cage  and  four  empty  cars  weighed  by  machine 

Cage  and  four  empty  cars  lifted  gently  ..................... 

Cage  and  four  empty  cars  with  3 inches  slack  chain 
Cage  and  four  empty  cars  with  6 inches  slack  chain 
Cage  and  four  empty  cars  with  12  inches  slack  chain 

Third  Test 

Cage  and  full  cars  weighed  by  machine 

No.  1,  lifted  gently 

No.  2,  lifted  gently 

No.  1,  with  3 inches  slack  chain 

No.  2,  with  3 inches  slack  chain 

No.  1,  with  6 inches  slack  chain 

No.  2,  with  6 inches  slack  chain 

No.  1,  with  9 inches  slack  chain - 

No.  2,  with  9 inches  slack  chain 


Tons. 

Cwts. 

1 

16 

2 

10 

4 

0 

5 

10 

2 

17 

3 

0 

5 

0 

5 

10 

7 

0 

5 

1 

5 

1 

5 

3 

8 

10 

8 

10 

10 

10 

11 

10 

12 

10 

11 

10 

WIRE-ROPE  CALCULATIONS. 

The  working  load,  also  called  the  proper  working  load,  is  the  maximum 
ioad  that  a rope  should  be  permitted  to  support  under  working  conditions. 
The  stress  on  a rope  to  which  a load  is  attached,  and  which  bends  over  a 
sheave,  is  made  up  of  two  parts:  (1)  That  due  to  the  load  on  the  rope,  known 
as  the  load  stress;  (2)  that  due  to  the  bending  of  the  rope  about  a sheave  or 
drum,  known  as  the  bending  stress.  That  is,  if 
S = total  safe  stress; 

Sb  = bending  stress; 

Si  = load  stress; 

S = Sb  + S,  and  Si  = S — Sb. 

The  total  stress  must  not  equal  the  elastic  limit  of  the  material  composing 
the  rope  and  is  usually  taken  as  from  one-third  to  one-fourth  the  approxi- 

mait  is  only  quite  recently  that  account  has  been  taken  of  this  second  stress 
in  wire-rope  problems,  and  it  is  riot,  as  yet,  by  any  means  universal  practice 
to  consider  it  in  calculating  the  size  of  rope  needed  for  a given  purpose. 

If  we  have  a given  weight  to  hoist  with  a wire  rope,  the 
to  use  may  be  taken  directly  from  the  tables  on  pages  120,  121,  122,  but  this 
does  not  take  account  of  the  bending  stress,  except  by  allowing  for  it  in  the 
factor  of  safety  assumed.  t 

A second  method  calculates  the  bending  stress.  

The  following  formulas  and  the  diagram  based  on  them,  given  on 
page 125,  are  given  bv  Mr.  E.  T.  Sederholm,  former  chief  engineer  for  Fraser 
& Chalmers,  and  will  be  found  in  the  hoisting-engine  catalogue  of  the 
Allis-Chalmers  Co. 

The  general  formula  for  the  bending  stress  is 

_EaA, 
bb  D > 

in  which  Sh  = bending  stress; 

E = modulus  of  elasticity; 
a = diameter  of  each  wire; 

D = diameter  of  drum  or  sheave;  . . 

A = total  area  of  the  wire  cross-section,  in  inches. 


WIRE  ROPES. 


124a 


For  a rope  of  19  wires  to  the  strand  the  diameter  of  each  wire  is  about  one- 
fifteenth  (exactly  ) of  the  diameter  of  the  rope.  That  is,  if  d = diameter 

of  rope,  a = and  by  substituting  this  in  the  above  formula  Sb 


E Ad 
15.527/ 


15.52’ 

The  modulus  of  elasticity  for  the  different  kinds  of  wire  is  given  different 
values  by  different  authorities.  Mr.  Sederholm  uses  29,400,000  in  his  formula 
and  diagram,  and  Mr.  Hewitt  28,500,000,  the  same  modulus  being  used  for 
the  different  materials  of  which  ropes  are  made. 

The  cross-section  of  metal  A in  a wire  rope  is  approximately  .4  d2,  or  it 
may  be  more  accurately  calculated  by  multiplying  the  cross-section  of  each 
wire,  as  given  by  a wire  table,  by  the  number  of  wires  in  the  rope. 

Find  the  bending  stress  in  a 19-wire,  cast-steel  hoisting  rope  2 in.  in  diam- 
eter, winding  on  an  8-ft.  drum,  if  A — .4  d2,  and  E = 29,400,000, 

„ 29,400,000  X 23  X .4 

Sb  = — . . ^ . . ~~  - . = 31.51  tons. 


is  124  tons,  and  if 


10  X 15.52  X 96  X 2,000 

The  approximate  breaking  stress  for  such  a rope 
124 

we  assume  a factor  of  3,  — = 41+  tons  for  the  safe  working  stress,  and 

O 

41  — 32  = 9 tons,  for  the  safe  lifting  load  under  the  given  conditions. 

The  diagram  given  on  page  125  is  based  on  the  above  formula. 

Mr.  Wm.  Hewitt,  of  the  Trenton  Iron  Co.,  has  given  a similar  but  more 
complicated  formula  for  the  bending  stress,  which  is  supposed  to  give  some- 
what more  accurate  results,  as  he  has  introduced  terms  which  allow  for  the 
actual  radius  of  the  bend  at  the  outside  fiber  of  the  rope,  while  the  Sederholm 
formula  assumes  the  radius  of  the  bend  to  be  the  radius  of  the  sheave. 

Mr.  Hewitt’s  formula  is  as  follows: 

EA 

&b  — 


2.06  ~ + C 


in  which 


Sb  = 
E = 


bending  stress,  in  pounds; 
modulus  of  elasticity  (28,500,000); 

A — aggregate  area  of  wires,  in  square  inches ; 

R te  radius  of  drum  or  sheave,  in  inches ; 
d = diameter  of  individual  wires,  in  inches; 

C = a constant  depending  on  number  of  wires  in  strands. 

The  values  of  d and  C are : 

7-Wire  Rope  19-Wire  Rope 

d = h diameter  of  rope  d = TV  diameter  of  rope 

C = 9.27  C = 15.45 

For  12-wire  and  16-wire  ropes  the  values  are  intermediate  in  proportion  to 
the  number  of  wires  In  the  case  of  ropes  having  strands  composed  of  dif- 
ferent sizes  of  wires,  take  the  larger  of  the  outer  layer  for  the  value  of  d. 

Mr.  Hewitt  assumes  one-third  of  the  approximate  breaking  stress  as  the 
maximum  safe  stress  and  uses  28,500,000  for  the  modulus  of  elasticity. 

If  the  problem  given  under  the  Sederholm  formula  is  worked  out  by  the 
Hewitt  formula  the  safe  working  load  will  be  11£  tons,  while  the  table  on 
pages  120  and  121  gives  24.8  tons. 

* The  Sederholm  diagram  on  page  125  gives  for  a load  of  24.8  tons  a sheave 
between  16  and  17  ft.  diameter,  the  Sederholm  formula  gives  a sheave  of 
15  ft.  in  diameter,  while  the  table  on  pages  120  and  121  gives  8 ft.  It  is  evi- 
dent that  there  is  a wide  difference  of  opinion  among  the  wire-rope  authori- 
ties and  a good  opportunity  for  experimental  work  along  this  line. 

In  using  the  Sederholm  or  Hewitt  formulas  there  are  two  unknown 
quantities,  the  diameter  of  the  rope  d and  the  diameter  D or  radius  R of  the 
drum,  d varies  inversely  as  D,  that  is,  for  a given  load  the  smaller  d is 
taken  the  larger  D must  be  to  give  the  same  conditions  of  safety. 

If  we  could  assume  a certain  ratio  between  Sh  and  St  in  the*  formula 
S.—-  Sb  + Si  the  problem  could  be  easily  solved,  but  an  examination  of  this 
ratio  in  a number  of  cases  where  good  results  have  been  obtained  from 

S S 2 

hoisting  ropes  shows  this  ratio  to  vary  from  ^ = 1 to 

bb  tsb 

S 1 

mission  of  power  by  wire  ropes,  Mr.  Hewitt  assumes  ~ = -,  but  this  relation 

will  scarcely  hold  in  a hoisting  problem,  and  the  above  problem  must  be 
solved  by  the  cut-and-try  method. 


= Inthetrans- 

5 


124b 


WIRE  ROPES. 


Wear  of  Wire  Ropes— The  deterioration  of  wire  ropes  may  he  either 

external  or  internal,  and  may  be  due  (1)  t0  abra^°£’  t^Ueoi0tohtheU internal 
the  outside  surface  of  the  rope  against  other  objects,  or  the  internal 
chafing  of  the  wires  composing  the  strands  against  one  another,  (2)  to 
iniurvgfrom  overloading,  to  shock  due  to  sudden  starting  of  the  load,  or  to 
reDeated  ^ndings  about  too  sharp  angles  or  over  sheaves  or  rollers  of  too 
small  a diameter  for  the  size  of  the  rope;  (3)  to  rust  or  corrosion  of  the  wi  e 
from  acid  waters  or  to  decay  of  the  hemp  cores. 

As  a result  of  abrasion,  the  wires  in  a rope  are  either  flattened  or  torn 
ar»art  With  properly  designed  drums  and  head-trame  and  properly  placed 
sheaves  a hofithig  rope  is  but  slightly  abraded,  and  the  wear  is  due  chiefly 
S hendina  or  to  overloading.  A haulage  rope  is  subjected  to  constant 
ahrasionin  passta°  over  rollers  and  sheaves  and  from  dragging  along  the 
hottom  and  S of  the  haulage  wavs  and  from  the  grips.  It  is  also  often 
subject  to  severe  shocks  and  abrasion  from  the  lashing  or  vibration  when 

“‘Vhewea?  a£§“ua  rope  increases  as  its  velocity  is  increased;  hence, 
conditiZs  lermittfng?it  is  better  to  increase  the  output  by  increasing  the 
load  within  allowable  limits  rather  than  by  increasing  the  velocity  of 

“Inspection  of  Ropes,_The  life  of  a hoisting  rope. depends  not  only  onits 
duality  but  also  on  the  conditions  under  which  it  is  used  and  en.the  eare- 

fulness'of  the  engineer  in  handling  the  load  hoisUng  ropes  are 

nffpn  and  at  regular  intervals.  At  some  mines  the  hoisting  ropes  aie 

insnected  everv  morning  before  lowering  the  men.  The  cage  is  slow  y 
lowered  and  then  raised,  each  rope  being  carefully  examined  b>  an 
insnector  to  detect  any  broken  wires.  Particular  attention  should  be  given 
to  the  nart  of  the  rope  where  it  is  attached  to  the  socket  at  the  cage, 
r»art  is  more  subject  to  corrosion  and  sharp  bending  than  any  other.  When 
tlm  core  fails  at  any  noint  the  rope  should  be  discarded  at  once,  usthe  wires 
are  likely  to  kink  and  break  internally  as  the  rope  passes  over  the ^sheave. 
At  some  mines  hoisting  ropes  are  discarded  at  regular  intervals,  whether 

while  the  rone  is  run  will  indicate  loose  wire  ends.  . 

Lubrication  of  Ropes  -Mine  water  has  a very  corrosive  action  on  wire 

comfngta  YoXc'I1  whhnthl  "/of  the 

W°For  MstoVroP>es"one  bushel  of  freshly  slacked  lime  to  one  barrel  of  pine 
nr  eoAl  tar  makes  a good  lubricant;  with  pine  tar,  which  contains  no  acid, 
tallow  mav  be  used  instead  of  lime.  Another  mixture  contains  tar,  summer 
oil^xl™  greas^and  a fittle  pulverized  mica,  mixed  to  such  a consistency 
that  it  wifi  penetrate  thoroughly  between  the  wires  and  will  n9t  dry  ?h 
strip  off  The  lubricant  should  not  be  thick  enough  to  render  difficult  the 
thorough  inspection  of  the  rope,  and  all  lubricants  of  this  ^ature  should  be 
nse^smrin^lv  after  the  first  application,  as  the  rope  should  be  kept  clean 
and  SfS  Graphite  is  also  used  for  the  purpose.  Lubricants  may 
he  applied  bv  running  the  engine  slowly  and  allowing  the  rope  to  pass 
through  a bunch  of  waste  saturated  with  lubricant,  by  ruling  the  lubricant 
into  the  rone  bv  means  of  a brush,  or  by  pouring  the  oil  into  the  groove  oi 
tbe  sheaveas  tL  ropeis  run  slowly  ba6k  and  forth.  A new  hoisting  rope 
should  be  passed  through  a bath  of  hot  lubricant  and  thus  be  thoroug  y 

1UbHaSla^e  roues  are  not  usually  lubricated  as  thoroughly  as  hoisting  ropes 
on  Account  of  ?he  grease  causing  slipping  of  grips  and  gathering  of  dirt  and 
dusl  but  they  can  be  treated  with  raw  linseed  oil  thickened  with  lamp 
black  boiled  ^vith  an  equal  portion  of  pine  tar,  and  the  mixture  applied 
while  hot.  Ordinary  black  oil,  such  as  is  used  to  oil  mine  cars  and  hoisting 
rones  can  be  used  on  haulage  ropes  where  no  friction  grips  are  emplo>ed. 
These  mixtures^  if  fluid  can  be  poured  on  the  rope  as  it  is  run  over  the 
Theave^r appUed  from  a leather-lined  box  filled  with  oil.  Patent  lubricants 
known’  as  cable  shields  or  rope  fillers,  which  fill  the  interstices  between  the 
strands,  are  often  used  on  tail  and  mam  ropes. 


WIRE  ROPES. 


125 


PROPER  WORKING  LOAD 


126 


WIRE  ROPES. 


Starting  Strain  on  Hoisting  Rope.— In  selecting  a hoisting  rope,  due  allow- 
ance must  be  made  for  the  shock  and  extra  strain  imposed  on  the  rope  when 
the  load  is  started  from  rest.  Experiments  made  by  placing  a dynamometer 
between  the  rope  and  the  cage  have  shown  that  starting  stress  may  be  from 
two  to  three  times  the  actual  load. 


Experiment  1. 


Strain  in  Rope. 
Pounds. 


Empty  cage,  lifted  gently 

Empty  cage,  started  with  2k  in.  of  slack  rope 
Empty  cage,  started  with  6 in.  of  slack  rope  . 
Empty  cage,  started  with  12  in.  of  slack  rope 


4,030 

5,600 

8,950 

12,300 


Experiment  2. 


Strain  in  Rope. 
Pounds. 


Cage  and  loaded  cars,  as  weighed 

Cage  and  loaded  cars,  lifted  slowly  and  gently  

Cage  and  loaded  cars,  started  with  3 in.  of  slack  rope 
Cage  and  loaded  cars,  started  with  6 in.  of  slack  rope 
Cage  and  loaded  cars,  started  with  9 in.  of  slack  rope 


11,300 

11,525 

19,025 

24,625 

26,850 


Horsepower  of  Manila  Ropes. 
( Link-Belt  Engineering  Co.) 


Diam.  of 
Rope. 

Weight  per 
Foot. 

Breaking 

Strain. 

Working 

Strain. 

1,000  Ft. 
per  Min. 

2,000  Ft. 
per  Min. 

3,000  Ft. 
per  Min. 

4,000  Ft. 
per  Min. 

5,000  Ft. 
per  Min. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

I 

0.15 

4,000 

121 

2* 

90 

4* 

90 

6* 

80 

7* 

80 

8* 

70 

* 

0.18 

5,000 

151 

2| 

110 

5* 

110 

7* 

100 

9* 

100 

10* 

90 

7 

8 

0.27 

7,500 

227 

4* 

170 

8* 

170 

11* 

160 

14* 

150 

16 

130 

1 

0.33 

9,000 

272 

5 

200 

10 

200 

14 

180 

17* 

170 

19 

150 

1* 

0.45 

12,250 

371 

7 

280 

13* 

270 

19 

250 

23* 

230 

26 

210 

1* 

0.50 

14,000 

424 

8 

320 

15* 

310 

22 

290 

27 

270 

29* 

240 

if 

0.65 

18,062 

547 

10* 

410 

20 

400 

28* 

370 

34* 

350 

38* 

310 

1* 

0.73 

20,250 

613 

11* 

460 

22 

440 

31* 

420 

39 

390 

43* 

350 

H 

0.82 

25,000 

760 

14* 

570 

27* 

550 

39* 

520 

49 

490 

554 

448 

1* 

1.08 

30,250 

916 

17 

680 

33* 

660 

47* 

630 

58* 

580 

64* 

520 

2 

1.27 

36,000 

1,000 

20* 

810 

40 

790 

56* 

740 

69* 

670 

77* 

620 

WIRE-ROPE  FASTENINGS. 

Thimble  spliced,  in  ordinary  style,  is  shown  in  Fig.  1 (a).  In  this  method, 
the  wires,  after  being  frayed  out  at  the  end  and  the  rope  bent  around  the 
thimble,  are  laid  snugly  about  the  main  portion  of  the  rope  and  securely 
fastened  by  wrapping  with  stout  wire,  the  extreme  ends  that  project  below 
this  wrapping  being  folded  back,  as  shown. 

Another  style  of  thimble  splicing  is  shown  in  Fig.  1(5).  In  this  case  the 
strands  are  interlocked  as  in  splicing,  and  the  joint  is  wrapped  with  wire  as 
in  the  former  method.  The  socket  fastening  is  sho  wn*in  Fig.  1 (c).  The  hole 
in  which  the  rope  end  is  fastened  is  conical  in  shape.  The  rope  is  generally 
secured  by  fraying  out  the  wires  at  the  end,  the  interstices  being  filled  up 
with  spikes  driven  in  tightly.  The  whole  is  finally  cemented  by  pouring  in 
molten  Babbitt  metal.  This  makes  a much  neater  fastening  than  either 
of  thos6  shown  in  (a)  and  (5),  but  it  does  not  possess  anything  like  as 
much  strength.  The  thimble  possesses  a serious  disadvantage;  it  is 
usually  made  of  a piece  of  curved  metal  bent  around  into  an  oval  shape, 


WIRE-ROPE  SPLICING. 


127 


Fig.  1. 


ns  shown  in  (a)  and  (6),  with  the  groove,  in  which  the  rope  lies,  outside, 
the  ends  coming  together  in  a sharp  point.  When  weight  is  placed  on  the 
rope  the  strain  on  the  thimble  is  apt  to  cause  one  end  to  wedge  itself 
beyond  or  past  the  other,  and  with  its  sharp  edge 
it  cuts  the  strands  in  the  splice  Mr.  William 
Hewitt,  of  Trenton,  N.  J.,  while  testing  the 
strength  of  wire  ropes,  discovered  this  tendency, 
and  experimented  with  sockets  with  the  idea 
of  devising  some  method  of  fastening  the  rope 
securely  in  the  socket.  He  found  that  by  adopt- 
ing the  following  plan  he  secured  good,  results: 

The  wires,  after  being  frayed  out  at  the  end, 
were  bent  upon  themselves  in  hook  fashion,  the 
prongs  of  some  being  longer  than  others,  so  that 
the  bunch  would  conform  to  the  conical  aperture 
of  the  socket,  and  the  melted  Babbitt  metal  was 
finally  run  in  as  usual.  The  rope  was  subjected 

thea  socket  The  sfmpHcUy  of  this  method  commends 

itself  to  practical  men.  . 

RAPID  METHOD  OF  SPLICING  A WIRE  ROPE.* 

The  only  tools  needed  are  a cold  cutter  and  hammer  for  cutting  and 
trimming-  the  strands,  and  two  needles  12  in.  long,  made  of  good  steel  and 
tapered'ovaUy  toa  point.  Cut  off  the  ends  of  the  ropes  to  be  ^phcedand 
unlav  three  adjacent  strands  of  each  back  15  ft.,  cut  out  the  nemp 
center  to  this  point  and  relay  the  strands  for  7 ft.  and cut  thenroff.  Pull 
the  ropes  by  each  other  until  they  have  the  position  shown  m Fig.  2 (a), 
cut  off  a and  d'  5 and  c',  Fig.  2 (6),  making  their  lengths  approximately  10 
and  12£  ft  respectively,  measured  from  the  point  where  the  hemp  centers 
were^cut.  Pllce  theses  together,  Fig.  2 (O^unlay 

\mp  *.  lfc'?Fi|n2  (hj^SimilOTlyl 

/,  it 

until  the  rope  appears  as  in 

2 (c).  Next  run  the 

u Hemp  Center  strands  into  the  middle  of 

(a>  the  rope.  To  do  this,  cut 


(b)  /'«■'  b 


Fig.  2. 

off  the  end  of  the  strand  e',  Fig.  2 (c),  so  that  when  it  is  put  in  place  it  will  just 
reach  to  the  end  x of  the  hemp  core,  and  then  push _ the  needle  A, , Fig.  2 1(c) 
through  the  rope  from  the  under  side,  leaving  two  strands  at  the  front  of  the 
needle,  as  shown.  Push  the  needle  B through  from  the  upper  side  and  as 
close  to  the  needle  A as  possible,  leaving  the  strands  e and  e between  them; 
place  the  needle  A on  the  knee  and  turn  the  needle  B around  with  the  coil  of 
the  rope,  and  force  the  strand  e'  into  the  center  of  the  rope.  Repeat  this 

# W.  H.  Morris,  “ Mines  and  Minerals,”  September,  1898. 


WIRE  ROPES. 


WIRE-ROPE  SPLICING. 


129 


ODeration  with  the  other  ends  and  cut  them  off*  so  that  the  ends  coming 
together  in  the  center  of  the  rope  will  butt  against  each  other  as  nearly  as 

possible.  . 

ORDINARY  LONG  SPLICE. 

Tools  Reauired— One  pair  wire  nippers,  for  cutting  off  strands;  one  pair 
nliers  for  pulling  through  and  straightening  ends  of  strands;  two  niarline- 
snikes  one  round  and  one  oval,  for  opening  strands;  one  knife  to  cut  hemp 
center-  two  clamps,  to  untwist  rope  to  insert  ends  of  strands,  or,  m place  of 
them  two  short  hemp-rope  slings,  with  a stick  for  each  as  a lever;  a wooden 
mallet  and  some  rope  twine.  Also,  a bench  and  yise  are  handy. 

The  length  of  the  splice  depends  on  the  size  of  the  rope.  The  larger  ropes 
require  the  longer  splices.  The  splice  of  ropes  from  f hi.  to  * m.  m diameter 
should  not  be  less  than  20  ft.;  from  ¥ m.  to  1¥  in.,  30  ft.,  and  from  la  in. 

UP,To  splice  a rope,  tie  each  end  with  a piece  of  cord  at  a distance  equal  to 
one-half  the  length  of  the  splice,  or  10  ft.  back  from  the  end,  for  a $ rope,  after 
which  unlay  each  end  as  far  as  the  cord.  Then  cut  out  the  hemp  center 
and  bring  the  two  ends  together  as  close  as  possible,  placing  the  strands  of 
the  one  end  between  those  of  the  other,  as  shown  m Fig.  3 (a).  Now  remove 
the  cord  k from  the  end  M of  the  rope,  and  unlay  any  strand,  as  a,  and  follow  it 
up  with  the  strand  of  the  other  end  M'  of  the  rope  that  corresponds  to  it  as 
a/P  Fig-  3 (a)  About  6 in.  of  a are  left  out,  and  a is  cut  off  about  6 m from  the 
rone  thus  leaving  two  short  ends,  as  shown  at  P in  Fig.  3 (h),  which  must  be 
tied  for  the  present  by  cords  as  shown.  The  cord  k should  again  be  wound 
around  the  end  M of  the  rope,  Fig.  3 (a),  to  prevent  the  unraveling  of  the 
strands-  after  which  remove  the  cord  k'  on  the  other  or  if  end  of  the  rope, 
and  unlay  the  strand  6;  follow  it  up,  as  above,  with  the  strand  b , leaving 
the  ends  out,  and  tying  them  down  for  the  present,  as  before  described  m 
the  case  of  strands  a and  a ',  see  Q,  Fig.  3 (6) ; also,  replac ie  the  cord  fc  for  the 
same  purpose  as  stated  above.  Now,  again  remove  the  cord  k and  unlay  the 
next  strand  as  c,  Fig.  3 (a),  and  follow  it  up  with  c',  stopping,  however,  this 
time  within  4 ft.  of  the  first  set.  Continue  this  operation  with  the  remaining 
6 strands  stopping  4 ft.  short  of  the  preceding  set  each  time.  The  strands 
are  now  in their  proper  places,  with  the  ends  passing  each  other  at  intervals 
of  4 ftas  shownin  Fig.  3(c).  To  dispose  of  the  loose  ends,  clamp  the  rope  m a 
vise  at  the  left  of  the  strands  a and  a',  Fig.  3 (c),  and  fasten  a clamp  to  the  rope 
at  the  right  of  these  strands;  then  remove  the  cords  tied  around  the  rope 
that  hold  these  two  strands  down;  after  which  turn  the  clamp  in  the  oppo- 
site direction  to  which  the  rope  is  twisted,  thereby  untwisting  the  rope,  as 
shownin  Fig  3 (d) . The  rope  should  be  untwisted  enough  to  allow  its  hemp 
cores' to  be  pulled  out  with  a pair  of  nippers.  Cut  off  24  in.  of  the  hemp  core 
12  in  at  each  side  from  the  point  of  intersection  of  the  strands  a and  a,and 
push  the  tSds  ofthe  strandsP  in  their  place  as  shown  in  Fig.  3 (d).  Then 
allow  the  rope  to  twist  up  to  its  natural  shape,  and  remove  the  clamps. 
After  the  rope  has  been  allowed  to  twist  up,  the  strands  tucked  m generally 
bulge  out  somewhat.  This  bulging  may  be  reduced  by  lightly  tapping  the 
bulged  part  of  the  strands  with  a wooden  mallet,  which  will  force  their  ends 
farther  into  the  rope.  Proceed  in  the  same  manner  to  tuck  m the  other  ends 
of  the  strands.  


CHAINS. 

The  links  of  iron  chains  are  usually  made  as  short  as  is  consistent  with 
easy  play,  so  as  to  make  them  less  liable  to  kink,  and  also  to  prevent  bending 

when  wound  around  drums,  sheaves,  etc.  . ■ . , . « 

The  weight  of  close-link  chain  is  about  three  times  the  weight  of  bar  from 

which  it  is  made,  for  equal  lengths.  , ' . , . , 

Karl  von  Ott,  comparing  weight,  cost,  and  strength  of  three  materials, 
hemp  iron  wire,  and  chain  iron,  concludes  that  the  proportion  between  cost 
of  hemp  rope,  wire  rope,  and  chain  is  as  2 : 1 : 3,  and  that,  therefore,  for 
equal  resistances,  wire  rope  is  only  half  the  cost  of  hemp  rope,  and  a third 

Chains  of  warranted  superior  iron  will  stand  25 } more  strain  before 
breaking  The  report  of  the  U.  S.  Test  Board,  1881,  shows  that  the  ultimate 
strength  of  chains  may  be  taken  at  1.6  that  of  the  iron  from  which  the  links 
are  made. 


130 


hydrostatics. 


The  strength  of  chains  varies,  owing  to  the  nature  of  the  iron  from  which 
they  are  made,  and  their  mechanical  construction.  The  following  table  is 
approximately  correct  for  ordinary  iron  chains: 


Table  of  Weight  an©  Strength  of  Chains. 


Diameter  of 

Weight  of 

Diameter  of 

Weight  of 

Rod  of 
Which  the 
Links  Are 
Made. 

Chain 

per 

Running 

Foot. 

Working 

Strength. 

Tons. 

Breaking 

Strain. 

Tons. 

Rod  of 
Which  the 
Links  Are 
Made. 

Chain 

per 

Running 

Foot. 

Working 

Strength. 

Tons. 

Breaking 

Strain. 

Tons. 

Inches. 

Pounds. 

Inches. 

Pounds. 

t3s 

■ A 
•4 

h 

T5 

1 

ll 

.325 

.19 

.773 

§ 

7.10 

4.40 

16.80 

.579 

.36 

1.37 

it 

8.14 

5.00 

19.32 

.904 

.45 

2.14 

1 

9.26 

5.71 

22.00 

1.30 

.85 

3.09 

11.70 

7.23 

26.44 

1.78 

1.09 

4.20 

li 

14.50 

9.00 

32.64 

2.31 

1.43 

5.50 

if 

17.50 

10.80 

39.42 

2.93 

1.80 

6.96 

l£ 

20.80 

13.00 

47.00 

3.62 

2.23 

8.58 

if 

24.40 

15.24 

55.14 

4.38 

2.70 

10.39 

n 

28.40 

17.65 

63.97 

1 6 
3 

5.21 

3.21 

12.36 

if 

32.60 

20.27 

73.44 

4 

13 

TS 

6.11 

3.80 

14.42 

2 

37.00 

23.10 

83.55 

HYDROSTATICS. 


Hydrostatics  treats  of  the  equilibrium  of  liquids,  and  of  their  pressures  on 
the  walls  of  vessels  containing  them;  the  science  depends  on  the  way  in 
which  the  molecules  of  a liquid  form  a mass  under  the  action  of  gravity 
and  molecular  attraction,  the  latter  of  which  is  so  modified  in  liquids  as  to 
give  them  their  state  of  liquidity.  While  the  particles  of  a liquid  cohere, 
they  are  free  to  slide  upon  one  another  without  the  least  apparent  friction; 
and  it  is  this  perfect  mobility  that  gives  them  the  mechanical  properties 
considered  in  hydrostatics.  . 

The  fundamental  property  may  be  thus  stated:  When  a pressure  is  exerted 
on  any  part  of  the  surface  of  a liquid , that  pressure  is  transmitted  undiminished 
to  all  parts  of  the  mass , and  in  all  directions.  This  is  a physical  axiom,  and  on 
it  are  based  nearly  all  the  principles  of  hydrostatics. 

Equilibrium  of  Liquids.— This  is  a property  of  liquids  that  can  be  easily 
demonstrated,  and  examples  are  frequently  seen.  Thus,  if  two  barrels  are 
connected  at  the  bottom  with  a pipe,  and  water  is  poured  in  one  until  it 
reaches  within  a foot  of  the  top,  the  water  in  the  other  will  be  found  to  have 


attained  the  same  height. 

Pressure  of  Liquids  on  Surfaces. — The  general  proposition  on  this  point  is  as 
follows*  The  pressure  of  a liquid  on  any  surface  immersed  m it  is  equal  to  the 
weiqht  of  a column  of  the  liquid  whose  base  is  the  surface  pressed , and  whose 
heiqht  is  the  perpendicular  depth  of  the  center  of  gravity  of  the  surface  below  the 
surface  of  the  liquid.  The  pressure  thus  exerted  is  independent  of  the  shape 
or  size  of  the  vessel  or  cavity  containing  the  liquid. 

The  pressure  of  a liquid  against  any  point  of  any  surface,  either  curved 

or  plane,  is  always  perpendicular  to  the  surface  at  that  point. 

At  any  given  depth  the  pressure  of  a liquid  is  equal  in  every  direction, 
and  is  in  direct  proportion  to  the  vertical  depth  below  the  surface. 

The  weight  of  a cubic  foot  of  fresh  water,  at  ordinary  temperature  of  the 
atmosphere,  that  is,  from  32°  F.  to  80°  F.,  is  usually  assumed  at  62.5  lb.  This 
is  a trifle  more  than  the  actual  weight,  but  is  sufficiently  close  for  purposes 
of  calculation.  . . f « 

To  Find  the  Pressure  Exerted  by  Quiet  Water  Against  the  Side  of  a Gangway  or 
Heading  —Multiply  the  area  of  the  side  in  square  feet  by  the  perpendicular 
distance  from  the  surface  of  the  water  to  a point  equidistant  between  the 
top  and  bottom  of  the  submerged  heading  or  gangway,  and  multiply  the 
product  bv  62.5.  The  result  will  be  the  pressure  in  pounds,  exclusive  of 
atmospheric  pressure.  This  latter  need  not  be  considered  in  ordinary 
mining  work. 


HYDROSTATICS . 


131 


Example.— If  an  abandoned  colliery,  opened  by  a slope  on  a pitch  of  25° 
and  100  yd.  long,  is  allowed  to  fill  with  water,  what  is  the  average  pressure 
exerted  on  each  square  foot  of  the  lower  rib  of  the  gangway,  assuming 
that  the  gangways  were  driven  dead  level,  and  that  the  length  of  the  slope 
was  measured  to  a point  on  the  lower  rib  equidistant  between  top  and 
bottom  of  gangway. 

We  here  have  a perpendicular  height  of  water  = 300  X sine  of  25° 
= 126.78  ft.  Then,  the  pressure  on  each  square  foot  of  the  lower  rib  of 
gangway  = 126.78  X 62.5  lb.,  or  the  weight  of  1 cu.  ft.,  or  a pressure  on  each 
square  foot  of  surface  of  7,923.75  lb.,  or  over  3i  gross  tons.  The  total  pressure 
exerted  along  the  gangwav  may  readily  be  found  by  multiplying  the 
7,923.75  lb.  by  the  number  of  square  feet  of  the  lower  rib  against  which 
it  rests. 

To  find  the  total  pressure  of  quiet  water  against  and  perpendicular  to  any 
surface  whatever,  as  a dam,  embankment,  or  the  bottom,  side  or  top  of  any 
containing  vessel,  water  pipe,  etc.,  no  matter  whether  said  surface  be 
vertical,  horizontal,  or  inclined;  or  whether  it  be  flat  or  curved;  or  whether 
it  reach  to  the  surface  of  the  water  or  be  entirely  below  it: 

Multiply  the  area,  in  square  feet , of  the  surface  pressed,  by  the  vertical  depth  in 
feet  of  its  center  of  gravity  below  the  surface  of  the  water,  and  this  product  by  62.5. 
The  result  will  be  the  pressure  in  pounds. 

Thus,  assuming  that  in  the  annexed  three  figures  the  depth  of  water  in 
each  dam  is  12  ft.,  and  the  wall  or  embankment  is  50  ft.  long,  then  in 
Fig.  1 the  total  pressure  will  equal  12  X 50  X 6 X 62.5  ==,  225,000  lb. 

In  Figs.  2 and  3 the  walls  or  embankments,  being  inclined,  expose  a 
greater  surface  to  pressure,  say  18  ft.  from  A to  B.  Then  the  total  pressure 
equals  18  X 50  X 6 X 62.5  = 337,500  lb. 

Now,  the  results  obtained  are  the  total  pressures  without  regard  to  direction. 

In  Fig.  1 the  total 
pressure  calculated, 
or  225,000  lb.,  is  hori- 
zontal,  tending 
either  to  overturn 
the  wall  or  make  it 
slide  on  its  base. 
The  center  of  pres- 
sure  is  at  C,  or  one-third  of  the  vertical  depth  from  the  bottom. 

In  Fig.  2 the  pressure  is  exerted  in  two  directions;  one  pressure,  acting 
horizontally,  tends  to  overthrow  or  slide  the  wall,  while  the  other,  acting 
vertically,  tends  to  hold  it  in  place. 

In  Fig.  3 the  pressure  is  also  exerted  in  two  directions;  one  pressure, 
acting  horizontally,  tends  to  overthrow  or  slide  the  wall,  while  the  other 
tends  to  lift.  , , _ . _ 

So  long  as  the  vertical  depth  of  water  remains  the  same,  the  horizontal 
pressure  remains  the  same,  no  matter  what  inclination  is  given  the  wall. 
Thus,  in  Figs.  2 and  3,  the  horizontal  pressure  is  the  same  as  in  Fig.  1, 
or  225,000  lb.  ^ ^ 

The  total  pressure  of  the  water  is  distributed  over  the  entire  depth  of  the 
submerged  part  of  the  back  of  the  wall,  and  is  least  at  the  top,  gradually 
increasing  toward  the  bottom.  But  so  far  as  regards  the  united  action  of 
every  portion  of  it,  in  tending  to  overthrow  the  wall,  considered  as  a single 
mass  of  masonry,  incapable  of  being  bent  or  broken,  it  may  all  be  assumed 
to  be  applied  at  C,  which  is  one-third  of  the  vertical  depth  from  the  bottom 
in  Fig.  1,  or,  what  is  the  same  thing,  one-third  of  the 
slope  distance  from  the  bottom  in  Figs.  2 and  3. 

No  matter  how  much  water  is  in  a dam  or  vessel, 
the  pressure  remains  the  same,  so  long  as  the  area 
pressed  and  the  vertical  depth  of  its  center  of  gravity 
below  the  level  surface  of  the  water  remains  un- 
changed. Thus,  if  the  water  in  dam  shown  in  Fig.  1 
extended  back  1 mile,  it  would  exert  no  more  pressure 
against  the  wall  than  if  it  extended  back  only  1 ft. 

In  any  two  vessels  having  the  same  base,  and  con- 
taining the  same  depth  of  water,  no  matter  what 
quantity,  the  pressures  on  the  bases  are  equal.  Thus, 
if  Figs.  4 and  5 have  the  same  base  and  be  filled  with 
water  to  the  same  depth,  the  pressure  on  the  bases 
Will  be  equal.  This  fact,  that  the  pressure  on  a given  surface,  at  a given 


Fig.  4. 


Fig.  5. 


132 


HYDROSTATICS. 


depth,  is  independent  of  the  quantity  of  water,  is  called  the  hydrostatic 

P<1  As  the  pressure  of  water  against  any  point  is  at  right  angles  to  the  surface 
at  that  point,  it  follows  that  props  or  other  strengthening  material  for  the 
strengthening  of  such  structures  as  a sloping  dam,  should  be  so  placed  as  to 
offer  the  greatest  resistance  in  a line  at  right  angles  to  the  sloping  surface, 
and  these  supports  should  be  strongest  and  closest  together  at  the  bottom. 
For  the  same  reason,  the  hoops  on  a circular  tank  should  be  strongest  and 
closest  at  the  bottom.  . ...  . . 

Transmission  of  Pressure  Through  Water-Water,  in  common  with  other 
Kauids  possesses  the  important  property  of  transmitting  pressure  equally  in 
4 all  directions.  Thus,  if  a vessel  is  constructed  with  two 

cylinders,  the  area  of  one  being  10  sq.  in.,  and  that  of  the 
other  100  sq.  in.,  and  the  vessel  is  filled  with  water  (Fig.  6), 
and  pistons  fitted  to  the  cylinders,  a pressure  of  100  lb. 
applied  at  the  smaller  will  balance  1,000  lb.  at  the  larger. 
This  is  the  principle  of  the  hydrostatic  press.  Air  and  other 
gaseous  fluids  transmit  pressure  equally  in  all  directions, 
like  liquids,  but  not  as  rapidly. 

To  Find  the  Pressure  on  a Plane  Surface  at  Any  Given  Depth 
of  Water.— For  pounds  per  square  inch,  multiply  depth  in 
feet  by  .434.  For  pounds  per  square  foot,  multiply  depth 
in  feet  by  62.5.  For  tons  per  square  foot,  multiply  depth 
in  feet  by  .0279.  The  pressure  per  square  foot  at  different 
depths  increases  directly  as  the  depths.  The  total  pressure 
against  a plane  1 ft.  wide  at  different  depths  increases  as  the  square  of  the 
depths. 

Pressure  in  Pounds  per  Sq.  Ft.  at  Different  Vertical  Depths,  and 
Also  the  Total  Pressure  Against  a Plane  1 Ft.  Wide  Extending 
Vertically  From  the  Surface  of  the  Water  to  the  Same  Depths. 


Fig.  6. 


Depth. 

Pressure. 

Pouuds 

Total 

Pressure. 

Depth. 

Pressure. 

Pounds 

Total 

Pressure. 

Depth. 

Pressure. 

Pounds 

Total 

Pressure. 

Feet. 

per  Sq.  Ft. 

Pounds. 

Feet. 

per  Sq.  Ft. 

Pounds. 

r cci. 

per  Sq.  Ft. 

Pounds. 

i 

62.5 

31 

27 

1,687 

22,781 

65 

4,062 

132,025 

X 

2 

125 

125 

28 

1,750 

24,500 

70 

4,375 

153,124 

3 

187 

281 

29 

1,812 

26,281 

75 

4,687 

175,779 

4 

250 

500 

30 

1,875 

28,125 

80 

5,000 

200,000 

K 

312 

781 

31 

1,937 

30,031 

85 

5,312 

225,775 

o 

Q 

375 

1,125 

32 

2,000 

32,000 

90 

5,625 

253,124 

7 

437 

1,531 

33 

2,062 

34,031 

95 

5,937 

282,025 

i 

g 

500 

2,000 

34 

2,125 

36,125 

100 

6,250 

312,500 

9 

562 

2,531 

35 

2,187 

38,281 

110 

6,875 

378,124 

10 

625 

3,125 

36 

2,250 

40,500 

120 

7,500 

450,000 

11 

687 

3,781 

37 

2,312 

42,781 

130 

8,125 

528,100 

12 

750 

4,500 

38 

2,375 

45,125 

140 

8,750 

612,496 

13 

812 

5,281 

39 

2,437 

47,531 

150 

9,375 

703.116 

14 

875 

6,125 

40 

2,500 

50,000 

160 

10,000 

800 j 000 

15 

937 

7,031 

41 

2,562 

52,531 

170 

10,625 

903,100 

16 

1,000 

8,000 

42 

2,625 

55,125 

180 

11,250 

1,012,496 

17 

1,062 

9,031 

43 

2,687 

57,781 

190 

11,875 

1,128,100 

18 

1,125 

10,125 

44 

2,750 

60,500 

200 

12,500 

1,250,000 

19 

1,187 

11,281 

45 

2,812 

63,281 

225 

14,062 

1,582,025 

20 

1,250 

12,500 

46 

2,875 

66,125 

250 

15,625 

1,953,100 

21 

1,312 

13,781 

47 

2,937 

69,031 

275 

17,187 

2,363,275 

22 

1,375 

15,125 

48 

3,000 

72,000 

300 

18,750 

2,812,500 

23 

1,437 

16,531 

49 

3,062 

75,031 

350 

21,875 

3,828,100 

24 

1,500 

18.000 

50 

3,125 

78,125 

400 

25,000 

5,000,000 

25 

1,562 

19,531 

55 

3,437 

94,531 

450 

28,120 

6,328,100 

26 

1,625 

21,125 

60 

3,750 

112,500 

500 

31,250 

7,812,500 

Pressure  of  Water  in  Pipes.— As  water  exerts  a pressure  equally  in  al. 
directions,  it  is  important  that  in  pipe  lines  the  pipe  should  be  sufficiently 
thick  to  assure  strength  enough  to  resist  a bursting  pressure.  In  ordinary 


H YD  ROST  A TICS. 


133 


practice,  the  thickness  of  cast-iron  water  pipes  of  different  bores  is  calculated 
by  Mr.  J.  T.  Fanning’s  formula,  given  in  his  Hydraulic  Engineering,  which 
is  as  follows: 

. _ (pressure  in  lb.  per  sq.  in.  + 100)  X bore  in  in. 

Thickness  m inches  — .4  X ultimate  tensile  strength 


+ .333 


bore  in  in.\ 
Too  )' 


This  formula,  worked  out  for  different  heads  and  different  sizes  of  bore, 
yields  the  following  results: 


Thickness  of  Pipe  for  Different  Heads  and  Pressures. 


Head  in  Ft 

50 

100 

200 

300 

500 

1,000 

Pressure  in  Lb. 

21.7 

43.4 

86.8 

130 

217 

434 

per  Sq.  In. 

Bore.  Inches. 

Thickness  of  Pipe.  Inches. 

2 

.36 

.37 

.38 

.39 

.42 

.48 

3 

.37 

.38  ■ 

.40 

.42 

.45 

.54 

4 

.39 

.40 

.42 

.45 

.50 

.61 

6 

.41 

.43 

.47 

.50 

.57 

.75 

8 

.45 

.47 

.52 

.57 

.66 

.90 

10 

.47 

.50 

.56 

.62 

.74 

1.04 

12 

.49 

.53 

.60 

.67 

.82 

1.18 

16 

.55 

.60 

.70 

.79 

.98 

1.46 

18 

.57 

.63 

.74 

.85 

1.06 

1.60 

20 

.61 

.67 

.79 

.91 

1.15 

1.75 

24 

.66 

.73 

.87 

1.02 

1.30 

2.03 

30 

.74 

.83 

1.01 

1.19 

1.55 

2.46 

36 

.82 

.93 

1.15 

1.36 

1.80 

2.88 

48 

.98 

1.13 

1.42 

1.70 

2.28 

3.73 

In  the  above  table,  the  ultimate  tensile  strength  of  cast  iron  is  taken  at 
18  000  lb.  per  sq.  in.  The  addition  of  100  lb.  to  the  pressure  is  made  to  allow 
for  water  ram.  The  valves  of  water  pipes  should  he  closed  slowly , and  the 
necessity  of  this  increases  as  the  pipes  increase  in  diameter.  If  this  rule  is 
not  observed,  the  momentum  of  the  running  water  is  arrested  suddenly,  and 
a great  pressure  is  created  against  the  pipes  in  all  directions,  and  through- 
out the  entire  length  of  the  line  above  the  valve,  even  if  it  be  many  miles, 
and  there  is  danger  of  their  bursting  at  any  point.  For  this  reason,  stop- 
gates  are  shut  by  screws,  because  they  prevent  any  very  sudden  closing;  but 
in  pipes  of  large  diameters,  even  the  screws  must  be  worked  very  slowly  to 

^^Com  prelss fifiUty  of  Liquids.— Liquids  are  not  entirely  incompressible,  but 
they  are  so  nearly  so,  that  for  most  purposes  they  may  be  considered  as 
incompressible.  The  bulk  of  water  is  diminished  about  by  a pressure  of 
324  lb  per  sq.  in.,  or  22  atmospheres;  varying  slightly  with  its  temperature. 
It  is  perfectly  elastic,  regaining  its  original  bulk  when  the  pressure  is 
r emo  v ed 

Construction  of  Dams  in  Mines.— Dams  may  be  constructed  in  mines,  either 
to  isolate  a portion  of  the  workings  so  that  they  can  be  flooded  to  extinguish 
fires  or,  in  cases  where  an  extremely  wet  formation  has  been  penetrated,  it 
is  sometimes  expedient  to  construct  a dam  so  as  to  prevent  the  water  from 
flowing  into  the  workings.  Mine  dams  should  be  of  sufficient  strength  to 
resist  any  column  of  water  that  will  be  likely  to  come  against  them.  The 
dam  should  be  arched  toward  the  direction  from  which  the  pressure  comes, 
and  should  be  given  a good  firm  bearing  in  both  walls  and  in  the  floor  and 
roof  Fig  7 illustrates  a brick  dam  that  was  constructed  in  Kehley’s  Run 
Colliery  at  Shenandoah,  Pa.,  to  isolate  a portion  of  the  seam  so  that  it  might 


134 


HYDROSTATICS. 


be  flooded  to  extinguish  a mine  fire.  This  is  one  of  the  largest  mine  dams 
that  has  ever  been  constructed.  It  is  composed  of  three  brick  arches,  each 
having  a thickness  of  5 ft.,  that  are  placed  one  against  the  other  so  that  they 
act  as  one  solid  structure.  The  gangway  at  this  point  is  about  20  ft.  wide, 
and  the  distance  to  the  next  upper  level  is  about  119  ft.  It  was  intended 
that  this  should  be  the  maximum  head  of  water  that  the  dams  would  ever  \ 
have  to  resist,  though  they  were  made  sufficiently  strong  to  resist  a head  of 
water  reaching  to  the  surface.  The  separate  walls  were  constructed  one  at 
a time,  and  the  cement  allowed  to  set  before  the  next  wall  was  placed.  The 
back  wall  was  carried  to  a greater  depth  and  height  than  the  others,  so  as  to 
make  sure  of  the  fact  that  all  slips  or  partings  had  been  closed.  The  total 
pressure  upon  the  dam  when  the  water  was  in  the  mine  was  about  70,000  lb. 
per  sq.  ft. 

Dams  constructed  to  permit  the  flooding  of  a mine  usually  require  no 
passages  through  them,  but  where  dams  are  constructed  to  confine  the 
water  to  certain  parts  of  the  workings,  and  so  reduce  pumping  charges,  it 
may  be  necessary  to  provide  both  manways  and  drain  pipes  through  the 


Fig.  7.  Fig.  8. 


dams.  Fig.  8 illustrates  a plan  and  cross-section  of  a dam  in  the  Curry 
Mine,  at  Norway,  Mich.  (“Mines  and  Minerals,”  Vol.  18,  page  177;  Trans. 
A I.  M.  E.,  XXVII,  402),  constructed  to  keep  the  water  that  came  from  some 
exploring  drifts  out  of  the  mine  workings.  As  originally  constructed,  it 
consisted  of  a sandstone  dam  10  ft.  thick  and  arched  on  the  back  face 
with  a radius  of  6 ft.  A piece  of  20"  pipe  provided  a manway  through  the 
masonry  and  was  held  in  place  by  three  sets  of  clamps  and  bolts  passing 
through  the  stonework.  A 5"  drain  pipe  was  also  carried  through  the  dam 
and  secured  by  clamps.  When  the  pressure  came  upon  the  dam  it  was 
found  to  leak,  so  the  water  was  drained  off  and  a 22"  brick  wall  built 
2 ft.  4 in.  back  of  the  dam,  the  space  between  being  filled  with  concrete,  and 
the  manway  and  drain  pipe  extended  through  the  brick  wall.  Before  closing 
the  drain  pipe,  horse  manure  was  fastened  against  the  face  of  the  brick  wall 
by  means  of  a plank  partition.  After  this  the  manway  and  drain  pipe  were 
closed,  and  when  the  pressure  came  on,  the  dam  was  found  to  leak  a small 


HYDRAULICS. 


135 


amount,  but  this  soon  practically  ceased,  showing  that  the  manure  had 
closed  the  leaks.  A gauge  in  the  head  of  the  manway  on  this  dam  showed  a 
pressure  of  211  lb.,  which  corresponded  to  a static  head  of  640  ft.  of  water. 
The  total  pressure  against  the  dam  was  something  over  800  tons,  which  it 
successfully  resisted. 


HYDRAULICS. 

Hydraulics  treats  of  liquids  in  motion,  and  in  this,  as  in  hydrostatics, 
water  is  taken  as  the  type.  In  theory  its  principles  are  the  same  as  those  of 
falling  bodies,  but  in  practice  they  are  so  modified  by  various  causes  that 
they  cannot  be  relied  on  except  as  verified  by  experiment.  The  discrepancy 
arises  from  changes  of  temperature  that  vary  the  fluidity  of  the  liquid,  from 
friction,  the  shape  of  the  orifice,  etc.  As  we  shall  deal  with  water  only,  the 
first  cause  may  be  thrown  aside  as  of  little  account. 

In  theory  the  velocity  of  a jet  is  the  same  as  that  of  a body  falling  from  the 
surface  of  the  water. 

To  Find  the  Theoretical  Velocity  of  a Jet  of  Water.— Let  v = the  velocity, 
g = the  acceleration  of  gravity  (32.16  ft.),  and  d = the  distance  of  the  orifice 
below  the  surface  of  the  water. 

Then,  v = V 2 g d,  or  v = the  square  root  of  twice  the  product  of  g x d. 

Example.— The  depth  of  water  above  the  orifice  is  64  ft.;  what  is  the 
velocity  ? 

Substituting  64  for  d , and  32.16  for  g , we  have,  v = ]/  2 X 32.16  X 64,  or 
64.16. 

To  Find  the  Theoretical  Quantity  of  Water  Discharged  in  a Given  Time.— Multi- 
ply the  area  of  the  orifice  by  the  velocity  of  the  water,  and  that  product  by 
the  number  of  seconds. 

Example.— What  quantity  of  water  will  be  discharged  in  5 seconds  from 
an  orifice  having  an  area  of  2 sq.  ft.,  at  a depth  of  16  ft.? 

\/  2 X 32.16  X 16  X 2 = 64.16  cu.  ft,,  or  the  amount  discharged  in  1 
second,  and  in  5 seconds  the  amount  will  be  5 X 64.16  = 320.8  cu.  ft. 

The  above  rules  are  only  theoretical,  and  are  only  useful  as  foundations 
on  which  to  build  practical  formulas. 

Flow  of  Water  Through  Orifices.— The  standard  orifice,  or  an  orifice  so 
arranged  that  the  water  in  flowing  from  it  touches  only  a line,  as  would  be 
the  case  in  flowing  through  a hole  in  a very  thin  plate,  is  used  for  the 
measurement  of  water.  The  contraction  of  the  jet,  which  always  occurs 
when  water  issues  from  a standard  orifice,  is  due  to  the  circumstance  that 
the  particles  of  water  as  they  approach  the  orifice  move  in  converging 
directions,  and  that  these  directions  continue  to  converge  for  a short  distance 
beyond  the  plane  of  the  orifice.  This  contraction  causes  only  the  inner 
corner  of  the  orifice  to  be  touched  by  the  escaping  water,  and  takes  place 
in  orifices  of  any  shape,  its  cross-section  being  similar  to  the  orifice  until 
the  place  of  greatest  contraction  is  passed.  Owing  to  this  contraction, 
the  actual  discharge  from  an  orifice  is  always  less  than  the  theoretical 
discharge. 

The  Coefficient  of  Contraction. — The  coefficient  of  contraction  is  the  number 
by  which  the  area  of  the  orifice  is  to  be  multiplied  in  order  to  find  the  area 
of  the  least  cross-section  of  the  jet.  In  this  way  by  experiment  this  coeffi- 
cient has  been  found  to  be  about  .62  (Merriman’s  “Hydraulics”);  or,  in 
other  words,  the  minimum  cross-section  of  the  jet  is  62$  of  the  cross-section 
of  the  orifice. 

The  Coefficient  of  Velocity.— The  coefficient  of  velocity  is  the  number  by 
which  the  theoretical  velocity  of  flow  from  the  orifice  is  to  be  multiplied  in 
order  to  find  the  actual  velocity  at  the  least  cross-section  of  the  jet.  This 
may  be  taken  for  practical  work  as  .98;  or,  in  other  words,  the  actual  flow 
at  the  contracted  section  is  98$  of  the  theoretical  velocity. 

The  Coefficient  of  Discharge  — The  coefficient  of  discharge  is  the  number  by 
which  the  theoretical  discharge  is  to  be  multiplied  in  order  to  obtain  the 
actual  discharge.  This  has  been  found  by  thousands  of  experiments  to  be 
equal  to  the  product  of  the  coefficients  of  contraction  and  velocity,  and  for 
practical  work  it  may  be  taken  as  .61;  or,  the  actual  discharge  from  standard 
orifices  is  61$  of  the  theoretic  discharge. 


136 


HYDRAULICS. 


Note  —While  the  coefficients  for  standard  orifices  with  sharp  edges  have 
been  determined  fairly  close,  those  for  the  more  complicated  cases  of  weirs, 
and  especially  for  the  flow  of  water  through  long  pipes,  are  simply  the 
nearest  approximation  to  the  truth  that  it  has  been  possible  to  obtain.  In 
all  cases  the  coefficient  should  be  one  that  has  been  determined  under  con- 
ditions similar  to  those  in  the  problem  in  hand.  For  instance,  it  is  not  prac- 
ticable to  use  the  coefficient  for  small  pipes  m solving  problems  relating  to 
large  ones,  or  for  short  pipes  in  solving  problems  relating  to  long  ones. 

Suppression  of  the  Contraction. — When  a vertical  orifice  has  its  lower  edge 
at  the  bottom  of  a reservoir,  the  particles  of  water  flowing  through  its  lower 
portion  move  in  lines  nearly  perpendicular  to  the  plane  of  the  orifice,  and 
the  contraction  of  the  jet  does  not  form  on  the  lower  side.  The  same  thing 
occurs  in  a lesser  degree  when  the  lower  edge  of  the  orifice  is  within  a dis- 
tance of  three  times  its  least  diameter  from  the  bottom.  The  suppression  of 
contraction  will  occur  on  the  side  if  it  is  placed  within  a distance  of  three 
times  its  least  diameter  from  the  side  of  a reservoir  the  suppression  of 
contraction  being  the  greater  the  nearer  the  orifice  is  to  the  side.  By  round- 
ino-  the  edge  of  the  orifice  sufficiently,  the  contraction  can  be  completely 
suppressed  and  the  discharge  can  be  increased.  As  stated  before  the  value 
of  the  coefficient  of  contraction  for  a standard  square-edged  orifice  is  .62,  but 
with  a rounded  orifice  it  may  have  any  value  between  .62  and  1.00,  depend- 
Sff  on  the  degree  of  rounding.  The  coefficient  of  discharge  for  square- 
edled  orifices  has  a mean  value  of  .61;  this  is  increased  with  rounded  edges 
and  may  have  any  value  between  .61  and  1.00,  although  it  is  not  probable 
that  values  greater  than  .95  can  be  obtained  except  by  the  most  careful 
adtustment  of  the  rounded  edges  to  the  exact  curve  of  a completely  con- 
tracted jet.  A rounded  interior  orifice  is  therefore  always  a source  of  error 
when  the  object  of  the  orifice  is  the  measurement  of  the  discharge. 


GAUGING  WATER. 

Water  is  sold  by  two  methods;  i.  e.,  the  flowing  unit  and  the  capacity 
unit  The  flowing  unit  is  a cubic  foot  per  second.  In  the  western  part  of 
North  America  the  miners'  inch  has  come  into  use  .quite  largely,  while  in 
Australia  and  New  Zealand  the  cubic  foot  per  second  is  the  common  measure, 
Australia  ai  being  x head  » and  10  heads  of  water  would  be  10  cu  ft. 

oer  second  regardless  of  the  actual  hydrostatic  head  under  which  the  water 
was  delivered:  Water  is  sometimes  sold  for  irrigation  by  the  capacity  unit, 
that  is  so  much  land  covered  to  a certain  depth,  as,  for  instance,  the  acre- 
foot  ” which  means  that  1 acre  has  been  covered  to  a depth  of  1 foot,  or  that 
an  amount  of  43,560  cu.  ft.  of  water  has  been  furnished. 

Miners’ Inch  -The  miners’  inch  may  be  roughly  defined  as  the  quantity  of 
water  that  wili  flow  in  1 minute  through  a vertical  standard  orifice  having  a 
section  of  lsq ! in  and  a head  of  6*  in.  above  the  center  of  the  orifice.  This 
ouantitv  equals  1.53  cu.  ft.,  and  the  mean  quantity  may  be  taken  at,  approxi- 
matelv  15q  cu  ft.  per  minute.  The  laws  or  customs  defining  the  miners 
inch  in  different  districts  vary  so  that  the  amount  of  water  actually  delivered 
varies  from  1.2  to  1.76  cu.  ft.  per  minute,  the  principal  reasons  for  these  varia- 
tions being  the  method  adopted  for  measuring,  the  water  where  large  quan- 
tities are  used"  as,  for  instance,  at  Smartsville,  m California,  an  opening  4 in. 
deep  250  in f long  with  a head’  of  7 in.  above  the  .top  edge  is  said  to  furnish 
i non  miners’  inches,  while  it  would  actually  furnish  considerably  over  1,000. 
Tu  othe? nlaces  the size  of  the  opening  for  measuring  the  amounts  is 
restricted  and  may  actually  furnish  less  than  the  rated  amount.  In  Montana 
the  common  method  of  measurement  was  formerly  through  a vertical  rect- 
anele TiS  hiSi . with  a head  on  the  center  of  the  orifice  of  4 m.  The  num- 
bef  of  minem’  inches  discharged  was  considered  to  be  the  same  as  the 
number  of  linear  inches  in  the  length  of  the  orifice;  thus,  under  the  given 
head  an  orifice  1 in.  deep  and  60  in.  long  could  discharge  60  miners  ^hes. 

The  State  Legislature  of  Montana  has  now  passed  a law  defining  the 
miners’  inch  as  the  number  of  gallons  of  water  discharged  m a given  time, 
regardless  of  the  character  of  the  openings  or  methods  of  measurement. 
Tffie  statement  is  as  follows;  “Where  water  rights,  expressed  m miners 
inches  hive  been  granted,  100  miners’  inches  shall  be.  considered  equivalent 
to  a flow  of  2*  cu  ft.  (18.7  gal.)  per  second,  and  this  proportion  shall  be 
observed  in  determining  the  equivalent  flow  represented  by  any  number  of 
miners’  inches.” 


MINERS’  INCH. 


137 


If  this  amount  is  reduced  to  cubic  feet  per  minute,  it  will  be  found  to 
be  equal  to  a flow  of  1.5  cu.  ft.  per  minute,  which  is  the  value  given  above 
for  the  miners’  inch. 

Duty  or  Work  Performed  by  a Miners’  Inch  of  Water.— Few  tests  have  been 
made  in  regard  to  the  duty  of  a miners’  inch  of  water,  but  the  North 
Bloomfield  mine  and  the  La  Grange  mine,  in  California,  have  carried  on 
a series  of  experiments  extending  over  several  years.  At  the  La  Grange 
mine  the  observations  were  carried  on  simultaneously  upon  several  differ- 
ent claims,  hence  parallel  dates  appear.  The  accompanying  tables  give 
the  results  of  these  experiments.  In  general  it  is  governed  by  the  size, 
capacity,  character  of  pavement,  and  grade  of  sluices,  together  with  the 
supplv  of  water.  A heavy  grade  will  compensate  for  a limited  supply. 
With  an  abundant  supply  of  water  and  material,  the  capacity  of  the  sluices, 
will  depend  on:  First , the  character  of  the  material  washed;  second , the 
size  and  minimum  grade  of  the  sluices;  third , the  character  of  the  riffles  used. 


Duty  of  Miners’  Inch. 

( Risdon  Iron  Works , Evans's  Elevator  Catalogue.) 
North  Bloomfield  Mine. 


Years. 

Cubic  Yards  of  Gravel 
Washed. 

Miners’  24-Hour 
Inches. 

Grades. 

Cubic  Yards  Washed 
per  Miners’  Inch. 

Cubic  Feet  of  Water  Used 
per  Cubic  Feet 
of  Gravel  Moved. 

Height  of  Bank. 

Remarks. 

1870-74 

1875 

1876 

1877 

3.250.000 

1.858.000 
2,919,700 
2,993,930 

710,987 

386,972 

700.000 

595.000 

6^  in.  to  12  ft. 
6H  in.  to  12  ft. 
6J^  in.  to  12  ft. 
6J^  in.  to  12  ft. 

4.60 

4.80 

4.17 

3.86 

18 

17 

20 

21 

100  ft. 
100  ft. 
200  ft. 
265  ft. 

Sluices  6 ft.  wide, 
32  in.  deep. 

Riffles  principally 
blocks  (wood),  but 
> rock  riffles  in  tail 
sluices. 

The  larger  portion 
of  the  material 
moved  was  top 
gravel. 

Totals 

11,021,630 

2,392,959 

4.60 

18 

La  Grange  Mine. 


1874- 76 

1875- 76 

1874- 76 

1875- 78 
1880-81 

676,968 

683,244 

284,932 

459,570 

329,120 

624.745 

375,155 

207,010 

302,960 

203,325 

4 in.  to  16  ft. 
4 in.  to  16  ft. 
4 in.  to  16  ft. 
4 in.  to  16  ft. 
4 in.  to  16  ft. 

1.08 

1.82 

1.37 

1.52 

1.57 

74.0 
43.9 

58.0 

52.0 

50.0 

10  to  48  ft. 

6 ft. 
50  to  80  ft. 
40  to  50  ft. 
10  to  80  ft. 

Sluices  4 ft.  wide 
and  30  in.  deep, 
> paved  with 
blocks. 

Totals 

2,433,834 

1,713,195 

1.42 

56.0 

The  right-angled  V notch  is  frequently  used  for  gauging  the  flow  of  compara- 
tively small  streams.  The  notch  is  usually  fitted  into  a box  provided  with 
baffle  boards,  Fig.  9,  or  where  this  is  not  practicable  the  water  should  be 
so  impounded  above  the  notch  as  to  remove  all  possibility  of  surface  cur- 
rents producing  a perceptible  velocity  of  approach.  The  distance  a of  the 
surface  of  the  water  below  the  top  of  the  box  is  taken  at  a point  some  dis- 
tance back  from  the  notch  (at  least  18  to  20  in.),  where  the  surface  of  the 
water  is  unaffected  by  the  flow  through  the  notch.  The  distance  a,  sub- 
tracted from  the  total  depth  of  the  notch  H,  gives  the  head  h of  the  water 
passing  over  the  notch.  The  discharge  in  cubic  feet  per  second  may  be 
found  by  the  formula  _ __ 

Q = .306/ hP  = .306  ft*/ ft, 

in  which  Q equals  the  quantity  in  cubic  feet  per  minute  and  h equals  the 


138 


HYDRAULICS. 


head  in  inches.  The  accompanying  table  gives  the  discharge  in  cubic  feet 
per  minute  through  a right-angled  V notch,  as  shown  m Fig.  9,  for  heads 
varying  from  1.05  in.  to  12  in. 

TABLE  I. 

Discharge  of  Water  Through  a Right-Angled  V Notch. 


h 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

h 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

h 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

h 

Head. 

Inches. 

Q 

Quantity 
per  Min.  - 
Cu.  Ft. 

h 

Head. 

inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

1 05 

.3457 

3.25 

5.827 

5.45 

21.22 

7.65 

49.53 

9.85 

93.18 

1 10 

.3884 

3.30 

6.054 

5.50 

21.71 

7.70 

50.34 

9.90 

94.37 

1 15 

.4340 

3.35 

6.285 

5.55 

22.20 

7.75 

51.16 

9.95 

95.56 

1 20 

.4827 

3.40 

6.523 

5.60 

22.70 

7.80 

51.99 

10.00 

96.77 

1 25 

.5345 

3.45 

6.765 

5.65 

23.22 

7.85 

52.83 

10.05 

97.98 

1 30 

5896 

3.50 

7.012 

5.70 

23.74 

7.90 

53.67 

10.10 

99.20 

1 35 

.6480 

3.55 

7.266 

5.75 

24.26 

7.95 

54.53 

10.15 

100.43 

1 40 

.7096 

3.60 

7.524 

5.80 

24.79 

8.00 

55.39 

10.20 

101.67 

1 45 

.7747 

3.65 

7.788 

5.85 

25.33 

8.05 

56.26 

10.25 

102.92 

1 50 

.8432 

3.70 

8.058 

5.90 

25.87 

8.10 

57.14 

10.30 

104.18 

.9153 

3.75 

8.332 

5.95 

26.42 

8.15 

58.03 

10.35 

105.45 

1 60 

9909 

3.80 

8.613 

6.00 

26.98 

8.20 

58.92 

10.40 

106.73 

* i 65 

1.0700 

3.85 

8.899 

6.05 

27.55 

8.25 

59.82 

10.45 

108.02 

1.70 

1.1530 

3.90 

9.191 

6.10 

28.12 

8.30 

60.73 

10.50 

109.31 

1.75 

1.2400 

3.95 

9.489 

6.15 

28.70 

8.35 

61.65 

10.55 

110.62 

L80 

1.3300 

4.00 

9.792 

6.20 

29.28 

8.40 

62.58 

10.60 

111.94 

L85 

1.4240 

4.05 

10.100 

6.25 

29.88 

8.45 

63.51 

10.65 

113.26 

1.90 

1.5220 

4.10 

10.410 

6.30 

30.48 

8.50 

64.45  - 

10.70 

114.60 

L95 

1.6250 

4.15 

10.730 

6.35 

31.09 

8.55 

65.41 

10.75 

115.94 

2^00 

1.7310 

4.20 

11.060 

6.40 

31.71 

8.60 

66.37 

10.80 

117.29 

2.05 

1.8410 

4.25 

11.390 

6.45 

32.33 

8.65 

67.34 

10.85 

118.65 

2.10 

1.9550 

4.30 

11.730 

6.50 

32.96 

8.70 

68.32 

10.90 

120.02 

2.15 

2.0740 

4.35 

12.070 

6.55 

33.60 

8.75 

69.30 

10.95 

121.41 

2/20 

2.1960 

4.40 

12.420 

6.60 

34.24 

8.80 

70.30 

11.00 

122.81 

2.25 

2.3230 

4.45 

12.780 

6.65 

34.89 

8.85 

71.30 

11.05 

124.21 

2.30 

2.4550 

4.50 

13.140 

6.70 

35.56 

8.90 

72.31 

11.10 

125.61 

2.35 

2.5900 

4.55 

13.510 

6.75 

36.23 

8.95 

73.33 

11.15 

127.03 

2.40 

2.7300 

4.60 

13.890 

6.80 

36.89 

9.00 

74.36 

11.20 

128.45 

2.45 

2.8750 

4.65 

14.270 

6.85 

37.58 

9.05 

75.40 

11.25 

129.90 

2.50 

3.0240 

4.70 

14.650 

6.90 

- 38.27 

9.10 

76.44 

11.30 

131.35 

2.55 

3.1770 

4.75 

15.040 

6.95 

38.96 

9.15 

77.49 

11.35 

132.81 

2.60 

3.3350 

4.80 

15.440 

7.00 

39.67 

9.20 

78.55 

11.40 

134.27 

A 65 

3.4980 

4.85 

15.850 

7.05 

40.38 

9.25 

79.63 

11.45 

135.  / 5 

2.70 

3.6660 

4.90 

16.260 

7.10 

41.10 

9.30 

80.71 

11.50 

137.23 

2.75 

3.8380 

4.95 

16.680 

7.15 

41.83 

9.35 

81.80 

11.55 

138.73 

2.80 

4.0140 

5.00 

17.110 

7.20 

42.56 

9.40 

82.90 

11.60 

140.23 

2.85 

4.1960 

5.05 

17.540 

7.25 

43.30 

9.45 

84.01 

11.65 

141.75 

2.90 

4.3820 

5.10 

17.970 

7.30 

44.06 

9.50 

85.12 

11.70 

143.28 

2.95 

4.5740 

5.15 

18.420 

7.35 

44.82 

9.55 

86.24 

11.75 

144.82 

3.00 

4.7700 

5.20 

18.870 

7.40 

45.58 

9.60 

87.37 

11.80 

146  36 

3.05 

4.9710 

5.25 

19.320 

7.45 

46.36 

9.65 

88.52 

11.85 

147.91 

3.10 

5.1780 

5.30 

19.790 

7.50 

47.14 

9.70 

89.67 

11.90 

149.48 

3.15 

5.3880 

5.35 

20.260 

7.55 

47.92 

9.75 

90.83 

11.95 

151.05 

3.20 

5.6050 

5.40 

20.730 

7.60 

48.72 

9.80 

92.00 

12.00 

152.64 

1 cu.  ft.  contains  7.48  U.  S.  gallons;  1 U.  S.  gallon  weighs  8.34  lb. 


Gauging  bv  Weirs.— A weir  is  an  obstruction  placed  across  a stream  for  the 
nurpose  of  diverging  the  water  so  as  to  make  it  flow  through  a desired  chan- 
nel which  may  be  l notch  or  opening  in  the  weir  itself  The  term  usually 
applies  to  rectangular  notches  in  which  the  water  touches  only  ^he  bottom 
and  ends,  the  opening  being  a notch  without  any  upper  edge.  Weirs  are  of 
two  general  classes:  weirs  with  end  contractions , Fig.  10  (a),  and  weirs  without 


GAUGING  BY  WEIRS. 


139 


Fig.  9. 


Let  l 
H 


h = 

c 
Q 
Q' 


end  contractions , Fig.  10  (6).  The  crest  and  edges  of  the  weir  with  end  con- 
tractions should  be  sharp,  as  shown  at  a , Fig.  10  (c)  and  (d).  The  head 
of  water  H producing  the  flow  over  the  weir  should  be  measured  at  a suffi- 
cient  distance  from  the  crest  to  avoid  the  effects  of  the  curve  of  the  surface 
as  it  flows  over  the  crest.  The 
water  above  the  weir  should 
be  motionless,  or  if  it  has  any 
perceptible  current  toward 
the  weir,  this  should  be  deter- 
mined and  taken  into  account 
in  the  formula.  Fig.  11  illus- 
trates a weir  constructed  across 
a small  stream  for  measuring 
its  flow.  The  head  is  measured 
from  the  stake  E some  distance 

back  of  the  weir,  the  top  of  the  stake  being  level  with  the  crest  of  the  weir 
B.  The  discharge  over  the  weir  may  be  calculated  from  tlje  following 
formula: 

length  of  weir  in  feet; 
head  in  feet; 

velocity  with  which  the  water  approaches  the  weir  in  feet; 

head  equivalent  to  the  velocity  with  which  the  water 
approaches  the  weir; 
coefficient  of  discharge; 
theoretic  discharge  in  cubic  feet  per  second; 
actual  discharge  in  cubic  feet  per  second. 

For  weirs  with  end  contractions  and  a velocity  of  approach,  the  actual 

discharge  is 

Q = 5.347  cl]/  (£T  + 1.4  h)3. 

Where  the  water  has  no 

velocity  of  approach,  _ 

Q = 5.347 cl  ]/ H3. 

For  weirs  without  end  con- 
tractions, but  with  a velocity 
of  approach,  the  actual  dis- 
charge is  ______ 

Q = 5.347  c l ]/\H  + | h)s. 

Where  the  water  has  no 
velocity  of  approach, 

Q = 5.347  c 1 1 /H*. 

The  velocity  with  which 
the  water  approaches  the  weir 
may  be  found  by  determining 
the  approximate  discharge 
from  the  stream  without  any  allowance  for  velocity  of  approach,  and  then 
dividing  this  discharge  in  cubic  feet  per  second  by  the  area  of  the  stream  in 
square  feet  where  it  approaches  the  weir,  which  will  give  the  velocity  of 
approach  in  feet  per 
second.  Having  ob- 

tained  the  value  oft;,  ^ ^ 

the  equivalent  head  h « 
may  be  found  by  the 
formula 

h = 0.01555  v-. 

Since  v is  small  in 
a properly  constructed 
weir,  it  is  usually  neg- 
lected unless  great 
accuracy  is  required. 

The  values  of  coeffi- 
cients of  discharge,  as 
determined  from  ex- 
periments for  weirs 
with  end  contractions, 
are  given  in  Table  II, 
and  for  weirs  without  end  contractions  in  Table  III.  The  values  of  the 
coefficients  in  Tables  II  and  III  are  given  in  feet  and  tenths.  Frequently 


140 


HYDRA  VLICS. 


in  measuring  water  where  only  a close  approximation  is  required  it  is 
desired  to  take  all  of  the  measurement  in  feet  and  inches.  See  Table  IV. 


TABLE  II. 

Values  of  the  Coefficient  of  Discharge  for  Weirs  With 
End  Contractions. 


Length  of  W7eir.  Feet. 


Enecnve  neau. 
Feet. 

1 

.66 

i 1 

2 

3 

5 

10  | 

19 

.10 

.632 

.639 

.646 

.652 

.653 

.655 

.656 

.15 

.619 

.625 

.634 

.638 

.640 

.641 

.642 

.20 

.611 

.618 

.626 

.630 

.631 

.633 

.634 

*25 

.605 

.612 

.621 

.624 

.626 

.628  | 

.629 

.30 

.601 

.608 

.616 

.619 

.621 

.624  ' 

.625 

.40 

.595 

.601 

.609 

.613 

.615 

.618  , 

.620 

.50 

.590 

.596 

.605 

.608 

.611 

.615 

.617 

.60 

.587 

.593 

.601 

.605 

.608 

.613  | 

.615 

;70 

.590 

.598 

.603 

.606 

.612 

.614 

ftfl 

.595 

.600 

.604 

.611 

.613 

•OU 

90 

.592 

.598 

.603 

.609 

.612 

1 00 

.590 

.595 

.601 

.608 

.611 

l.V/U 
1 20 

.585 

.591 

.597 

.605 

.610 

1 . AAJ 

1 40 

.580 

.587 

.594 

.602 

.609 

1.60 

.582 

I 

.591 

1 

.600 

.607 

TABLE  III. 

Values  of  the  Coefficient  of  Discharge  for  Weirs  Without 
End  Contractions. 


Effective  Head. 
Feet. 

Length  of  W'eir. 

. Feet. 

19  f 

10  1 

7 

5 ! 

4 

3 

2 

10 

.657 

.658 

.658 

.659 

.lu 

.15 

.643 

.644 

.645 

.645 

.647  i 

.649 

.652 

[20 

.635 

.637 

.617 

.638 

.641  I 

.642 

.645 

*25 

.630 

.632 

.633 

.634 

.636  j 

.638  | 

.641 

.30 

.626 

.628 

.629 

.631 

.633  ! 

.636 

.639 

.40 

.621 

.623 

.625 

.628 

.630 

.633 

.636 

"'SO 

.619 

.621 

.624 

.627 

.630 

.633 

.637 

.60 

.618 

.620 

.623 

.627 

.630 

.634 

.638 

.70 

.618 

.620 

.624 

.628 

.631 

.635 

.640 

"on 

.618 

.621 

.625 

.629 

.633 

.637 

.643 

.oU 

00 

.619 

.622 

.627 

.631 

.635 

.639 

.645 

• «7 \j 
1.00 

.619 

.624 

.628 

.633 

.637 

.641 

.648 

1.20 

.620 

.626 

.632 

.636 

.641 

.646 

1.40 

.622 

.629 

.634 

.640 

.644 

L60 

.623 

.631 

.637 

.642 

.647 

L 


CONVERSION  FACTORS. 


141 


TABLE  IV. 

Weir  Table  Giving  Cubic  Feet  Discharged  per  Minute  for  Each  Inch 
in  Length  of  Weir  for  Depths  From  £ In.  to  25  In. 

This  table  should  not  be  used  unless  the  length  of  the  crest  is  at  least 
B or  4 times  the  depth  of  water  passing  over  the  weir,  for  if  this  is  not  the 
case,  there  will  be  serious  errors  caused  by  end  contractions. 


Inches. 

0 

8 

1 

4 

1 

£ 

£ 

7 

8 

0 

.01 

.05 

.09 

.14 

.20 

.26 

.33 

1 

.40 

.47 

.55 

.65 

.74 

.83 

.93 

1.03 

2 

1.14 

1.24 

1.36 

1.47 

1.59 

1.71 

1.83 

1.96 

3 

2.09 

2.23 

2.36 

2.50 

2.63 

2.78 

2.92 

3.07 

4 

3.22 

3.37 

3.52 

3.68 

3.83 

3.99 

4.16 

4.32 

5 

4.50 

4.67 

4.84 

5.01 

5.18 

5.36 

5.54 

5.72 

6 

5.90 

6.09 

6.28 

6.47 

6.65 

6.85 

7.05 

7.25 

7 

7.44 

7.64 

7.84 

8.05 

8.25 

8.45 

8.66 

8.86 

8 

9.10 

9.31 

9.52 

9.74 

9.96 

10.18 

10.40 

10.62 

9 

10.86 

11.08 

11.31 

11.54 

' 11.77 

12.00 

12.23 

12.47 

10 

12.71 

13.95 

13.19 

13.43 

13.67 

13.93 

14.16 

14.42 

11 

14.67 

14.92 

15.18 

15.43 

15.67 

15.96 

16.20 

16.46 

12 

16.73 

16.99 

17.26 

17.52 

17.78 

18.05 

18.32 

18.58 

13 

18.87 

19.14 

19.42 

19.69 

19.97 

20.24 

20.52 

20.80 

14 

21.09 

21.37 

21.65 

21.94 

22.22 

22.51 

22.79 

23.08 

15 

23.38 

23.67 

23.97 

24.26 

24.56 

24.86 

25.16 

25.46 

16 

25.76 

26.06 

26.36 

26.66 

26.97 

27.27 

27.58 

27.89 

17 

28.20 

28.51 

28.82 

29.14 

29.45 

29.76 

30.08 

30.39 

18 

30.70 

31.02 

31.34 

31.66 

31.98 

32.31 

32.63 

32.96 

19 

33.29 

33.61 

33.94 

34.27 

34.60 

34.94 

35.27 

35.60 

20 

35.94 

36.27 

36.60 

36.94 

37.28 

37.62 

37.96 

38.31 

21 

38.65 

39.00 

39.34 

39.69 

40.04 

40.39 

40.73 

41.09 

22 

41.43 

41.78 

42.13 

42.49 

42.84 

43.20 

43.56 

43.92 

23 

44.28 

44.64 

45.00 

45.38 

45.71 

46.08 

46.43 

46.81 

24 

47.18 

47.55 

47.91 

48.28 

48.65 

49.02 

49.39 

49.76 

CONVERSION  FACTORS. 

Cubic  feet  Into  Gallons: 

1 728 

1 cu.  ft.  = 1,728  cu.  in.  = gal.  = 7.4805194  gal. 

Gallons  Into  Cubic  Feet: 

231 

1 United  States  liquid  gal.  = 231  cu.  in.  = — cu.  ft.  = .133680555  cu.  ft. 

1|  /2o 

Feet  per  Second  Into  Miles  per  Hour: 

3 600  15 

1 ft.  per  sec.  = 3,600  ft.  per  hr.  = , or  miles  per  hour. 

D}Z£5\)  ZZ 

Miles  per  Hour  Into  Feet  per  Second: 

5 280  22 

1 mi.  per  hr.  = 5,280  ft.  per  hr.  = r,  or  — ft.  per  sec. 

* UjOUi)  lv 

Second-Feet  per  Day  Into  Gallons: 

lsecond-foot,  or  7.4805194  gal.  per  sec.  for  1 day,  or  86,400  sec.  = 646,316.87616  gal. 

Millions  of  Gallons  Into  Second-Feet  per  Day:j 

231  000  000 

] ,000,000  gal.  per  24  hr.  = r728  X 86  400  CU’ ft’  persec-’  or  1.5472286  second-feet. 

Second-Feet  per  Day  Into  Acre-Feet: 

1 second-foot  flow  for  1 day  = 86,400  cu.  ft.  = or  1.983471  acre-feet. 


142 


HYDRAULICS. 


Acre-Feet  Into  Second-Feet  Flow  for  24  Hours: 

One  acre-foot  each  24  hr.  = 43,560  cu.  ft.  each  86,400  sec. 

= 43’--,  or  second-foot  flow  for  24  hr. 

86,400  ’ 240 


Acre-Feet  Into  Gallons: 

1 acre-foot  = 43,560  cu.  ft.  = 


43,560  X 1,728  75,271,680 

231  ’ 231 


or  325,851.428  gal. 


Millions  of  Gallons  Into  Acre-Feet: 

1,000,000  United  States  liquid  gal.,  or  231,000,000  cu.  in.  = 

or  133,6~  = 3.0688832  acre-feet. 
43,560 


133,680.555  cu.  ft., 


Second-Feet  Into  Minute  Gallons: 

Factors:  1 cu.  ft.  contains  1,728  cu.  in.;  1 gal.  has  a caPac“y  of  231  cu.  iir; 
1 second-foot  equals  [(1,728  -4-  231)  X 60]  gal.  per  min.,  or  448.831164  minute- 
gallons. 


Minute-Gallons  Into  Second-Feet: 

Tf' a ptotis*  • 1 ffal  contains  231  cu.  in.;  1 cu.  ft.  contains  1,728  cu.  in.;  1 gal. 
perFmh™equal!  [(231  4-  1,728)  -*■  60]  second-feet,  or  .0022280092  second-foot. 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 

Ditches  —In  the  case  of  hydraulic  mining  and  irrigation,  water  is  usually 
conveyed  through  ditches.  The  ditch  line  should  be  carefully  surveyed  and 
ail  brush  and  trees  removed,  and  the  underbrush  cut  away  and  burned, 

^^T^e^ftSlowtag^tetters  ^ifl  be  useiTin  the  formulas  for  determining  the 
various  factors  rela tin bejWgen  en(js  0f  canal  or  ditch,  or  between  two 

uoints  under  consideration;  ,. 

I — horizontal  length  of  portion  of  canal  or  ditch  under  consideration; 

s = slope  = ratio  - = sin  of  slope; 

n = area  of  water  cross-section  in  square  feet;  . _ A 

“ = wet  perimeter  = portion  of  outline  of  cross-section  of  stream  m 
p contact  with  channel,  in  feet;  ^ 

r _ hydraulic  radius,  or  hydraulic  mean  depth  = ratio 

C’  = coefficient,  depending  on  nature  of  surface  of  the  ditch; 
c = coefficient  depending  on  nature  of  surface  of  ditch,  as  determined  by 
Kutter’s  formula; 

v = mean  velocity  of  flow  m feet  per  second; 
v'  = surface  velocity  of  a stream; 

Vx  = bottom  orune  side  of  a section,  the  form  of  which  is  half  a regular 
hexagon,  in  feet;  , . _ . 

o = quantity  of  water  flowing,  m cubic  feet  per  second; 

n = coefficient  of  roughness  in  Kutter’s  formula. 

The  form  of  ditch  and  its  grade  will  depend  largely  on  the > amount  of 
water  to  be  conveyed  and  the  character  of  the  soil  in  the  section  ll^der 
consideration  As  a general  rule,  the  average  flow  of  water  in  a ditch 
should  not  be  less  than  2 ft.  per  second,  and  under  most  circumstances 
should  not  exceed  4 ft.,  though  in  rare  cases  where  the  formation  is  suitable, 
mean  velocities  of  5 ft.  per  second  are  employed.  Sand  will  deposit  from  a 
Sirrent  flowing  at  the  rate  of  H ft.  per  second,  and  if  the  current  does  not 
have  a velocity  of  at  least  2 ft.  per  second,  vegetation  is  liable  to  block  the 
ditch  line.  „ 

Safe  Bottom  Velocity.— The  bottom  velocity  of  a stream  may  be  obtained 

from  the  average  velocity  by  the  following  formula:  vh  = v — 10.87  y rs. 

The  following  table  gives  values  of  safe  bottom  and  mean  velocities,  cor 
responding  with  certain  materials,  as  given  by  Ganguillet  and  Kutter: 


FLOW  OF  WATER  IN  CHANNELS. 


143 


Material  of  Channel. 

Safe  Bottom  Velocity  vb. 
Feet  per  Second. 

Mean  Velocity  v. 
Feet  per  Second. 

Soft  brown  earth 

.249 

.328 

Soft  loam  

.499 

.656 

Sand 

1.000 

1.312 

Gravel 

1.998 

2.625 

Pebbles  

2.999 

3.938 

Broken  stone,  flint 

4.003 

5.579 

Conglomerate,  soft  slate 

4,988 

6.564 

Stratified  rock 

6.006 

8.204 

Hard  rock 

10.009 

13.127 

Resistance  of  Soils  to  Erosion  by  Water. — W.  A.  Burr,  “ Engineering  News,” 
February  8, 1894,  gives  a diagram  showing  the  resistance  of  various  soils  to 
erosion  by  water.  The  following  values  have  been  selected  from  Mr.  Burr’s 
work  for  different  kinds  of  soil: 


Pure  sand  resists  erosion  by  flow  of 1.10  ft.  per  sec. 

Sandy  soil,  15 0 clay 1.20  ft.  per  sec. 

Sandy  loam,  40 0 clay 1.80  ft.  per  sec. 

Loamy  soil,  650  clay  3.00  ft.  per  sec. 

Clay  loam,  850  clay 4.80  ft.  per  sec. 

Agricultural  clay,  950  clay 6.20  ft.  per  sec 

Clay  7.35  ft.  per  sec. 


Carrying  Capacity  of  Ditches.— Ditches  should  never  be  run  full,  but  should 
be  constructed  large  enough  so  that  they  will  carry  the  desired  amount  of 
water  when  from  £ to  i full.  For  any  given  cross-section,  the  greatest  flow 
will  be  attained  when  the  hydraulic  radius  or  hydraulic  mean  depth  is  equal 
to  one-half  of  the  actual  depth  of  the  channel.  The  cross-section  of  a ditch 
or  conduit  that  has  the  greatest  possible  carrying  capacity  is  a half  circle, 
and  the  nearest  practical  approach  to  this  is  a half  hexagon.  Knowing 
the  cross-section  of  a ditch,  its  dimensions  may  be  found  by  the  formula: 


/ 2a 
X ~ \ 2.598 

As  the  obtuse  angle  between  the  side  and  bottom  of  the  ditch  is  120°,  the 
form  can  be  easily  laid  off.  The  carrying  capacity  of  ditches  generally 
increases  after  they  have  been  in  use  some  time,  as  the  ditch  becomes  lined 
with  a fine  scum  that  closes  the  pores  in  the  soil  and  prevents  leakage.  This 
may  increase  the  amount  to  as  much  as  100. 

Grade.— The  grade  of  the  ditch  must  be  sufficient  to  create  the  desired 
velocity  of  flow,  and  depends  largely  on  the  character  of  the  material  com- 
posing the  surfaces  of  the  ditch.  If  the  surface  is  smooth,  as,  for  instance, 
where  the  ditch  is  cut  through  clay  or  is  lined  with  masonry,  the  grade  can 
be  considerably  less  than  where  the  surface  is  rough,  or  when  cut  through 
coarse  gravel  or  when  lined  with  rough  stone.  In  mountainous  countries, 
where  the  ground  is  hard,  deep  narrow  ditches  with  steep  grades  are  gener- 
ally preferred  to  larger  channels  with  gentle  slopes,  as  the  cost  of  excavation 
is  considerably  less;  but  steep  grades  and  narrow  ditches  are  suitable  only 
when  the  banks  can  resist  the  rapid  flow.  In  California,  grades  of  from  16  to 
20  ft.  per  mile  are  used,  and  10  ft.  per  mile  is  quite  common.  Water  channels 
of  a uniform  cross-section  should  have  a uniform  grade,  otherwise,  the  flow 
will  be  checked  in  places,  which  will  result  in  deposits  of  sand  or  silt  in 
some  portions  of  the  ditch,  which  are  liable  to  cause  the  banks  to  be  o ver- 
flowed and  the  ditch  to  be  ultimately  destroyed.  In  designing  any  given 
ditch,  the  grade  is  generally  assumed  to  correspond  to  the  formation  of  the 
country  and  the  velocity  figured  from  the  grade.  In  case  v is  found  to  be  so 
great  that  it  would  cut  the  banks,  it  will  be  necessary  either  to  reduce  the 
grade  or  to  change  the  form  of  the  ditch  so  as  to  reduce  the  velocity. 

Ditch  banks,  when  possible,  should  be  composed  of  solid  material,  but 
frequently  it  is  necessary  to  use  excavated  material.  Where  this  is  the  case, 
care  must  be  taken  to  see  that  the  material  is  so  placed  as  to  avoid  settling 


144 


HYDRAULICS. 


sSv  iUs  beltto  build  them  of  masonry,  provided  the  expense  is  not  too 

Stonework  ■ lafd up in. order  and  carefully  bonded  together.  Sometimes  the 

able  innue  rnnoh  greater  average  velocity  can  be  attained  in  a 

deeD  stream*5  than  SaSwC  wlthSut  causing*  an  excessive  velocity 
oft^fwateP  to  “intact  with  the  wet  perimeter.  For  toWBW/ m cases 
where  banks  will  stand  it,  it  is  best  to  use  narrow  deep  ditches  rather  than 
wide  flat  ditches,  though  each  location  has  to  be  tre,a*e,^/? /f®”rdan  th 

its  own  sto'0i;dc“di‘Vwater“i<:i  Chafneto-TheTws^ to toe  resistance  to  the 
flow  may  b! expressed  by  the  relation  (see  page  142  for  significance  of  letters) : 


ha  = c'lpv*  or,  v = X | ^ X * X r. 


If  C = the  formula  becomes  v = c V'  n 


The  coefficient  c is  usually  found  by  means  of  Kutter’s  formula,  one  form 

of  which  is  as  follows:  * 

1 .00155 

23  + b — — 


c = 


/ „ .00155  \ n 

.5521  + (23  + — ) 


The  values  for  n,  the  coefficient  of  roughness,  under  various  conditions, 
are  as  follows: 


Character  of  Channel. 


Clean,  well-planed  timber ------ 

fOpan  smooth,  glazed  iron,  and  stoneware  pipes 

Masonry,  smoothly  plastered  with  cement,  and  for  very  clean, 

Unvaried  timber,  ordinary  cast-iron  pipe,  and  selected  pipe 

sewers,  well  laid  and  thoroughly  flushed -■■■■—  - 7," 

Rough  iron  pipes  and  ordinary  sewer  pipes,  laid  under  the 

usual  conditions - v - 

Tirpsscd  masonry  and  well-laid  brickwork  vw'-'V \ 

Good  rubble  masonry  and  ordinary  rough  or  fouled  brickwork 
Coarse  rubble  masonry  and  firm,  compact  gravel 

£v“  canals  in“moc  1 era  tel  y perfbcUy  *£ 

RWeS  antPcMials  in  rather  bad  condition  and  somewhat 

Rivers  and  canals  in  bad  condition,  overgrown  with  vegeta- 
tion and  strewn  with  stones  and  other  detritus,  according  to 
condition  - 


Value  of  7i. 


.009 

.010 

.011 

.012 

.013 

.015 

.017 

.020 

.0225 

.025 

.030 


.035  to  .050 


FLUMES . 


145 


As  it  is  quite  difficult  to  obtain  the  value  of  c by  Kutter’s  formula,  the  fol- 
lowing three  approximate  formulas  for  v are  given: 


For  canals  with  earthen  banks, 

If  the  ditch  is  lined  with  dry  stonework, 


100,000  r2s 
9 r -f  35 


v 

; 100, 000  r2s 
* = ■>/  8r  + 16" 
,100,000  r2s 


If  the  ditch  is  lined  with  rubble  masonry,  t»  = . y 

To  find  the  quantity  Q of  water  flowing  through  any  channel  in  a given 
time,  multiply  the  velocity  by  the  area,  or  Q = a v. 

Flow  in  Brooks  and  Rivers.— When  a stream  is  so  large  that  it  becomes 
impracticable  to  employ  a weir  for  measuring  its  flow,  fairly  accurate 
results  may  be  arrived  at  by  determining  the  velocity  of  the  current  at 
various  points  in  a carefully  surveyed  cross-section  of  the  stream,  thus 
determining  both  v and  a.  The  greatest  velocity  of  current  occurs  at  a point 
some  distance  below  the  surface,  in  the  deepest  part  of  the  channel.  When 
determining  the  current  velocities  in  the  different  portions  of  a stream,  it  is 
freauentlv  advantageous  to  divide  the  stream  into  divisions.  Ihis  may  be 
accomplished  by  stretching  a wire  across  and  tying  strings  or  rags  about  the 
wire  at  various  points.  The  mean  velocity  of  the  current  between  these 
points  can  be  determined  by  current  meters,  or  by  floats.  The  points  for 
observation  should  be  chosen  where  the  channel  is  comparatively  straight 
and  the  current  uniform.  Surface  floats  may  be  used,  in  which  case  the 
mean  velocity  of  the  point  where  the  float  is  used  may  be  found  as  follows: 
If  equals  the  observed  velocity,  then  the  mean  velocity  will  be  v = .9  v'. 

Bv  taking  observations  of  the  velocity  of  the  current  m each  section  of 
a stream  the  amount  of  water  flowing  may  be  determined  for  each  separate 
section  ’ The  total  amount  of  water  flowing  in  the  stream  will  be  the  sum 
of  the  amounts  in  each  section.  The  average  velocity  of  the  entire  stream 
mav  be  found  by  dividing  the  total  amount  of  water  flowing  by  total  area  of 
the  cross-section  of  the  stream.  The  correction  necessary  to  reduce  surface 
velocity  to  mean  velocity  may  be  made  as  follows:  Measure  off  x%  of  the 
ordinary  distance,  and  figure  the  time  as  though  for  the  full  distance.  For 
instance,  if  only  90  ft.  were  employed,  the  time  would  be  taken  and  the 
problem  figured  as  though  it  were  100  ft.,  on  account  of  the  fact  that  the 
mean  velocity  is  only  T%  of  the  surface  velocity. 


FLUMES. 

Flumes  are  used  for  conveying  water  when  a ditch  line  would  be 
abnormally  long,  or  when  the  material  to  be  excavated  is  very  hard.  They 
may  be  constructed  of  timber  or  of  metal,  but  metal  flumes  are  compara- 
tively rare  as  piping  can  be  used  instead.  The  line  of  the  proposed  flume 
should  be  carefully  cleared  of  all  standing  timber,  and  the  brush  burned  for 
at  least  20  ft.  each  side  of  the  flume  line  to  prevent  danger  from  fire.  The 
life  of  an  ordinary  flume,  which  is  supported  on  or  constructed  of  timber,  is 
always  short,  varying,  as  a rule,  from  10  to  20  years,  depending  on  whether 
the  flume  is  allowed  to  run  dry  a portion  of  the  year  or  is  always  full  of 
water,  the  care  with  which  it  was  originally  constructed,  and  the  attention 

paid  to  repairs.  „ , , , ,, 

Grade  of  Flumes.— Flumes  are  usually  set  on  a much  steeper  grade  than  is 
possible  in  ditches,  the  grade  frequently  being  as  much  as  25  to  30  ft.  per 
mile  and  in  special  cases  even  more.  The  result  of  this  is  that  the  carrying 
capacity  of  flumes  is  much  greater  than  that  of  ditches  of  the  same  size. 

The  form  of  flume  depends  largely  on  the  material  of  which  it  is  constructed. 
Metal  flumes  may  have  a semicircular  form,  while  wooden  flumes  are  either 
rectangular  or  V-shaped.  The  former  is  used  almost  exclusively  for  con- 
veying water,  and  the  latter  quite  extensively  for  fluming  timber  or 
cord  wood  from  the  mountains  to  the  shipping  point  in  the  valley. 

Timber  flumes  should  be  so  constructed  that  the  water  will  meet  with  but 
small  resistance,  and  the  bottom  and  side  should  be  enclosed  in  a frame  of 
timbers  so  braced  or  secured  that  there  is  no  possible  chance  of  the  sides 
spreading  or  lifting  from  the  bottom,  and  thus  cause  leakage.  As  a rule,  all 
mortised  and  tenoned  joints  should  be  avoided  in  flume  construction, 


m mm  * « 

W ■* 

Thai  Inmw  -nar  liare  -hen-  hil  -ar— tnc  ranarity^  hey  have  ha  <* 

n -n mlM  if  i Parser  ma  wrtiitn  u mfh  *he  -niranr*  amt  the*  ft.  In 

mrt  --r»n ntm*»  i 31*.  ' le  iese  T»  rniunrut  "he  Inm*  3aiTna<ir  than  it  deeo. 
» n *nwt  ▼-rarher  -He  jtk  31  'tie  aarm<r  lume  'mat  *mnrf  wmw 

lw*  airtw  * "tin*  imiemna  -tie  water  brim  :Sirther  irtum  <*f  the  *nimi» 
uut  taraoBty  ',rr,Mru?:ne  *he  4i*w  hmmm  the  tiime  fhr  *ver*i  ee*e 
Ttuln  rit>*  Aailfiv  Imm-i  r:Il  nnt  in  *he  flrfrr  • 'jmrki.jr  .it  will 

tp-eze  n tnm  t*>  uvt  ates  inrii  "he-r  an?  nraearmily  a *>t*f*a»‘W 

When  a 'tnnie  * awi  in  hie  rrinmt  an-ne  a Tank  it  eu  uni  «aaf  aw 
vi  hu?  «*na  t»  payable.  •>  a»  si  imteri  it  ftnm  «wa  <ir  Lamt-i  ^ and 
m rttmr  n tie  r nier  tie*  wu»w  wtH  trtft  .n  imier  amf  balum*  th«» 
vrprrenf.ne  he  nmiacnn  if  he  ur  innnc  the  1nn».  Thia  will  pcact  the 
inme*  mrt  tuv  imiomr  he  low  hr  *une  line  liter  mid  weather  ■*  im. 


TUNNELS. 


147 


TUNNELS. 

Tunnels  are  sometimes  used  for  conveying  water,  in  connection  with 
flume  or  ditch  lines.  Where  a tunnel  is  unlined,  it  is  best  to  give  the  roof 
the  shape  of  the  Gothic  arch,  owing  to  the  fact  that  this  stands  better  and 
resists  scaling  to  a greater  extent  than  the  round  arch,  which  usually  scales 
off  until  it  has  the  form  of  the  Gothic  arch.  If  tunnels  are  to  be  used  as 
water  conduits,  without  lining,  care  should  be  taken  to  make  the  inside  of 
the  tunnel  as  smooth  as  possible.  In  some  cases,  in  order  to  increase  the 
carrying  capacity  of  the  tunnel,  they  have  been  lined  with  wooden-stave 
pipe,  backed  with  concrete,  the  pipe  requiring  no  metal  bands,  but  depend- 
ing on  the  concrete  to  keep  it  in  place.  When  such  linings  are  employed,  it 
is  not  practicable  to  have  them  exposed  to  the  alternate  action  of  the  water 
and  the  atmosphere,  hence  the  tunnel  should  be  kept  continually  full  of 
water.  To  accomplish  this,  the  tunnel  may  be  dropped  below  the  grade  of 
the  ditch  or  flume  line,  so  that  it  is  always  under  a slight  hydrostatic 
pressure,  and  even  if  the  water  were  turned  off  from  the  line,  the  tunnel 
would  remain  full  of  water,  the  same  as  an  inverted  siphon.  Sometimes 
tunnels  are  lined  with  cement,  being  given  either  a circular  or  oval  form, 
or  they  may  have  a flat  bottom,  with  flat  sides  and  an  arched  roof.  The 
cement  may  be  placed  directly  on  the  country  rock  composing  the  walls  of 
the  tunnel,  or  the  tunnel  may  be  lined  with  brick  or  stone,  and  then 
cemented  on  the  inside. 

Flow  Through  Tunnels.— The  flow  of  water  through  tunnels,  when  they  are 
only  partially  filled,  is  calculated  by  the  formulas  for  flow  in  open  channels, 
while  in  the  case  of  lined  tunnels  that  are  run  full,  the  flow  is  calculated  by 
formulas  for  calculating  the  flow  through  pipes. 


FLOW  THROUGH  PIPES. 

Hydraulic  Gradient.— If  a pipe  of  uniform  cross-section  be  connected  with 
a reservoir,  and  water  allowed  to  discharge  through  its  open  end,  it  has  been 
found  that  the  pressure  on  the  pipe  at  any  point  is  equal  to  the  vertical  dis- 
tance from  the  center  of  the  pipe  at  that  point  to  an  imaginary  line,  called 
the  hydraulic  gradient  or  hydraulic  grade  line.  This  is  a line  drawn  from  a 
point  slightly  below  the 
surface  of  the  water  in  the 
reservoir  to  the  outlet  of 
the  pipe,  as  ab , Fig.  14. 

The  distance  from  the  sur- 
face of  the  water  to  the 
point  a is  equal  to  the  head 
lost  in  overcoming  the  fric- 
tion at  the  entrance  to  the 
pipe,  and  is  rarely  over  1 ft. 

If  the  pipe  were  laid  along 
the  line  a b,  it  would  carry 
exactly  the  same  amount 
of  water  as  when  laid  hori- 
zontally, as  shown,  but 
there  would  be  practically 
no  pressure  tending  to 
burst  the  pipe  at  any  point 
along  this  line;  while  if  it 
were  laid  along  the  line  from  the  point  a'  (the  reservoir  being  made 
deeper),  it  would  still  deliver  exactly  the  same  amount  of  water,  but  the 
pressure  tending  to  burst  the  pipe  would  be  greatly  increased.  In  order 
that  a pipe  may  have  a maximum  discharge,  no  point  in  the  line  must  rise 
above  the  hydraulic  gradient,  and  it  makes  no  difference  in  the  discharge 
how  far  below  the  gradient  it  may  fall. 

In  Fig.  15,  the  pipe  rises  above  the  hydraulic  gradient  a c,  and  in  this  case 
a new  hydraulic  gradient  ab  would  have  to  be  established,  and  the  flow 
calculated  for  this  head,  the  pipe  b c simply  acting  to  carry  off  the  water 
delivered  to  it  at  b.  If  the  upper  side  of  the  pipe  were  ©pen  at  the  point  b , 
the  water  would  have  no  tendency  to  escape,  but,  on  the  contrary,  air  would 
probably  enter,  and  the  pipe  flow  only  partially  full  from  b to  c. 

Flow  in  Pipes.— Darcy,  a French  engineer,  made  a series  of  experiments  on 
different  diameters  of  cast-iron  pipe,  with  different  degrees  of  internal 


148 


HYDRA  ULICS. 


roughness,  from  which  he  calculated  a series  of  formulas.  The  following 
are  some  of  these  formulas,  as  arranged  by  Mr.  E.  Sherman  Gould.  C.  E.,  E.  M., 
one  of  the  most  experienced  hydraulic  engineers  in  America.  Darcy  found 

that  the  character  of  the  inside 
surface  of  the  pipe  played  a 
very  important  part  in  its  dis- 
charge, and  he  deduced  a 
formula  and  determined  a 
series  of  coefficients  for  it,  but 
Mr.  Gould  calls  attention  to  the 
fact  that  the  coefficients  for 
pipes  from  8"  to  48"  in  diam- 
eter practically  cancel  the 
numerical  factor  employed  in 
Darcy’s  formula,  and  that  a 
slightly  different  factor  applies  to  pipes  from  3 to  8 in.,  so  that  we  may  have 
the  following  simple  formulas,  in  which  the  factors  given  apply: 

Q = amount  of  water  in  cubic  feet  per  second; 
q = U.  S.  gallons  per  minute; 

D = diameter  of  pipe  in  feet; 
d = diameter  of  pipe  in  inches; 

H = total  head  in  feet; 
h = head  per  1,000  ft.; 

V = velocity  in  feet  per  second. 

Pipes  above  8 in.  in  diameter,  rough  inside  surface, 

Q = = D^VDh\  y = 1*271 /Dh. 


Fig.  15. 


For  diameter  in  inches, 


Pipes  between  3 and  8 in.  in  diameter,  rough  inside  surface, 
Q = 0.89 \/Wh  = 0.89  DVM;  V = 1.13 /ZT/i. 


Large  pipes,  smooth  inside  surface, 

Q = 1.4/x^/i  = 1.4  dV^J  y = 1*781 /'Dh. 

Small  pipes,  smooth  inside  surface, 

Q = 0.89/2  H>h  = 1.25  D2/d7;  V = l.G]/ Dh. 

As  a rule,  it  is  best  to  calculate  any  pipe  line  by  the  formula  for  pipes 
having  a rough  internal  surface,  for  if  this  is  not  done  the  results  are  liable 
to  be  disappointing,  since  all  pipes  become  more  or  less  rough  with  use. 

Eytetwein’s  Formula  for  the  Delivery  of  Water  in  Pipes: 

D = diameter  of  pipe  in  inches; 

H = head  of  water  in  feet; 

L = length  of  pipe  in  feet; 

IF  = cubic  feet  of  water  discharged  per  minute 


IF  =4.71^^-.  D 


.538 


5 L X IF2 

\ II  ■ 


Hawksley’s  Formula: 

G 
L 
H 
D 


number  of  gallons  delivered  per  hour: 
length  of  pipe  in  yards; 
head  of  water  in  feet; 
diameter  of  pipe  in  inches. 


D 


= 4“ 


(15  Df  II 


Neville’s  General  Formula: 

v = velocity  in  feet  per  second; 
r = hydraulic  mean  depth  in  feet; 

s = sine  of  inclination,  or  total  fall  divided  by  total  length. 
v = 140  / r s — 11  / r s. 

In  cylindrical  pipes,  v multiplied  by  47.124  d2  gives  the  discharge  per 
minute  in  cubic  feet,  or  v multiplied  by  293.7286  d*  gives  the  discharge  per 
minute  in  gallons,  d being  the  diameter  of  the  pipe  in  feet. 


COMPARISON  OF  FORMULAS . 


149 


COMPARISON  OF  FORMULAS. 

R = mean  hydraulic  depth  in  feet  = area  -i-  wet  perimeter  = - for 
circular  section  of  pipe;  4 

S = sine  of  slope  = j-; 

v = velocity  in  feet  per  second; 
d = diameter  of  pipe  in  feet; 

L = length  of  pipe  in  feet; 

H = head  of  water  in  feet. 


Prony,  v 

Eytelwein, 

Eytelwein, 

Hawksley, 

Neville, 

Darcy, 


= 97.05]/ RS  — .08;  or,  v = 99.88 \/RS-  .154. 


f dH 
L + 50  d' 


v = 108]/.RS-.13. 
V = + 


v = U0\/RS  — llfr  RS. 

v = C]/  R S;  for  value  of  C,  see  following  Table. 


Diameter  of  pipe  (inches) 

1 

2 

1 

2 

3 

4 

5 

6 

7 

8 

Value  of  C. 

65 

80 

93 

99 

102 

103 

105 

106 

107 

Diameter  of  pipe  (inches) 

9 

10 

12 

14 

16 

18 

20 

22 

24 

Value  of  C 

108 

109 

109.5 

110 

110.5 

110.7 

111 

111.5 

111.5j 

Maximum  value  of  C for  very  large  pipes,  113.3. 
v = C \Zr~s, 


Kutter, 

where 

Weisbach, 


181  + 


.00281 


C = 


.026/  . , .00281  \ 
l + -7=(  416  + -S  ~) 


y' d'- 


V 2 


ft  = ^.0036  + ^V 

»'  V Vv 


where  h = head  necessary  to  overcome  the  friction  in  a pipe;  r = the  mean 
radius  of  the  pipe  in  feet;  and  g = gravity  = 32.2. 


Siphons.— When  any  part  of  the  pipe  line  rises  above  the  source  of  supply, 
such  a line  is  called  a siphon.  If  this  rise  is  greater  than  the  height  of  the 
water  barometer  (34  ft.  at  sea  level),  water  will  not  flow  through  the  siphon. 
The  flow  through  the  siphon  will  be  the  same  as  that  through  any  pipe  line 
so  long  as  there  is  no  accumulation  of  air  at  the  highest  point  of  the  line; 
but  such  an  accumulation  will  decrease  or  entirely  stop  the  flow.  All 
siphons  should  be  provided  at  their  highest  points  with  valves  for  discharging 
the  air  and  introducing  water  to  fill  the  siphon,  and  it  is  usually  best  to  trap 
the  lower  end  of  the  pipe  so  that  air  cannot  enter  it,  and  to  enlarge  the 
upper  end  so  as  to  reduce  the  loss  of  the  stream  in  entering.  For  a siphon 
to  work  well,  the  fall  between  the  intake  and  the  discharge  end  should  be 
considerable,  if  the  rise  amounts  to  much. 


Table  Showing  the  Actual  Amount,  or  80$  of  the  Theoretical  Flow  in  Pipes  From  $ In.  to  30  In.  Diameter. 

( Supplement  to  “Industry”  No.  45,  April,  1892.)  


150 


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Fall  or 
Slope. 

1 in  1,000 

2 in  1,000 

3 in  1,000 

4 in  1,000 

5 in  1,000 

6 in  1,000 

7 in  1,000 
Sin  1,000 

9 in  1,000 

1 in  100 

2 in  100 

3 in  100 

4 in  100 

5 in  100 

0 in  100 

7 in  100 

8 in  100 

9 in  100 

1 in  10 

2 in  10 

3 in  10 

4 in  10 

5 in  10 

6 in  10 

7 in  10 

8 in  10 

9 in  10 

10  in  10 

The  quantities  above  are  American  gallons  per  minute.  For  cubic  feet,  divide  by  7.5. 


FRICTION  IN  PIPES. 


151 


LOSS  OF  HEAD  IN  PIPE  BY  FRICTION 

In  each  100  ft.  in  length  of  different  diameters,  when  discharging  the  follow- 
ing quantities  of  water  per  minute,  as  given  by  Pel  ton  Water  Wheel  Co. 

Inside  Diameter  of  Pipe.  Inches. 


Velocity. 
Ft.  per  Sec. 

1 

2 

3 

4 

5 

6 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.'  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

! 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft.  | 

1 

Cu.  Ft. 
per  Min. 

2.0 

2.37 

.65 

1.185 

2.62 

.791 

5.89 

.593 

10.4 

.474 

16.3 

.395 

23.5 

2.2 

2.80 

.73 

1.404 

2.88 

.936 

6.48 

.702 

11.5 

.561 

18.0 

.468 

25.9 

2.4 

3.27 

.79 

1.639 

3.14 

1.093 

7.07 

.819 

12.5 

.650 

19.6 

.547 

28.2 

2.6 

3.78 

.86 

1.891 

3.40 

1.260 

7.65 

.945 

13.6 

.757 

21.3 

.631 

30.6 

2.8 

4.32 

.92 

2.160 

3.66 

1.440 

8.24 

1.080 

14.6 

.864 

22.9 

.720 

32.9 

3.0 

4.89 

.99 

2.440 

3.92 

1.620 

8.83 

1.220 

15.7 

.978 

24.5 

.815 

35.3 

3.2 

5.47 

1.06 

2.730 

4.18 

1.820 

9.42 

1.370 

16.7 

1.098 

26.2 

.915 

37.7 

3.4 

6.09 

1.12 

3.050 

4.45 

2.040 

10.00 

1.520 

17.8 

1.220 

27.8 

1.021 

40.0 

3.6 

6.76 

1.19 

3.380 

4.71 

2.260 

10.60 

1.690 

18.8 

1.350 

29.4 

1.131 

42.4 

3.8 

7.48 

1.26 

3.740 

4.97 

2.490 

11.20 

1.870 

19.9 

1.490 

31.0 

1.250 

44.7 

4.0 

8.20 

1.32 

4.100 

5.23 

2.730 

11.80 

2.050 

20.9 

1.640 

32.7 

1.370 

47.1 

4.2 

8.97 

1.39 

4.490 

5.49 

2.980 

12.30 

2.240 

22.0 

1.790 

34.3 

1.490 

49.5 

4.4 

9.77 

1.45 

4.890 

5.76 

3.250 

12.90 

2.430 

23.0 

1.950 

36.0 

1.620 

51.8 

4.6 

10.60 

1.52 

5.300 

6.02 

3.530 

13.50 

2.640 

24.0 

2.110 

37.6 

1.760 

54.1 

4.8 

11.45 

1.58 

5.720 

6.28 

3.810 

14.10 

2.850 

25.1 

2.270 

39.2 

1.900 

56.5 

5.0 

12.33 

1.65 

6.170 

6.54 

4.110 

14.70 

3.080 

26.2 

2.460 

40.9 

2.050 

58.9 

5.2 

13.24 

1.72 

6.620 

6.80 

4.410 

15.30 

3.310 

27.2 

2.650 

42.5 

2.210 

61.2 

5.4 

14.20 

1.78 

7.100 

7.06 

4.730 

15.90 

3.550 

28.2 

2.840 

44.2 

2.370 

63.6 

5.6 

15.16 

1.85 

7.580 

7.32 

5.060 

16.50 

3.790 

29.3 

3.030 

45.8 

2.530 

65.9 

5.8 

16.17 

1.91 

8.090 

7.58 

5.400 

17.10 

4.040 

30.3 

3.240 

47.4 

2.700 

68.3 

6.0 

17.23 

1.98 

8.610 

7.85 

5.740 

17.70 

4.310 

31.4 

3.450 

49.1 

2.870 

70.7 

7.0 

22.89 

2.31 

11.450 

9.16 

7.620 

20.60 

5.720 

36.6 

4.570 

57.2 

3.810 

82.4 

Inside  Diameter  of  Pipe.  Inches. 


. o 

7 

8 

9 

10 

11 

12 

Velocity 
Ft.  per  S< 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

-w  S3 

*3 

* 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

2.0 

.338 

32.0 

.296 

41.9 

.264 

53.0 

.237 

65.4 

.216 

79.2 

.198 

g 94.2 

2.2 

.401 

35.3 

.351 

46.1 

.312 

58.3 

.281 

72.0 

.255 

87.1 

.234 

103.0 

2.4 

.468 

38.5 

.410 

50.2 

.365 

63.6 

.327 

78.5 

.297 

95.0 

.273 

113.0 

2.6 

.540 

41.7 

.473 

54.4 

.420 

68.9 

.378 

85.1 

.344 

103.0 

.315 

122.0 

2.8 

.617 

44.9 

.540 

58.6 

.480 

74.2 

.432 

91.6 

.392 

111.0 

.360 

132.0 

3.0 

.698 

48.1 

.611 

62.8 

.544 

79.5 

.488 

98.2 

444 

119.0 

.407 

141.0 

3.2 

.785 

f 1.3 

.686 

67.0 

.609 

84.8 

.549 

105.0 

.499 

127.0 

.457 

151.0 

3.4 

.875 

54.5 

.765 

71.2 

.680 

90.1 

.612 

111.0 

.557 

134.0 

.510 

160.0 

3.6 

.969 

57.7 

.848 

75.4 

.755 

95.4 

.679 

118.0 

.617 

142.0 

.566 

169.0 

3.8 

1.070 

60.9 

.936 

79.6 

.831 

101.0 

.749 

124.0 

.680 

150.0 

.624 

179.0 

4.0 

1.175 

64.1 

1.027 

83.7 

.913 

106.0 

.822 

131.0 

.747 

158.0 

.685 

188.0 

4.2 

1.280 

67.3 

1.122 

87.9 

.998 

111.0 

.897 

137.0 

.816 

166.0 

.749 

198.0 

4.4 

1.390 

70.5 

1.220 

92.1 

1.086 

116.0 

.977 

144.0 

.888 

174.0 

.815 

207.0 

4.6 

1.510 

73.7 

1.320 

96.3 

1.177 

122.0 

1.059 

150.0 

.963 

182.0 

.883 

217.0 

4.8 

1.630 

76.9 

1.430 

100.0 

1.270 

127.0 

1.145 

157.0 

1.040 

190.0 

.954 

226.0 

5.0 

1.760 

80.2 

1.540 

105.0 

1.370 

132.0 

1.230 

163.0 

1.122 

198.0 

1.028 

235.0 

5.2 

1.890 

83.3 

1.650 

109.0 

1.470 

138.0 

1.320 

170.0 

1.200 

206.0 

1.104 

245.0 

5.4 

2.030 

86.6 

1.770 

113.0 

1.570 

143.0 

1.410 

177.0 

1.280 

214.0 

1.183 

254.0 

5.6 

2.170 

89.8 

1.890 

117.0 

1.680 

148.0 

1.510 

183.0 

1.370 

222.0 

1.260 

264.0 

5.8 

2.310 

93.0 

2.010 

121.0 

1.800 

154.0 

1.610 

190.0 

1.460 

229.0 

1.340 

273.0 

6.0 

2.460 

96.2 

2.150 

125.0 

1.920 

159.0 

1.710 

196.0 

1.560 

237.0 

1.430 

283.0 

7.0 

3.260 

112.0 

2.850 

146.0 

2.520 

185.0 

2.280 

229.0 

2.070 

277.0 

1.910 

330.0 

Example. — Have  200  ft.  head  and  600  ft.  of  11"  pipe,  carrying  119  cu.  ft.  of 
water  per  minute.  To  find  effective  head:  In  right-hand  column,  under  11" 
pipe,  find  119  cu.  ft.  Opposite  this  will  be  found  the  coefficient  of  friction  for 
this  amount  of  water,  which  is  .444.  Multiply  this  by  the  number  of  hun- 
dred feet  of  pipe,  which  is  6,  and  you  will  have  2.66  ft.,  which  is  the  loss  of 
head.  Therefore,  the  effective  head  is  200  — 2,66  = 197,34. 


152 


HYDRA  ULICS. 


LOSS  OF  HEAD  IN  PIPE  BY  FRICTION 

Tn  each  100  ft  in  length  of  different  diameters,  when  discharging  the  follow- 
ing quaXies  of  water  per  minute,  as  given  by  Pelton  Water  Wheel  Co. 

Inside  Diameter  of  Pipe.  Inches. 


% a 


13 

14 

15 

16 

18 

20 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 

| per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

£.5 

3 t- 
O <u 

0. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

.183 
.216 
.252 
.290 
.332 
.375 
.422 
; .471 

.522 
.576 
.632 
.691 
.751 
.815 
.881 
.949 
1.020 
j 1.092 
j 1.167 
1 1.245 
i 1.325 
! 1.750 

110 

121 

133 

144 

156 

.169 

128 

.158 : 

147 

.147 

167 

.132  j 

212 

.119 

262 

.200  1 

141 

.187  | 

162 

.175 

184 

.156  I 

233 

.140  j 

288 

234 

154 

.218  j 

176 

.205 

201 

.182 

254 

.164  | 

314 

.270 

167 

.252 

191 

.236  ! 

218 

.210 

275 

340 

1308 

179 

.288 

206 

.270  1 

234 

.240 

297 

.216  1 

366 

166 

177 

.349 

192 

.325 

221 

.306  | 

251 

.271 

318 

.245 

393 

.392 

205 

.366  1 

235 

.343 

268 

.305 

339 

.275 

419 

188 

.438 

218 

.408 

250 

.383 

284 

.339 

360 

.306 

445 

199 

.485 

231 

.452 

265 

.425 

301 

.377 

382 

.339 

471 

210 

.535 

243 

.499 

280 

.468 

318 

.416 

403 

.374 

497 

221 

.587 

256 

.548 

294 

.513 

335 

.456 

424 

.410 

523 

232 

.641 

269 

.598 

309 

.561 

352 

.499 

445 

.449 

550 

243 

.698 

282 

.651 

324 

.611 

1 368 

.542 

466 

.488 

576 

254 

.757 

295 

.707 

339 

.662 

385 

.588 

488 

.529 

602 

265 

.818 

308 

.763 

353 

.715 

! 402 

.636 

509 

.572 

628 

276 

.881 

321 

.822 

368 

.770 

419 

.685 

530 

.617 

654 

287 

.947 

333 

.883 

383 

.828 

435 

.736 

551 

.662 

680 

298 

1.014 

346 

i .947 

397 

.888 

452 

.788 

572 

.710 

707 

309 

1.083 

359 

1.011 

412 

| .949 

469 

.843 

594 

! .758 

733 

321 

1.155 

372 

1.078 

427 

1.011 

486 

.899 

I 615 

.809 

759 

332 

1.229 

385 

1.148 

442 

1.076 

502 

.957 

; 636 

.861 

785 

387 

1.630 

449 

1.520 

515 

1 

1.430 

586 

1.270 

j 742 

j 

1.143 

916 

» i i-j 


2.0 

2.2 

2.4 
2.6 
2.8 

3.0 

3.2 

3.4 

3.6 

3.8 

4.0 

4.2 

4.4 

4.6 

4.8 

5.0 

5.2 

5.4 

5.6 

5.8 

6.0 

7.0 


Inside  Diameter  of  Pipe.  Inches. 


Velocity. 
Ft.  per  Sec. 

22 

24 

2< 

Loss  of 
Head.  Ft. 

5f| 

0 g. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

2.0 

.108 

316 

.098 

377 

.091 

2.2 

.127 

348 

.116 

414 

.108 

2.4 

.149 

380 

.136 

452 

.126  1 

2.6 

.171 

412 

.157 

490 

.145  I 

2.8 

.195 

443 

.180 

528 

.165  ; 

3.0 

.222 

475 

.204 

565 

.188 

3.2 

.249 

507 

.229 

603 

.211 

3.4 

.278 

538 

.255 

641 

.235 

3.6 

.308 

570 

.283 

678 

.261 

3.8 

.340 

601 

.312 

716 

.288 

4.0 

.373 

633 

.342 

754 

.315 

4.2 

.408 

665 

.374 

791 

.345 

4.4 

.444 

697 

.407 

829 

.375 

4.6 

.482 

728 

.441 

867 

.407 

4.8 

.521 

760 

.476 

905 

.440 

5.0 

.561 

792 

.513 

942 

.474 

5.2 

.602 

823 

.552 

980 

.510 

5.4 

.645 

855 

.591 

1,018 

.546 

5.6 

.690 

887 

.632 

1 ,055 

.583 

5.8 

.735 

918 

.674 

1.093 

.622  1 

6.0 

.782 

950 

.717 

1,131 

.662 

7.0 

1.040 

1 

1,109 

.953 

! 1 ,319 

.879  , 

O 

CO 

00 

cs 

36 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

442 

.084 

513  .079  ; 

589  j 

.066 

848 

486 

.099 

564  .093 

648  , 

.078 

933 

531 

.116 

616  .109 

707  { 

.091 

1,018 

575 

.134 

667  ; .126 

766  ! 

.104 

1,100 

619 

.153 

718  .144 

824  1 

.119 

1,188 

663 

.174 

770  .163 

883  I 

.135 

1 ,273 

708 

.195 

821  ' .182 

942  l 

.152 

1.357 

752 

.218 

872  .204 

1,001  ! 

.169 

1.442 

796 

.242 

923  .226 

1,060 

.188 

1,527 

840 

.267 

974  j .249 

1,119 

.207 

1,612 

885 

.293 

1,026  .273 

1,178 

.228 

1 ,697  • 

929 

.320 

1,077  : .299 

1,237 

.249 

1,782 

973 

.348 

1,129  .325 

1,296 

.271 

1,866 

1,017 

.378 

1,180  I .353 

1,355 

.294 

1,951 

1,062 

.409 

1,231  .381 

1,414 

.318 

2,036 

1,106 

.440 

1,283  , .411 

1,472 

.342 

2,121 

1.150 

.473 

1.334  .441 

1,531 

.368 

2,206 

1,194 

.507 

1,385  ! .473 

1,590 

.394 

2,291 

1,239 

.542 

1.437  .506 

1,649 

.421 

2,376 

1,283 

.578 

1,488  .540 

1,708 

.450 

2,460 

1,327 

.615 

1.539  .574 

1,767 

.479 

2,545 

1,548 

.817 

1,796  .762 

2,061 

.636 

2,968 

FRICTION  IN  PIPES. 


153 


The  following  formula,  deduced  by  William  Cox,  gives  practically 
the  same  results  as  the  foregoing  table  and  will  be  found  useful  in  many 

instances:  F = fo^2>(4r2  + 5F_2),  where/1  = friction  head;  L = length 

of  pipe  in  feet;  D = diameter  of  pipe  in  inches;  V = velocity  in  feet  per 
second. 

Friction  of  Knees  and  Bends. -This  subject  has  not  been  investirated  suffi- 
ciently  to  enable  the-  engineer  to  make  exact  allowance  for  this  factor,  but 


the  following  formulas  may  be  taken  as  giving  close  approximate  results. 
It  is  well  to  bear  in  mind  that  right  angles  should  be  avoided  whenever 
possible,  and  that  bends  should  be  made  with  as  large  a radius  as  circum- 

A = angle  of  bend  or  knee  with  forward  line 
of  direction; 

V = velocity  of  water  in  feet  per  second; 

R ==  radius  of  center  line  of  bend; 
r = radius  of  bore  of  pipe  (or  i diameter); 

K = coefficient  for  angles  of  knees; 

L = coefficient  for  curvature  of  bends; 

H = head  of  water  in  feet  necessary  to  over- 
come the  friction  of  the  bends,  or  knees. 
H = .0155  V2K. 

The  value  of  iTis  as  follows  for  different  angles: 


20° 

40° 

60° 

I 80° 

90° 

100° 

120° 

.046 

.139 

.364 

1 '74 

1 .98 

1.26 

1.86 

stances  will  allow. 


For  bends, 


H = .0155  V2  (Ai). 


154 


HYDRA  ULICS. 


Values  of  L with  various  ratios  of  the  radius  of  bend  to  radius  of  bore: 


When  = 

j .1  ' 

.2  ! 

.3 

•4  | 

1 .5 

.6  j 

• 4 

.8  | 

.9  i 

1 

1.0 

In  circular  section  L 

.131  ! 

.138 

.158 

. '206  ! 

.294 

.44 

.66 

.98 

1.4 

2.0 

In  rectangular  L 

.124  ; 

.135 

.18 

.25 

.4 

.64 

1.01 

1.55  , 

2.3  | 

3.2 

RESERVOIRS. 

Reservoir  Site.— In  selecting  a site  for  a reservoir,  the  following  points 
should  be  observed: 

1.  A proper  elevation  above  the  point  at  which  the  water  is  required. 

2.  The  total  supply  available,  including  observations  as  to  the  rainfall 
and  snowfall. 

3.  The  formation  and  character  of  the  ground,  with  reference  to  the 
amount  of  absorption  and  evaporation. 

The  most  desirable  formation  of  ground  for  a reservoir  site  is  one  of  com- 
pact rock,  like  granite,  gneiss,  or  slate;  porous  rocks,  like  sandstones  and 
limestones,  are  not  so  desirable.  Steep  bare  slopes  are  best  for  the  country 
surrounding  a reservoir,  as  the  water  escapes  from  them  quickly.  The 
presence  of  vegetation  above  the  reservoir  causes  a considerable  amount  of 
absorption;  but,  at  the  same  time,  the  rainfall  is  usually  greater  in  a region 
covered  with  vegetation  than  in  a barren  region,  hence  the  streams  have  a 
more  uniform  flow.  A reservoir  must  be  made  large  enough  to  hold  a 
supplv  capable  of  meeting  the  maximum  demand.  The  area  of  a reservoir 
should  be  determined,  and  a table  made  showing  its  contents  for  every  foot 
in  depth,  so  that  the  amount  of  water  available  can  always  be  known. 


DAMS. 

Dams  are  used  for  retaining  water  in  reservoirs,  for  diverting  streams  in 
placer  mining,  and  for  storing  debris  coming  from  placer  mines  in  canons 
or  ravines. 

Foundations  for  dams  must  be  solid  to  prevent  settling,  and  water-tight  to 
prevent  leakage  under  the  base  of  the  dam.  Whenever  possible,  the  founda- 
tion should  be  solid  rock.  Gravel  is  better  than  earth,  but  when  gravel  is 
emploved  it  will  be  necessary  to  drive  sheet  piling  under  the  upper  toe  of 
the  dam,  to  prevent  water  from  seeping  through  the  formation  under  the 
dam.  Vegetable  soil  should  be  avoided,  and  all  porous  material,  such  as 
«and,  gravel,  etc.  should  be  stripped  off  until  hard  pan  or  solid  rock  is 
reached.  In  case  springs  occur  in  the  area  covered  by  the  foundation  of  the 
dam,  it  will  be  necessary  to  trace  them  up,  and  if  they  originate  on  the 
upper  side  to  confine  their  flow  to  that  side  of  the  dam.  so  that  they  will 
have  no  tendency  to  ultimately  become  passageways  for  water  from  the 
upper  face  to  the  lower  face  of  the  dam,  thus  providing  holes  which  may 
ultimatelv  destrov  the  entire  foundation  of  the  structure. 

Wooden  Dams.— Wooden  dams  are  constructed  of  round,  sawed,  or  hewn 
logs.  The  timbers  are  usually  at  least  1 ft.  square,  or,  if  round,  from  18  to 
^4  in  in  diameter.  A series  of  cribs  from  8 to  10  ft.  square  are  constructed  by 
building  up  the  logs  log-house  fashion  and  securing  them  together  with 
treenails.  The  individual  cribs  are  secured  to  one  another  with  treenails 
or  by  means  of  bolts.  The  cribs  are  usually  filled  with  loose  rock  to  keep 
them  in  place,  and  in  many  cases  are  secured  to  the  foundation  by  means 
of  bolts  A laver  of  planking  on  the  upper  face  of  the  dam  makes  it  water- 
tight. and  if  the  spillway  is  over  the  crest  of  the  dam  it  will  be  necessary  to 
plank  the  top  of  the  cribs,  and.  in  most  cases,  to  provide  an  apron  for  the 
water  to  fall  on.  The  apron  may  be  set  on  small  cribs,  or  on  timbers  pro- 
‘ecting  from  the  cribs  of  the  dam  itself. 

J Abutments  and  Discharge  Gates.— Abutments  are  structures  at  the  ends  of  a 
dam  They  mav  be  constructed  from  timber,  masonry,  or  dry  stonework. 
If  possible'  abutments  should  have  a curved  outline,  and  should  be  so 
placed  that  there  is  no  possibility  of  the  water  overflowing  them,  or  getting 
behind  them  during  floods.  If  the  regular  discharge  from  a dam  takes  place 
from  the  main  face,  the  gates  may  be  arranged  in  connection  with  one  of 
the  abutments,  or  by  means  of  a tunnel  and  culvert  through  the  dam.  In 


DAMS. 


155 


either  case,  some  structure  should  he  constructed  above  the  outlet  so  as  to 
prevent  driftwood,  brush,  and  other  material  from  stopping  the  discharge 
gates.  When  the  discharge  gates  are  placed  at  one  side  o£  the  dam,  they  are 
usually  arranged  outside  of  the  regular  abutment,  between  it  and  another 
special  abutment,  the  discharge  being  through  a series  of  gates  into  a flume, 

dltSpillwaysPor  Waste  Ways— These  are  openings  provided  in  a dam  for  the 
discharge  of  water  during  floods  or  freshets,  or  tor  the  dischargeofaportioii 
not  being  used  at  any  time.  The  spillway  may  be  over  the  crest  of  the  dam, 
or  where  the  topography  favors  such  a construction,  the  mam  dam  may  be 
of’ sufficient  height  to  prevent  water  from  ever  passing  its  crest,  the  spillway 
being  arranged  at  another  outlet  over  the  lower  dam.  Waste  ways,  proper, 
are  openings  through  the  dam,  and  are  intended  for  the  discharge  of  the 
large  quantities  of  water  that  come  down  during  freshets  or  floods.  In  the 
case  of  timber  dams,  the  waste  ways  are  usually  surrounded  by  heavy  cribs, 
and  have  an  area  of  from  40  to  50  sq.  ft.  each.  There  are  two  general 
forms  of  construction  employed  for  waste  ways.  One  consists  of  a compara- 
tively narrow  opening  in  the  dam,  extending  to  a considerable  depth  (8  or 


Fig.  18. 


10  ft ) Water  is  allowed  to  discharge  through  this  during  flood  time,  but 
when  it  is  desired  to  stop,  the  flow  planks  are  placed  across  the  up-stream 
face  of  the  opening  in  such  a manner  as  to  close  it.  The  opening,  which  is 
usually  not  over  8 or  4 ft.  wide,  is  provided  with  guides  on  the  upper  face  of 
the  dam,  and  between  which  the  planks  are  slid  down,  the  individual  pieces 
of  planking  being  at  least  1 ft.  longer  than  the  opening  that  they  are  to 
cover.  The  other  device  frequently  used  consists  m providing  the  waste 
way  at  one  side  of  the  regular  spillway,  with  a crest  2 or  3 ft.  lower  than  the 
rejmlar spillway.  The 
and  4 or 


spillway. 
5 ft.  abc 


. e VV<X^  io 

>ove  there  is  arranged  a parallel  timber,  the  space  between 
’ ■ ” flash  boards.  These  are  made  from 


the  two  being  closed  by  what  are  called  uasn  ^ — ~rr 

nieces  of  2"  or  3"  plank,  6 or  8 in.  wide.  The  planks  are  placed  against  both 
timbers  so  as  to  close  the  space.  The  individual  p anks  are  made  long 
enough  so  that  they  extend  from  1 to  2 ft.  above  the  upper  timber,  and 
through  the  upper  end  of  each  plank  is  bored  a hole  through  which  a piece 
of  rope  is  passed  and  a knot  tied  in  the  end  of  the  rope.  These  ropes  are 
secured  by  staples  to  the  upper  timber.  When  it  becomes  necessary  to  open 
the  waste  way,  men  go  under  with  peevies,  cant  hooks,  or  pmch  bars,  and 
pry  up  the  planks  in  such  a way  as  to  draw  the  longer  end  out  of  contact 
with  the  lower  timber,  when  the  force  of  the  water  will  immediately  carry 
the  plank  down  the  stream  as  far  as  the  rope  will  allow  it  to  go.  After  the 
first  plank  has  been  loosened,  the  succeeding  ones  can  be  pulled  up  with 
comparative  ease,  and  two  men  can  open  a 25'  or  30  section  of  waste  way  in 
a very  few  minutes.  The  ropes  keep  the  plank  from  being  lost,  and  the 
opening  can  be  closed  again  by  passing  the  plank  down  into  the  water  to 
one  side  of  the  opening  and  moving  them  into  the  current.  Some  skill  is 
required,  both  in  opening  and  closing  the  waste  ways. 

Stone  Dams— Where  cement  or  lime  is  expensive  and  suitable  rubble 
stone  can  be  obtained,  dams  are  frequently  constructed  without  the  use  of 
mortar.  The  upper  and  lower  faces  of  the  dam  should  be  of  hammer- 
dressed  stone,  carefully  bonded,  and  the  stones  m the  lower  face  of  the  dam 
are  sometimes  anchored  by  means  of  bolts.  The  dam  can  be  made^ter- 
tight  by  means  of  a skin  of  planking  on  the  upper  face.  In  case  water 
should  ever  pass  over  the  crest  of  such  a dam,  much  of  it  would  settle 
through  the  openings  in  the  stone  into  the  interior  of  the  dam,  and  this 
would  subject  the  stones  in  the  lower  portion  of  the  face  to  a hydrostatic 


156 


HYDRAULICS. 


pressure,  provided  an  opening  was  not  made  for  the  escape  of  such  water. 
For  this  reason,  culverts  or  openings  should  be  made  through  the  lower 
portion  of  the  dam,  to  discharge  any  such  water.  When  such  dams  as  this 
are  constructed,  the  regular  spillway  is  not  placed  over  the  face  of  the  dam, 
but  at  some  other  point,  and  usually  over  a timber  dam. 

Earth  Dams.— Earth  dams  are  used  for  reservoirs  of  moderate  height. 
They  should  be  at  least  10  ft.  wide  on  top,  and  a height  of  more  than  60  ft.  is 
unusual  When  the  material  of  which  the  dam  is  composed  is  not  water- 
tight as  for  instance,  gravel,  sand,  etc.,  it  is  sometimes  necessary  to  con- 
struct a puddle  wall  of  clav  in  the  center  of  the  regular  dam.  This  consists 
of  a narrow  dam  of  clay  mixed  with  a certain  proportion  of  sand.  The 
nuddle  wall  should  not  be  less  than  from  6 to  8 ft.  thick  at  the  top  of  the 
dam  and  should  be  given  a slight  batter  on  each  side.  It  is  constructed 
during  the  building  of  the  dam,  and  should  be  protected  from  contact  with 
the  water  bv  a considerable  thickness  of  earth  on  the  upper  face.  The 
unner  face  of  an  earthen  dam  is  frequently  protected  by  means  of  plank  or 
a pavement  of  stone.  The  lower  face  is  frequently  protected  by  means  of 
cod  or  sod  and  willow  trees.  Sometimes  earth  dams  are  provided  with  a 
masonrv  core  in  place  of  the  puddle  wall,  to  render  them  water-tight.  This 
consists  of  a masonrv  wall  carried  to  an  impervious  stratum,  and  up  through 
the  center  of  the  dam.  The  masonry  core  should  never  be  less  than  2 or  3 ft. 
thick  at  the  top,  and  should  be  given  a batter  of  at  least  104  on  each  side. 
At  the  regular  water  level,  earthen  dams  are  liable  to  have  a small  bench 
or  shelf  formed,  and  on  this  account,  during  the  construction,  such  a bench 
or  shelf  is  sometimes  built  into  the  earth  dam.  Fig.  18  shows  a dam  with  a 
masonry  core,  with  the  upper  face  covered  with  rubble  and  the  lower  face 
covered  with  grass.  . , , , 

Debris  Dams  —These  are  dams  or  obstructions  placed  across  the  bed  of 
streams  to  hol’d  back  tailings  from  mines,  and  to  prevent  damage  to  the 
vallevs  below.  They  are  made  of  stone,  timber,  or  brush.  No  attempt  is 
made  to  render  the  debris  dam  water-tight,  the  only  object  being  that  it 
should  retard  the  flow  of  the  stream  and  give  it  a greater  breadth  of  dis- 
charge co  that  the  water  naturally  drops  and  deposits  the  sediment  that- 
it  is  carrying  The  sediment  soon  silts  or  fills  up  against  the  face  of  the 
dam  the ‘area  above  the  dam  becoming  a flat  expanse  or  plain  over  which 
the  water  finds  its  way  to  the  dam.  When  these  darns  are  constructed  of 
stone  the  individual  stones  on  the  lower  face  and  crest  of  the  dam  should 
be  so  laro-e  that  the  current  will  be  unable  to  displace  them,  while  the  upper 
face  and  core  of  the  dam  mav  be  composed  of  finer  material.  In  case  a 
breach  should  occur  in  the  debris  dam,  it  will  not  necessarily  endanger  the 
region  farther  down  the  stream,  as  is  the  case  when  a break  occurs  m a 
water  dam  The  reason  for  this  is  that  the  debris  dam  is  not  made  water- 
tight and  hence  there  is  never  much  pressure  against  it,  or  a large  volume 
of  water  held  back  that  can  rush  suddenly  down  the  stream  should  a break 
occur  The  only  result  of  the  break  would  be  that  more  or  less  of  the  gravel 
behind  the  dam* would  be  washed  through  the  breach. 

wing  Dams  —Wing  dams  are  used  for  turning  streams  from  their  courses, 
so  as  to  expose  all  or  a portion  of  the  bed  for  placer  mining  or  other  pur- 
poses They  are  usually  of  a temporary  nature,  and  are  constructed  of 
brush  and  stones,  light  cribs  filled  with  stones,  and  of  large  stones  or  timber 
Sometimes  the  course  of  a stream  is  turned  by  an  obstruction  inade  of  sand 
bao-s  and  a wing  dam  constructed  behind  this  of  frames  of  timoer,  the  inter- 
vening space  being  filled  with  gravel  or  earth,  and.  in  some  cases,  the  timber 
being  covered  with  stone,  and  the  surface  nprapped  so  that  if  the  flow  ever 
comes  over  the  top  of  the  structure  it  will  not  destroy  it. 

Masonrv  Dams  —When  high  masonry  dams  are  to  be  employed  they  should 
be  designed  bv  a competent  hydraulic  engineer.  Masonry  dams  are  not,  as 
a rule  used  for  hydraulic  mining,  owing  to  the  fact  that  the  length  of  time 
during  which  the  dam  is  required  rarely  warrants  the  expense  ot  the  con- 
struction of  a masonry  dam. 


WATER-POWER. 

The  Theoretical  Efficiency  of  the  Water-Power.-The  gross  power  of  a fall  of 

water  is  the  product  of  the  weight  of  water  discharged  in  a unit  of  time,  and 
the  total  head  or  difference  in  elevation  of  the  surface  of  the  water,  above 
and  below  the  fall.  The  term  head,  used  in  connection  with  waterwheels, 


WATER-POWER. 


157 


is  the  difference  in  height  between  the  surface  of  water  in  the  penstock  and 
that  in  the  tailrace,  when  the  wheel  is  running. 

If  q = cubic  feet  of  water  discharged  per  minute, 

W = weight  of  a cubic  foot  of  water  = 62.5  lb., 
and  H = total  head  in  feet, 

then  WQH  = gross  power  in  foot-pounds  per  minute, 
and  = the  horsepower. 

Substituting  the  value  for  W,  we  have 

= .00189  Q H.  as  the  horsepower  of  a fall. 

83  000 

The  total  power  can  never  be  utilized  by  any  form  of  motor,  owing  to  the 
fact  that  there  is  a loss  of  head,  both  at  the  entrance  to,  and  exit  from,  the 
wheel,  and  there  are  also  losses  of  energy,  due  to  friction  of  the  -water  m 
passing  through  the  wheel.  The  ratio  of  the  power  developed  by  the  wheel 
to  the  gross  power  of  the  fall,  is  the  efficiency  of  the  wheel.  A head  of  water 
can  be  made  use  of  in  any  one  of  the  following  ways: 

1 By  its  weight,  as  in  the  water  balance,  or  overshot  wheel. 
i.  By  its  pressure,  as  in  the  hydraulic  engine,  hydraulic  presses,  cranes, 
etc.,  or  in  a turbine  water  wheel.  , , , . . , , , 

3.  By  its  impulse,  as  in  the  undershot  and  impulse  wheels,  such  as 


Peltons,  etc. 

4.  By  a combination  of  the  above. 

The  Horsepower  of  a Running  Stream.— The  gross  horsepower,  as  seen  above,  is 

H.  P.  = — .00189  Q if, 

33,000  . ... 

in  which  Q is  the  quantity  in  cubic  feet  per  minute  actually  impinging  on 
the  float  or  bucket,  and  if  the  theoretical  head  added  to  the  velocity  of  the 


stream,  or 


H 2 g 64.4’ 

in  which  v is  the  velocity  in  feet  per  second.  , 

For  example,  if  the  floats  of  an  undershot  waterwheel  were  2 ft.  X 10  ft.  .and 
the  stream  had  a velocity  of  3 ft.  per  second,  i.  e.,  v = 3,  we  would  have 


H = = .139,  and  Q = 2 x 10  X 3 x 60  = 3,600  cu.  ft.  per  min. 

From  this,  H.  P.  = 3,600  X .139  X .00189  = .945  H.  P.,  or  a gross  horse- 
power for  practically  .05  sq.  ft.  of  wheel  surface;  but,  under  ordinary  circum- 
stances, it  would  be  impossible  to  attain  more  than  40^  of  this,  or  practically 
.02  horsepower  per  sq.  ft.  of  surface,  which  would  require  50  sq.  ft.  of  float 

surface  to  each  horsepower  furnished. 

Current  Motors.— A current  motor  fully  utilizes  the  energy  of  a stream 
only  when  it  is  so  arranged  that  it  can  take  all  of  the  velocity  out  of 
the  water;  that  is,  when  the  water  leaves  the  floats  or  vanes  with  no 
velocity.  It  is  evident  that  in  practice  we  can  never  even  obtain  a close 
approximation  to  these  results,  and  hence  only  a small  fraction  of  the 
energy  of  a running  stream  can  be  utilized  by  the  current  motor.  Current 
motors  are  frequently  used  to  obtain  small  amounts  of  power  from  a large 
stream,  as,  for  instance,  for  pumping  a limited  amount  of  water  for  irrigation. 
For  this  work,  an  ordinary  undershot  wheel  having  radial  paddles  is  usually 
employed.  At  one  end  of  the  wheel  a series  of  small  buckets  are  placed,  and 
so  arranged  that  each  bucket  will  dip  up  water  at  the  bottom  of  the  wheel 
and  discharge  it  into  the  launder,  near  the  top  of  the  wheel.  The  shape  of 
the  buckets  should  be  such  that  only  the  amount  of  water  which  the  bucket 
is  capable  of  carrying  to  the  launder  will  be  dipped  up,  for  if  the  bucket 
is  constantly  slopping  or  pouring  water  as  it  ascends,  a large  amount 
of  useless  work  is  performed  in  raising  this  extra  water  and  then  pouring  it 
out  again,  as  only  the  portion  that  reaches  the  launder  can  be  of  any  service. 
Current  motors  are  not  practicable  for  furnishing  large  amounts  of  power. 


UTILIZING  THE  POWER  OF  A WATERFALL. 

The  power  of  a waterfall  may  be  utilized  by  a number  of  different  styles 

of  motors,  but  each  has  certain  advantages. 

Breast  and  Undershot  Wheels.— When  the  head  is  low  (not  over  5 or  6 ft  ), 
breast  or  undershot  wheels  are  frequently  employed.  If  these  are  properly 


158 


HYDRAULICS . 


proportioned,  it  is  possible  to  realize  from  25#  to  50#  of  the  theoretical  power 
of  the  fall,  but  the  wheels  are  large  and  cumbersome  compared  with  the  duty 
they  perform,  and  not  often  installed  at  present,  especially  near  manufac-  | 
turing  centers.  „ , A , . 

Overshot  Wheels.— For  falls  up  to  40  or  50  ft.,  overshot  wheels  are  very 
commonly  employed,  and  they  have  been  used  for  even  greater  heads  than 
this.  The  overshot  wheel  derives  its  power  both  from  the  impulse  of  the 
water  entering  the  buckets,  and  from  the  weight  of  the  water  as  it  descends 
on  one  side  of  the  wheel  in  the  buckets.  The  latter  factor  is  by  far  the, more 
important  of  the  two.  When  properly  proportioned,  overshot  wheels  may 
realize  from  70#  to  90#  of  the  power  of  the  waterfall,  but  they  are  large  and 
cumbersome  compared  with  the  power  that  they  give,  and  are  not  often 
installed  except  in  isolated  regions,  where  they  are  made  from  timber  by 
local  mechanics.  „ . 

Impulse  Wheels.— For  heads  varying  from  60  ft.  up,  impulse  wheels  are 
very  largely  used.  These  are  also  sometimes  called  hurdy  gurdies,  and  are 
usually  of  the  Felton  type,  consisting  of  a wheel  provided  with  buckets,  so 
arranged  about  its  periphery  that  they  receive  an  impinging  jet  of  water  and 
turn  it  back  upon  itself,  discharging  it  with  practically  no  velocity,  and  con- 
verting practically  all  the  energy  into  useful  work.  The  efficiency  of  these 
wheels  varies  from  85#  to  90#  under  favorable  circumstances.  This  style  of 
wheel  is  especially  adapted  for  very  high  heads  and  comparatively  ^small 
amounts  of  water.  There  are  a number  of  instances  where  wheels  are 
operating  under  a head  of  as  much  as  2,000  ft.  This  style  of  impulse  wheel  i 
is  an  American  development;  in  Europe,  a style  of  impulse  turbine  has  been  li 
used  to  some  extent,  but  has  not  found  very  much  favor  in  the  United  States. 

Turbines.— Turbines  or  reaction  wheels  are  very  largely  employed,  espe- 
cially for  moderate  heads.  When  properly  designed  to  fit  the  working 
conditions,  they  can  be  used  for  heads  varying  from  4 or  5 ft.  up  to  consider- 
ably over  100  ft.,  and  when  properly  placed  are  capable  of  utilizing  the 
entire  head,  a factor  that  gives  them  a decided  advantage  over  any  other 
style  of  waterwheel.  Turbines  are  capable  of  returning  85#  to  90#  of  the 
theoretical  energy  as  useful  power,  and  are  largely  used,  especially  where  a 
considerable  volume  of  water  at  a low  head,  or  a smaller  volume  at  a 
moderate  head,  can  be  obtained. 


PUMP  MACHINERY. 


Pumps  are  employed  for  unwatering  mines,  handling  water  at  placer 
mines,  irrigation,  water-supply  systems,  boiler  feeds,  etc. 

For  un watering  mines,  two  general  systems  of  pumping  are  employed. 
(1)  The  pump  is  placed  in  the  mine  and  is  operated  by  a motor  on  the  sur- 
face, the  power  being  transmitted  through  a line  of, moving  rods.  (2)  Both 
the  motor  and  pump  are  placed  in  the  mine,  the  motor  being  an  engine 
driven  by  steam,  compressed  air,  hydraulic  motor,  or  an  electric  motor. 

Cornish  Pumps.— Any  method  of  operating  pumps  by  rods  is  commonly 
called  a Cornish  system.  Formerly,  the  motor  in  the  Cornish  system  con- 
sisted of  a steam  engine  placed  over  the  shaft  head,  which  operated  the 
pump  by  a direct  line  of  rods.  With  this  arrangement,  there  is  great  danger 
of  accident  to  the  engine  from  the  settling  of  the  ground  around  the  shaft, 
or  from  fire  in  the  shaft;  also,  the  position  of  the  motor  renders  access  to  the 
shaft  difficult.  To  overcome  these  objections,  the  engine  is  frequently 
placed  at  one  side  of  the  shaft,  and  the  rods  operated  by  a bob;  this  has 
become  the  common  practice,  and  is  generally  called  the  Cornish  rig.  The 
engine  employed  in  the  most  modern  plants  is  generally  of  the  Corliss 
type,  and  is  provided  with  a governor  to  guard  against  the  possibility  of  the 
engine  running  away,  in  case  the  rods  should  break. 

This  svstem  requires  no  steam  line  down  the  shaft,  and  is  independent  of 
the  depth  of  water  .in  the  mine,  so  that  the  pump  is  not  stopped  by  the 
drowning  of  a mine,  but  the  moving  rods  are  a great  inconvenience  in  the 
shaft,  and  they  absorb  a great  amount  of  power  by  friction. 

Simple  and  Duplex  Pumps.— In  the  simple  pump,  a steam  cylinder  is  con- 
nected directly  to  a water  cylinder,  and  the  steam  valves  are  operated  by 
tappets.  Such  a pump  is  more  or  less  dependent  on  inertia  at  certain  points 
of  the  stroke  to  insure  the  motion  of  the  valves,  hence  will  not  start  from 


P VMP  M A C MINER  Y. 


159 


anyplace,  but  is  liable  to  become  stalled  at  times.  In  the  duplex  pump, 
two  steam  cylinders  and  two  water  cylinders  are  arranged  side  by  side, 
and  the  valves  so  placed  that  when  one  piston  is  at  mid-stroke  it  throws 
the  steam  valve  for  the  other  cylinder,  etc.  With  this  arrangement,  the 
pump  will  start  from  anv  point,  and  can  never  be  stalled  tor  lack  of  steam, 
due  to  the  position  of  the  valves.  Ordinarily,  duplex  pumps  are  to  be  pre- 
ferred for  mine  work.  , ...  , . , 

The  packing  for  the  water  piston  of  a pump  maybe  either  inside  or  outside. 
Any  form  of  packing  that  is  inside  the  cylinder,  either  upon  a moving  piston 
or  surrounding  the  ram, 
and  so  situated  that  any 
wear  will  allow  communi- 
cation between  the  oppo- 
site ends  of  the  cylinder, 
is  called  inside  packing. 

It  may  consist  simply  of 
piston  rings  about  the  pis- 
ton, as  in  the  case  of  an 
ordinary  steam-engine  pis- 
ton G,  Fig.  19,  or  stationary 
rings  may  be  employed 
about  the  outside  of  a mov- 


Fig.  19. 


In^either  case,  the  cylinder  heads  have  to  be  removed  before  the  condition 
of  the  packing  can  be  inspected,  and  any  leak  does  not  make  itself  visible. 

When  outside  packing  is  employed,  separate  rams  are  used  in  opposite 
ends  of  the  cylinder,  there  being  no  internal  communication  between  the 
chambers  in  which  the  rams  work.  The  rams  are  packed  by  ordinary 
outside  stuffingboxes  and  glands.  The  arrangement  consists  practically  ot 
two  single-acting  pumps  arranged  to  work  alternately,  so  that  one  is  forcing 
water  while  the  other  is  drawing  water.  Fig.  20  shows  a horizontal  section 
of  a cylinder  so  arranged,  together  with  the  yoke  rods  that  operate  the  ram 
at  the  farther  end  of  the  cylinder.  . , , . . , 

As  a rule,  inside-packed  pumps  should  be  avoided  m mines,  on  account  of 
the  fact  that  acid  or  gritty  waters  are  liable  to  cut  the  packing,  and  make  the 
pumps  leak  in  a very  short  time.  For  dipping  work  m single  stopes  or 
entries,  small  single  or  duplex  outside-packed  pumps  may  be  employed. 
It  is  generally  best  to  operate  such  pumps  by  compressed  air,  for  the  exhaust 
will  then  be  beneficial  to  the  mine  air.  If  steam  is  employed,  it  is  frequently 
necessary  to  introduce  a trap  and  remove  entrailed  water  from  the  steam 
before  it  enters  the  pump,  and  to  dispose  of  the  exhaust  by  piping  it  out  or 
condensing  it.  Such  isolated  steam  pumps  are  about  the  most  waste! ul  form 
of  steam-driven  motor  in  existence. 

For  sinking,  center-packed  single  or  duplex  pumps  are  usually  employed, 
the  duplex  style  being  the  better.  For  station  work,  where  much  water  is  to 
be  handled,  large  compound,  or  triple-expansion,  condensing,  duplex  pump- 
ing engines  are  employed.  They  may,  or  may  not,  be  provided  with  cranks 
and  a flywheel.  Engineers  differ  greatly  upon  this  point,  and,  as  a rule,  for 
very  high  lifts  and  great  pressures,  the  flywheel  is  employed. 

The  main  points  in  consideration  are  the  first  cost  of  the  pump,  and  the 
amount  that  will  be  saved  by  using  the  more  expensive  engine.  The  large 
flywheel  pumping  engines  are  several  times  as  expensive  as  the  direct- 
acting  steam  pumps,  and  the  question  is  as  to  whether  their  greater  efficiency 
6 * * > ^ will  more  than  coun- 

terbalance the  in- 
creased outlay.  Most 
engineers  favor  fly- 
wheel pumps  for 
handling  large  vol- 
umes of  water  where 
the  work  is  approxi- 
mately constant,  and  direct-acting  pumps,  without  fly  wheels  or  cranks, 
for  handling  small  amounts  of  water,  or  for  very  irregular  service,  owing 
to  the  fact  that  if  the  flywheel  pump  is  driven  below  its  normal  speed  it  does 
not  govern  properly,  nor  work  economically.  Until  recently,  water  was 
removed  from  mines  in  lifts  of  about  300  to  350  ft.,  pumps  being  placed  at 
stations  along  the  shaft. 

While  a series  of  station  pumps  are  still  employed,  m some  cases  they  are 


Fig.  20. 


160 


PUMP  MACHINERY. 


generallv  intended  to  take  care  of  water  coming  into  the  shaft,  or  workings 
at  or  near  their  level,  and  are  not  employed  for  handling  water  in  successive 
stages  or  lifts.  For  handling  the  bulk  of  the  water  from  the  bottom  of  the 
shaft  large  pumping  engines  are  employed  that  frequently  force  the  water 
to  the  surface  from  depths  of  over  1,000  ft.  These  high-dutv  pumping  plants, 
when  near  the  shaft  and  operated  by  steam  with  a condenser,  frequently 
show  a verv  high  efficienev.  When  air  is  employed  to  operate  such  a plant 
a much  higher  efficienev  can  be  obtained  if  the  compressed  air  is  heated 
before  using  in  the  high-pressure  cylinder,  and  during  its  passage  from  the 
high-pressure  to  the  low-pressure  cylinder.  This  has  been  very  successfully 
accomplished  bv  means  of  a steam  reheater,  the  small  amount  of  steam 
necessarv  being  ‘conveyed  to  the  station  in  the  small  pipe,  and  entirely  con- 
densed in  the  reheater*  from  which  it  is  trapped  as  water.  . 

The  dutv  of  steam  pumps  is  approximately  as  follows:  For  small-sized 
steam  pumps,  the  steam  consumption  is  from  180  to  200  lb.  per  horsepower 
uer  hour  when  operating  in  the  workings  of  a mine  at  some  distance  from 
the  boiler.  For  larger  sizes  of  simple  steam  pumps,  the  consumption  runs 
from  SO  to  130  lb.  of  steam  per  horsepower  per  hour.  Compound-condensing 
numps,  such  as  are  commonly  used  as  station  pumps,  consume  from  40  to 
70  lb.  of  steam  per  horsepower  per  hour.  Tnple-expansion.  condensing, 
hi°h-class  pumping  engines  consume  from  24  to  26  lb.  per  hoi^epowerper 
hemr  The  Cornish  pump  consumes  varied  amounts  of  steam  in  proportion 
to  the  water  delivered,  depending  largely  on  the  friction  of  the  geanng 
bobs,  rods,  etc.,  but  its  efficiency  is  usually  considerably  below  the  best  class 

0f  CTonf  wTtfr1 Through  Valves,  Pipes  end  Pump 

through  the  valves  and  passages  of  a pump  should  not  exceed  ^A)  ft.  per 
minute  and  care  should  be  taken  to  see  that  the  passages  are  not  too 
abruntlV  deflected.  The  flow  of  water  through  the  discharge  pipe  should 
not  exceed  500  ft  per  minute,  but  for  single-cylindered  pumps  it  is  usually 
figured  Id between  250  and  400  ft.  per  minute.  In  the  case  of  very  large 
SSS  ^reafer velocities  maybe  allowed.  The  suction  pipe  for  the  pump 
Should  be  larger  than  the  discharge  pipe.  Ordinarily,  the  suction  pipe  for  a 
D^ns^uld  not  exceed  250  ft.  in  length,  and  should  not  contain  more  than 
two  elbows.  The  following  formula  gives  the  diameter  of  the  suction  and 

discharge  pipes  of  a pump: 

G = U.  S.  gallons  per  minute;  _ 

d'  = diameter  of  suction  pipe  in  inches: 

d"=  diameter  of  discharge  pipe  in  inches; 

I G 

d'  = -4.95^^; 

<*"=  495\'-^-  . . . 

= velocity  of  water  in  feet  per  minute  in  the  suction  pipe  - from 

50  v"  to  75 

v"  = velocity  of  water  in  feet  per  minute  in  the  discharge  pipe. 


RATIO  OF  STEAM  AND  WATER  CYLINDERS  IN  A 
DIRECT-ACTING  PUMP. 

A = area  of  steam  cylinder; 

D = diameter  of  steam  cylinder: 

P = steam  pressure  in  pounds  per 

p = pressure  per’ square  inch,  corresponding  to  the  head  H 
**  ^ wnrk  done  in  nump  cylinder 


H = head  of  water  = 2.309  p; 
a = area  of  pump  cylinder; 
d = diameter  of  pump  cylinder; 

.433  H\ 


E = 

A = 

a = 


pressure  per  squar. 

efficiency  of  pump  — work  done  in  steam  cylinder 
ap 


D = d 


EP ’ 
EAP . 

P 

I P . 


D 


P = 


P = 


iE  P 

M~V' 

op. 
EA’ 
EAP . 

a 


JL_ 

EP 


.433  H 

EP  ’ 


H=  2.309  E P X — 


CAPACITY  AND  HORSEPOWER  OF  PUMPS. 


161 


If  E = 75 $,  then  H = 1.732  PX^. 

E is  commonly  taken  at  from  .7  to  .8  for  ordinary  direct-acting  pumps. 
For  the  highest  class  of  pumping  engines  it  may  amount  to  .9.  The  steam 
pressure  P is  the  mean  effective  pressure,  according  to  the  indicator  dia- 
gram; the  pressure  p is  the  mean  total  pressure  acting  on  the  pump  plunger 
or  piston,  including  the  suction,  as  would  be  shown  by  the  indicator  dia- 
gram of  the  water  cylinder.  The  pressure  on  the  pump  cylinder  is  frequently 
much  greater  than  that  due  to  the  height  of  the  lift,  on  account  of  the 
friction  in  the  valves  and  passages,  which  increases  rapidly  with  the  velocity 
of  the  flow.  . . 

Piston  Speed  of  Pumps.— For  small  pumps,  it  is  customary  to  assume  a 
speed  of  100  ft.  per  minute,  but,  in  the  case  of  very  small  short-stroke  pumps, 
this  is  too  high,  owing  to  the  fact  that  the  rapid  reverses  make  the  flow 
through  the  valves  and  change  in  the  direction  of  the  current  too  frequent. 
When  the  stroke  of  the  pump  is  somewhat  longer  (18  in.  or  more),  higher 
speeds  can  be  employed,  and  in  the  case  of  large  pumping  engines  having 
long  strokes,  speeds  of  as  much  as  200  to  250  ft.  per  minute  are  successfully 
used  without  jar  or  hammer. 

Boiler  Feed-Pumps.— In  practice,  it  has  been  shown  that  a piston  speed 
greater  than  100  ft.  per  minute  results  in  excessive  wear  and  tear  on  a 
boiler  feed-pump,  especially  when  the  water  is  warm.  This  is  due  to  the 
fact  that  vapor  forms  in  the'  cvlinderst  and  results  in  a water  hammer.  In 
determining  the  proper  size  of  a pump  for  feeding  a steam  boiler,  not  only 
the  steam  employed  in  running  the  engine,  but  that  necessary  for  the 
pumps,  heating  system,  etc.  must  be  taken  into  consideration. 


THEORETICAL  CAPACITY  OF  PUMPS  AND  THE  HORSEPOWER 
REQUIRED  TO  RAISE  WATER. 


Q 

G 

G> 

d 

l 

N 

v 

W 

P 

£ 


Let  Q = cubic  feet  of  water  per  minute; 

= U.  S.  gallons  per  minute; 

= U.  S.  gallons  per  hour; 

= diameter  of  cylinder  in  inches; 

= stroke  of  piston  in  inches; 

= number  single  strokes  per  minute; 

= speed  of  piston  in  feet  per  minute; 

==  weight  moved  in  pounds  per  minute; 

= pressure  in  pounds  per  square  feet  = 62.5  X H; 

= pressure  in  pounds  per  square  inch  = .433  X H • 

= height  of  lift  in  feet; 

H.  P.  = horsepower. 

Then,  Q = \ ■ ^ ~ = .0004545  Nd- 1. 

O = "■  = .0034  Nd- 1.  G>  = .204  Nd"- 1. 

The  diameter  of  piston  required  for  a given  capacity  per  minute  will  be 

d = 46-9Vj n = 17'15\fe ord  - 13-54V*  = 4-95Vf- 

The  actual  capacity  of  a pump  will  vary  from  60$  to  95$  of  the  theoretical 
capacity,  depending  on  the  tightness  of  the  piston,  valves,  suction  pipe,  etc. 

QP  QHX  144  X .433  = QH  = Gp 
33,000  33,000  529.2  1,714.5* 

The  actual  horsepower  required  will  be  considerably  greater  than  the 
theoretical,  on  account  of  the  friction  in  the  pump;  hence,  at  least  20$  should 
be  added  to  the  power  for  friction  and  usually  about  50$  more  is  added  to 
cover  leaks,  etc.,  so  that  the  actual  horsepower  required  by  the  pump  is 
about  70$  more  than  the  theoretical. 

Example  1.— If  it  is  desired  to  find  the  size  of  a pump  that  will  throw 
30  gal.  of  water  per  minute  up  125  ft.,  from  the  bottom  of  a pit  or  prospect 
shaft  to  the  station  pump  at  the  main  shaft,  it  may  be  accomplished  as 
follows: 

An  allowance  of  probably  25$  should  be  made  with  a small  pump  of  this 
character,  to  overcome  slippage  or  leaking  through  the  valves,  past  the  piston, 


162 


PUMP  MACHINERY. 


etc  and  hence  we  will  call  the  total  amount  of  water  to  he  handled  40  gal 
ner  mfnute?  The  formula  for  the  diameter  of  piston  is 

F G 

d = 4.95  yj-. 

Assuming  that  v = 100  ft.  per  minute,  we  have 

d = 4.95]/  .4  = 4.95  X .63  = 3.13. 

Tn  -nractice  a 31"  pump  would  probably  be  employed. 

Fx?mple  2 -If  it  is  desired  to  find  the  approximate  horsepower  necessary 
to  THtwSl /per  minute  in  the  above  example,  without  determimng  the  size 
of  the  pump,  it  can  be  done  as  follows: 

w p __  Q X P = 30  X -433  X 125  __  ^ or  practiCally  1 H.  P. 

H,P,~  1,714.5  1,714-5 

Tn  order  to  cover  leakage  through  valves,  friction,  etc.,  an  addition  of  at 
leas?  ^^should°ber  nmde  to  a very"  small  pump  like  this,  and  so  we  would 

co“  Auction  —Theoretically,  a perfect  pump  will  raise  water  to  a 
, Pepthf  f ^bucnon  ^ sea level;  but,  owing  to  the  fact  that  a perfect 

ti^Son  it  is  never 'possible  to  reach  this  theoretical  limit,  and,  in  practice, 
wlfe^tKter il°coWW  Wa“ ter wlter“ 

pn£F£ir«eodr  ai 

with  a clack  valve  in  the  plunger,  the  amount  lifted  may  actually  exceed 

more  water  through  the  valve  than  would  pass  through  it  on  account  of  the 
^ce  passed  through  This  increases  as  the  speed  or  number  of  strokes 

inc|“ v»lves.-As  a rule,  a large  number  of  small  valveshaving  a compar- 
ativelvsmall  opening  are  preferable  to  a small  number  of  large  valves  with 
a Jreatironening  and  most  modern  pumps  are  built  upon  these  lines.  A 
small  valveP represents  a proportionately  larger  surface  of  discharge  with  the 
same  lift  than  the  large  valve,  hence  whatever  the  total  area  o[  the  \ah  e 
onening  its  full  contents  can  be  discharged  with  less  lilt  througn 
numerous  s&all  valves  than  through  one  large  valve.  Cornish  pumps 

gelpower'V Pumps  —Where  comparatively  small  amounts  of  water  are  to  be 
handfed,  andPpower  is  available,  belt-driven  power  pumps  are  very  much 

"‘'Eleohic^y  DHven^e^P^s^bere  water  is  to  be  delivered  from 
isolated  wordings  to  the  sumps  for  the  large  station  pumps,  electrically 
driven  power  pumps  are  far  more  efficient  than  steam  pumps.  In  some 
cases  It  Fs°mobSy  best  to  equip  the  entire  mine  with  electnc  pumps  both 
?n  the  isolated  workings  and  at  the  stations,  on  account  of  the  fact  that  they 
can^e^rivenl^0^  high-class  compound-condensing  ^n^^e  °n  the  ^irface, 
directly  connected  to  a generator,  and  furnishing  electricity  through  con- 

^UTheSf^al1efflciency?fIa^series  of  small,  electric  pumps  that  aggregate  a 
sufficient  amount  of  power  to  enable  this  arrangement  to  be  used,  is  very 
sufficient  amount  y efficiencv  of  a number  of  small  isolated  steam  or 

ra^uresfe^-ai^  wmps^SroducedClntoa  the  workings.  With  compound- 
condensing  engines  upon  the  surface,  operating  electric  pumps  underground 
?he  st^amconsumption  per  pump  horsepower  per  hour  for  the  smaller 
2“  e would  onlvbe  about  40  lb.  per  horsepower  per  hour;  for  medium-sized 
electric° pump?,  about  30  lb.  of  steam  per  hour,  and  larger  sizes  from  20  to 
30  lb.  per  horsepower  per  hour.  It  will  be  seen  from  these  figures  that  for 


PUMP  AND  WATER  MEMORANDA, 


163 


pumping  from  isolated  portions  of  the  mine  the  electric  pump  is  much  more 
efficient  than  the  steam  pump,  and  owing  to  the  fact  that  the  current  can 
frequently  be  obtained  from  the  lines  operating  the  underground  haulage 
system,  furnishing  light,  etc.,  it  is  evident  that  this  system  of  pumping  has 
a great  future  before  it  in  connection  with  mining. 

The  following  table  gives  the  gallons  per  minute  delivered  from  various 
sized  pumps  operating  at  different  piston  speeds: 

Pump  and  Water  Memoranda. 


Gallons  per  Minute  Delivered  at  Indicated  Piston  Speeds. 

500 

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400 

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350 

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300 

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275 

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175 

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150 

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125 

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001 

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HHHHHHHHHM 

Contents  for 
1 Ft.  Length 

Gallons. 

OOCMCMQOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 
O CO  IH  OI  © 05  tP  05  lO  H GO  lO  CM  © GO  IH  CO  lO  iO  »0  CO  Ih  GCt  O H O OOOOOOOOO 
HcOCDiOCMcOCMC50HHOOOOOC5COO>NH05f005NGOOHH020(NCOeOH(NO 
OHCocoo^t^05Ncoo5cocoo^qMcoMoq^qqHoo^HH^qqHiocoiO 

* * ’ ' rH  rH  rH  rH  CM  CM  CM*  CO  CO  H3  H3  H3  lO  lO  CO  CO  IH  IH  00  05  05  © rH  rH  CM*  CO  CO  H3  lO  CO  CO 

THrHrHrHrHrHrHrHrHCM 

Cubic 

Feet. 

8Ss!eS®SeSs!3SaS383SSS88gg8S88SRg8S8a 

OCM'HQ0C005C0C0OHtH05'H05'HOC0CMG0i0CM05C0TtrCMrH05G0lHtHCCC0C0lHG0'H 

OOOOHHWCMCOCOM'T^iO®qi>l>OOqqpH(NCOMrjJiqqi>OOqpHH 

rH  rH  rH  rH  rH  rH  rH  rH  rH  tH  rH  CM  CM  CO 

Area. 
Sq.  In. 

.7854 

3.1416 

7.0686 

12.5660 

19.6350 

28.2740 

33.1830 

33.4850 

44.1790 

50.2650 

56.7450 

63.6170 

70.8820 

78.5400 

86.5900 

95.0330 

103.8700 

113.1000 

122.7200 

132.7300 

143.1400 

153.9400 

165.1300 

176.7100 

188.6900 

201.0600 

213.8200 

226.9800 

240.5300 
254.4700 
268.8000 

283.5300 
298.6500 
314.1600 
452.3900 

| japmi^o 
j jaioureia 

^ ^ i v Hst^;  Her^:  -Isrt;  Her^  Hcr^;  He>t;  2|cr^  Hsr^  v 

^ i;  ^ ^ i ^ — iloiir  -le.5-  -taOOHH(M(NCOCOH'ctMOlCCOCDNHOOX05C50H 

HCMM^iC)CDCOIh1HOOG005C5HHHHHHHHHHHHHHHHHHHHCMN 

1 gal.  = 231  cu.  in.  = .13368  cu.  ft.  1 gal.  of  water  at  39.2°  = 8.33888  lb. 
1 cu.  ft.  of  water  = 7.48052  gal.,  and  weighs  62.423  lb. 


164 


PUMP  MA  C II IS  EE  Y. 


MISCELLANEOUS  FORMS  OF  WATER  ELEVATORS. 

Jet  Pump. — In  this  form,  the  energy  of  the  jet  of  water  is  utilized  for 
raising  a larger  volume  through  a small  distance,  or  a mixture  of  w ater  a 
solid  material  through  a short  distance. 

Vacuum  Pump.—' The  pulsometer,  which  is  the  most  important  representa- 
tive of  this  class,  consists  of  two  chambers  in  a large  casting, with  smtable 
automatic  valves  arranged  at  the  top  and  bottom  of  the  chambers,  ^eain  is 
fnttcS into o^of the  chambers,  then  the  valve  at  the  top  closed.  This 
steam  will  condense,  forming  a vacuum  that  draws  tv  ater  from  the  suction 
into^th”  chamber,  when  tie  chamber  is  filled  with  water,  steam  is  again 
introduced  and  forces  the  water  out  through  the  discharge  pipe.  The 
oneratioTis  then  repeated,  more  water  being  drawn  in  by  the  condensation 

thp  steam  The  two  chambers  work  alternately,  one  being  engaged  m 
driving  wSer  in  while  the  other  forces  it  out.  The  total  steam  efeciency 
of  this  form  of  pump  is  small,  though  it  may  actually  be  abo\e  that  of  -ma 
steam  nummseumloyed  in  isolated  portions  of  a mine.  The  advantages  are 
that  th^ ^pSLp  Assesses  no  intricate  mechanism,no  reciprocating , parts, 
reauires  no  lubrication,  and  is  not  injured  by  gntty  or  acid  materials.  On 
this  account  it  may  be  emploved  for  pumping  water  in  concentration  lvork s, 
coal-washing  plants,  and  similar  places  where  the  water  is  liable  to  contain 

gntA i r-Lift^P u m p s.  — By  introducing  compressed  air  at 
submerged  in  anv  liquid,  the  air  in  the  pipe  rises  as  bubbles, 
the^iecific  gravity  of  the  fluid  in  the  pipe.  This  causes  the  fluid  m the  pipe 
to  rise  above  the'  level  of  that  surrounding  the  pipe.  The  difference  m 
soecific  gravitv  can  never  be  great,  and  hence  the  fluid  can  never  be 
llevated  to  anv  considerable  height  withput  having  the  lower  endunmersed 
to  a correspondingly^  great  depth.  On  this  account  it  is  frequently  necessary 
to  drill  a well  considerably  below  the  water-bearing  strata,  so  as  to  obtain 
the  proper  ratio  between  the  submerged  portion  of  the  pipe 
to  which  the  water  is  to  be  lifted.  Some  advantages  of  this  form  of  pump 
are  that  there  are  no  moving  parts,  no  lubrication  is  required,  and  gntty 
material  does  not  interfere  with  the  operation.  If  the  pump  is  constructed 
of  suitable  material,  it  may  be  employed  for  handling  acids  or  solutions  in 
electrolvtic  or  chemical  works.  This  style  of  pump  is  also  quite  extensiy  ely 
employed  fo? pumping  water  from  Artesian  wells.  It  has  not  been  successful 
as  a mine  pump,  owing  to  the  ratio  between  the  part  immersed  and  the  lift. 

Centrifugal  Pumps.-The  height  of  lift  depends  on  the  tangential  velocity 
of  the  revolving  disk  of  pump  and  the  quantity  of  water  discharged,  and  is 
proportional  to  the  area  of  the  discharge  orifices  at  the  circumference  of  the 
disk  The  most  efficient  total  lift  for  the  centrifugal  pump  is.  approximately , 
17  ft'  and  for  small  lifts  the  centrifugal  pump  is  much  more  efficient  than 
anv  stvle  of  piston  pump.  For  a given  lift,  the  total  efficiency  of  a centrif- 
ugal pump  increases  with  the  size  of  the  pump.  Centrifugal  pumps  are 
always  designated  bv  the  size  of  their  outlet,  as.  for  instance,  a 2"  or  4 pump 
meaning  with  a 2"' or  4"  discharge  pipe.  Centrifugal  pumps  are  not  at 
all  effective  for  dealing  with  great  heads,  and  hence  have  never  come 
into  competition  with  piston  pumps  for  this  class  of  work.  For  lifting 
large  volumes  of  water  against  a low  head,  as  in  irrigation  or  drainage 

problems,  they  are  remarkably  efficient.  Under  th^m(^ ' ■^hait  is" 

stances  the  efficiency  of  the  centrifugal  pump  may  be  practically  /(K.  that  is, 
the^ pump  ^ma/v  do  an  amount  of  work  upon  the  water  that  is  theoretically 
equal  to  7(K  of  the  power  furnished  to  the  pump,  Pumping  engines  work- 
ing against  high  heads,  and  operated  by  the  most  improved  class  of  engines, 
may  attain  an  efficiency  of  practically  85ft. 

Centrifueal  Pump  as  a Dredge.— When  dredging  is  done  by  means  of  centrif- 
ugal pumps,  a greater  amount  of  power  is  necessary,  and  the  pump 
be  run  at  a greater  speed  than  when  pumping  water,  owing  to  the i fact ; that 
the  fluid  being  handled  has  a greater  density  than  water  When  dealing 
with  fine  sand,  as  much  as  50 ft  of  the  bulk  of  the  material  handled  may  be 
sand,  though,  as  a rule,  the  amount  of  solid  material  m the  water  dredged 
only  runs  from  30#  to  35#  of  the  total.  n , . 

Water  Buckets.— Where  only  a limited  amount  of  water  collects  m the 
mine  workings  it  is  frequentlv  removed  by  means  of  a special  water  bucket 
^r  ^ater  ca?  during  the  houre  that  the  hoisting  engine  would  otherwise  be 
i^e  Where  very  large  amounts  of  water  are  to  be  removed,  it  has  also 


SINKING  PUMPS. 


165 


been  found  economical  to  remove  them  by  means  of  special  water  buckets. 
This  is  especially  true  in  the  case  of  deep  shafts. 

One  of  the  best  illustrations  of  this  class  of  work  is  the  Gilberton  water 
shaft,  which  has  been  equipped  at  the  Gilberton  Colliery  of  the  Phila- 
delphia and  Reading  Coal  & Iron  Co.  The  collieries  draining  to  this  shaft 
require  the  removal  of  6,000,000  gal.  of  water  per  24  hours  during  the  wet 
season,  and  this  has  to  be  lifted  from  a depth  of  1,100  ft.  In  order  to  accom- 
plish the  work  by  means  of  steam  pumps,  it  required  a number  of  pump 
stations  in  different  parts  of  the  mine,  each  of  which  had  to  be  attended  by 
a pumpman,  and  a large  number  of  steam  lines  were  required  in  the  mine. 
In  order  to  remove  the  danger  of  fire  caused  by  these  steam  lines,  and  to 
dispense  with  the  large  amount  of  labor  otherwise  necessary,  it  was  decided  to 
hoist  the  water,  and  a shaft  22  ft.  x 26  ft.  8 in.  outside  of  timbers,  was  sunk. 
This  shaft  contains  two  compartments  7 ft.  X 7 ft.,  in  which  the  water 
buckets  are  operated,  and  two  compartments  7 ft.  X 11  ft.  8 in.  that  are 
utilized  for  cages  to  lower  men,  timber,  and  other  supplies.  The  water 
tanks  employed  in  the  special  water  compartments  are  5 ft.  6 in.  in  diameter, 
and  14  ft.  long.  They  are  provided  with  a special  device  sliding  on  regular 
cage  guides,  and  empty  themselves  automatically  at  the  surface  by  means 
of  a trip  or  sliding  valve.  Two  pairs  of  direct-acting  hoisting  engines,  with 
45"  X 60"  cylinders,  operating  drums  14  ft.  8 in.  in  diameter  by  15.  ft.  face, 
are  employed.  These  operate  the  water  buckets  in  cages  by  means  of  2" 
crucible  steel  ropes,  at  50  revolutions  per  minute,  which  is  equivalent  to  a 
piston  speed  of  500  ft.  per  minute.  The  drums  will  hoist  two  tanks  of  2,400 
gal.  per  minute.  This  gives  an  output  of  7,000,000  gal.  per  24  hours.  By 
slightly  increasing  the  speed  of  the  engine  this  amount  can  be  increased  10#, 
which  is  25#  in  excess  of  the  calculated  maximum  demand  on  the  shaft. 
The  cages  in  the  cage  compartments  are  so  arranged  that  they  can  be  discon- 
nected, and  water  buckets  substituted  for  them.  This  would  be  a total 
output  of  over  14,000,000  gal.  per  24  hours  at  the  normal  speed  of  the 
engine.  One  great  advantage  of  this  style  of  pumping  plant  is  that  there  is 
absolutely  no  fear  of  drowning  the  pumps. 

Some  years  ago  the  Hamilton  iron  mine,  in  Michigan,  was  drowned  by 
a sudden  inrush  of  water  that  drove  the  pumpmen  from  the  pumps.  In 
order  to  remove  this  large  volume  of  water,  special  bailing  buckets  were 
substituted  for  the  ordinary  mine  skips.  These  bailing  buckets  ran  on  the 
inclined  skip  road,  and  un watered  the  mine  in  a remarkably  short  time. 

Sinking  Pumps.— Sinking  pumps  may  be  either  single  or  duplex  in  their 
action,  and  may  be  inside  or  outside  packed.  Outside-packed  single-acting 
pumps  are  in  many  ways  preferable,  owing  to  the  fact  that  they  are  less 
liable  to  get  out  of  order.  One  requisite  of  any  sinking  pump  is  that  it  should 
have  as  few  exposed  parts  as  possible,  and  that  these  parts  should  be  so  placed 
that  they  will  be  protected  from  injury  by  blasting  to  as  great  an  extent  as 
possible.  Sinking  pumps  are  usually  provided  with  a telescopic  section  in  the 
suction  pipe,  and  sometimes  also  in  the  discharge  pipe,  so  that  they  can  be 
moved  down  several  feet  without  having  to  break  the  joints  of  the  piping. 

Pumps  for  Acid  Waters.— Where  mine  waters  are  acid  in  their  nature,  brass 
or  brass-lined  pumps  are  usually  employed, 
and  in  some  cases  even  wooden  pumps 
have  been  used,  as,  for  instance,  in  the 
Swedish  copper  mines,  though  this  prac- 
tice is  disappearing  in  favor  of  the  use  of 
brass  or  copper  linings.  The  pipes  for  such 
pumps  should  be  of  brass  or  copper  tubing, 
or  should  be  lined  with  some  substance 
that  will  not  be  affected  by  the  acid  of  the 
water.  Sometimes  wooden  linings  are  em- 
ployed, placed  as  shown  in  Figs.  21  and  22, 

Fig.  21  being  a section  of  the  pipe  with  the 
lining  complete,  and  Fig.  22  a cross-section 
of  one  of  the  individual  boards  used  in  the 
lining.  These  are  usually  made  of  pine 
about  | in.  thick,  and  are  grooved  on  each 
end  as  shown.  They  are  sprung  in  so  as  to  complete  a circle  on  the  inside 
of  the  pipe,  and  then  long,  thin,  wooden  keys  driven  into  the  grooves. 
When  the  water  is  allowed  to  go  into  the  pipes,  the  linings  swell  and  make 
all  joints  perfectly  tight.  Elbows  and  other  crooked  sections  are  lined  with 
sheet  lead  beaten  in  with  a mallet, 


Fig.  21. 


166 


FUELS. 


FUELS. 


The  value  of  any  fuel  is  measured  by  the  number  of  heat  units  that  its 
combustion  will  generate,  a unit  of  heat  being  the  amount  required  to  heat 
1 lb  of  water  1°  F.  The  fuels  used  in  generating  steam  are  composed  mainly 
of  carbon  and  hydrogen,  ash,  and  moisture,  with  sometimes  small  quantities 
of  other  substances  not  materially  affecting  their  value. 

Combustible  is  that  portion  which  will  burn;  the  ash  or  residue  vanes 
from  2$  to  36$  in  different  fuels.  , , 

The  following  table  gives,  for  the  more  common  combustibles,  the.  air 
reauired  for  complete  combustion,  the  temperature  with  different  proportions 
of  air  the  theoretical  value,  and  the  highest  attainable  value  under  a steam 
boiler  assuming  that  the  gases  pass  off  at  320°,  the  temperature  of  steam  at 
75  lb  pressure,  and  the  incoming  draft  to  be  at  60°;  also  that  with  chimney 
draft  twice  and  with  blast  only  the  theoretical  amount  of  air  is  required  for 
combustion. 

Table  of  Combustibles. 


Kind  of 
Combustible. 


ft  3 
< & 


oft 
ft  ft 

t- 1 3 

|I 

o o 
ft 


Temperature  of 
Combustion. 


i Highest 

Theoretical  Attainable 


;ite....  J 


Hydrogen  .... 

Petroleum . .. 

( Charcoal 
Carbon  -<  Coke 

(Anthracite 
Coal,  Cumberland, 

Coal,  Coking  bituminous 

Coal,  Cannel 

Coal,  Lignite 

Peat,  Kiln  dried 

Peat,  Air  dried,  25$  water 

Wood,  Kiln  dried 

Wood,  Air  dried, 20$  water 


36.00  5,750 
15.43  5,050 

| 

12.13,4,580 


. 

O Sh 

S3 

So 

ft  >> 
^ ft 

ft  ft 
ft  3 


© . 

0”-\ 

©<1 

in  . 

© >> 

3ft 

ft^ 
73  o 


3,860 

3,515 

3,215 


aj  f-i 

ft 

©v* 

- <X>  r— ; 

O ft 


© t-' 

ft- 
© O 

3ft 

ft  ft 
^ ft 
© 3 


ft  o 
^O 


2.8601,940 

2,710;1,850 


Value. 


3®© 

f-l  'ft  Q 

Sb 

c3  CO 

■SSS 

CO  Q.  O 

•So  « 

f 


62,032 

21,000 


2,440  1,650  14,500 


12.06,4,900  3,360 
11.73  5,140  3,520 
11.80  4,850  3,330 
9.30  4,600  3,210 
7.6814,47013,140 
5.76  4,000  2,820 
6.00  4,08012,910 
4.80  3, 700 ; 2, 607 1 2, 100 j 1 ,490 


2,550|l,730 
2,680,1,810 
2,5401,720 
2,490:1,670 
2,4201,660 
2,2401,550 
2,260;  1,530 


c5  0 © 

ft^ft 

■ga 

o 

o 

^ C l— t 

£|£rH 

°ft  ft 

,dftft 

- © > 


u C 
© o3 


64.20 

21.74 

15.00 


Value  Un- 
der Boiler. 


o3 

Ut 

ft 

© 

a 

3 

ft 

o 

ft 


15,370  15.90 
15,837  16.00 
15,080  15.60 
11,745!  12.15 


9,660 
7,000 
7,245 
5,600 | 


10.00 

7.25 

7.50 

5.80 


18.55 

13.30 

14.28 

14.45 

14.01 

10.78 

8.92 

6.41 

6.64 

4.08 


19.90 

14.14 

15.06 

15.19 

14.76 

11.46 

9.42 

6.78 

7.02 

4.39 


The  effective  value  of  all  kinds  of  wood  per  pound  when  dry,  is  substan- 
tially the  same.  This  is  usually  estimated  at  .4,  the  value  of  the  same  weight 
of  coal.  The  following  are  the  weights  and  comparative  values  of  different 
woods  by  the  cord:  


Wood. 


Hickory  (shell  bark) 
Hickory  (red  heart) 

White  oak 

Red  oak.. 

Spruce 

New  Jersey  pine 


Weight. 


4,469 

3,705 

3,821 

3,254 

2,325 

2.137 


Wood. 


Beech 

Hard  maple.... 
Southern  pine. 
Virginia  pine . 
Yellow  i>ine.. ... 
White  pine 


Weight. 


3,126 

2,878 

3,375 

2,680 

1,904 

1,868 


SLACK. 


167 


Much  is  said  nowadays  about  the  wonderful  saving  that  is  to  be  expected 
from  the  use  of  petroleum  for  fuel.  This  is  all  a myth,  and  a moment’s 
attention  to  facts  is  sufficient  to  convince  any  one  that  no  such  possibility 
exists.  Petroleum  has  a heating  capacity,  when  fully  burned,  equal  to  from 
21,000  to  22,000  B.  T.  U.  per  lb.,  or,  say,  50$  more  than  coal.  But,  owing  to 
the  ability  to  burn  it  with  less  losses,  it  has  been  found,  through  extended 
experiments  by  the  pipe  lines,  that  under  the  same  boilers,  and  doing  the 
same  work,  1 lb.  of  petroleum  is  equal  to  1.8  lb.  of  coal.  The  experiments  on 
locomotives  in  Russia  have  shown  practically  the  same  value,  or  1.77.  Now, 
a gallon  of  petroleum  weighs  6.7  lb.  (though  the  standard  buying  and  selling 
weight  is  6.5  lb.),  and  therefore  an  actual  gallon  of  petroleum  is  equivalent 
under  a boiler  to  12  lb.  of  coal,  and  190  standard  gallons  are  equal  to  a gross 
ton  of  coal.  It  is  very  easy  with  these  data  to  determine  the  relative  cost. 
At  the  wells,  if  the  oil  is  worth,  say,  2 cents  a gallon,  the  cost  is  equivalent 
to  $3.80  per  ton  for  coal  at  the  same  place,  while  at,  say,  3 cents  per  gallon, 
the  lowest  price  at  which  it  can  be  delivered  in  the  vicinity  of  New  York,  it 
costs  the  same  as  coal  at  $5.70  per  ton.  The  Standard  Oil  Company  estimates 
that  173  gal.  are  equal  to  a gross  ton  of  coal,  allowing  for  incidental  savings, 
as  in  grate  bars,  carting  ashes,  attendance,  etc. 

Sawdust  can  be  utilized  for  fuel  to  good  advantage  by  a special  furnace 
and  automatic  feeding  devices.  Spent  tan  bark  is  also  used,  mixed  with 
some  coal,  or  it  may  be  burned  without  the  coal  in  a proper  furnace.  Its 
value  is  about  one-fourth  that  of  the  same  weight  of  wood  as  it  comes  from 
the  press,  but,  when  dried,  its  value  is  about  85$  of  the  same  weight  of  wood 
in  same  state  of  dryness. 

It  has  been  estimated  that,  on  an  average,  1 lb.  of  coal  is  equal,  for  steam- 
making purposes,  to  2 lb.  dry  peat,  2}  to  2\  lb.  dry  wood,  2\  to  3 lb.  dried  tan 
bark,  2f  to  3 lb.  cotton  fetalks,  3i  to  3£  lb.  wheat  or  barley  straw,  and  6 to  8 lb. 
wet  tan  bark. 

Natural  gas  varies  in  quality,  but  it  is  usually  worth  2 to  2£  times  the  same 
weight  of  coal,  or  about  30,000  cu.  ft.  are  equal  to  a ton  of  coal. 

Slack,  or  the  screenings  from  coal,  when  properly  mixed— anthracite  and 
bituminous— and  burned  by  means  of  a blower  on  a grate  adapted  to  it,  is 
nearly  equal  in  combustible  value  to  coal,  but  its  percentage  of  refuse  is 
greater. 

The  accompanying  table  of  proximate  analyses  and  heating  values  of 
American  coals  was  compiled  by  Mr.  William  Kent,  for  the  1898  edition  of 
the  Babcock  & Wilcox  Co.’s  book,  “ Steam.”  The  analyses  are  selected 
from  various  sources,  and,  in  general,  are  averages  of  many  samples.  The 
heating  values  per  pound  of  combustible  are  either  obtained  from  direct 
calorimetric  determinations  or  calculated  from  ultimate  analyses,  except 
those  marked  (?),  which  are  estimated  from  the  heating  values  of  coals 
of  similar  composition.  The  figures  in  the  last  column  are  obtained#by 
dividing  the  figures  in  the  preceding  column  by  965.7,  the  number  of  heat 
units  required  to  evaporate  1 lb.  of  water  - at  212°  into  steam  of  the  same 
temperature. 

The  heating  values  per  pound  of  combustible  given  in  the  table,  except 
those  marked  (?),  are  probably  within  3$  of  the  average  actual  heating  values 
of  the  combustible  portion  of  the  coals  of  the  several  districts.  When  the 
percentage  of  moisture  and  ash  in  any  given  lot  of  coal  is  known,  the 
heating  value  per  pound  of  coal  may  be  found,  approximately,  by  multi- 
plying the  heating  value  per  pound  of  combustible  of  the  average  coal  of  the 
district  by  the  difference  between  100$  and  the  sum  of  the  percentages  of 
moisture  and  ash. 

The  heating  effect  is  calculated  on  the  basis  of  the  coal  burned  to  carbon 
dioxide  and  liquid  water  at  100°  C.,  and  is  stated  either  in  calories  per  kilo- 
gram or  English  heat  units  per  pound.  The  theoretical  evaporative  effect  is 
calculated  by  dividing  the  number  of  calories  per  kilogram  by  536,  or  the 
number  of  English  heat  units  per  pound  by  965.  In  either  case,  it  expresses 
the  theoretical  number  of  kilograms  or  pounds  of  water  converted  into  steam 
from  and  at  100°  C.,  by  1 kilogram  or  1 lb.  of  coal. 

A committee  of  the  Western  Society  of  Engineers,  of  Pittsburg,  report 
that  1 lb.  of  good  coal  = 7£  cu.  ft.  of  natural  gas.  When  burned  with  just 
enough  air,  its  temperature  of  combustion  is  4,200°  F.  The  Westinghouse 
Air  Brake  Co.  found  from  experiment  that  1 lb.  Youghiogheny  coal 
= 12£  cu.  ft.  natural  gas,  or  1,000  cu.  ft.  natural  gas  = 81.6  lb.  coal.  Indiana 
natural  gas  gives  1,000,000  B.  T.  U.  for  1,000  cu.  ft.  and  weighs  .045  lb.  per 
cu.  ft. 


168 


FUELS. 


Proximate  Analyses  and  Heating  Values  of  American  Coals. 


Coal. 


Anthracite. 
Northern  Coal  Field  . 
East  Middle  Coal  Field 
West  Middle  Coal  Field 
Southern  Coal  Field  . 

Semianthracite. 
Loyalsock  Field  . . 

Bernice  Basin  . . . 

Semibituminous. 
Broad  Top,  Pa.  . . . 

Clearfield  Co.,  Pa.  . . 

Cambria  Co.,  Pa.  . . 
Somerset  Co.,  Pa.  . . 
Cumberland,  Md.  . . 

Pocahontas,  Ya.  . . . 

New  River,  W.  Ya.  . 

Bituminous. 
Connellsville,  Pa.  . . 

Youghiogheny,  Pa.  . 
Pittsburg,  Pa.  . . . 

Jefferson  Co.,  Pa.  . . 


and  Ohio  .... 
Thacker,  W.  Va.  . . 

Jackson  Co.,  Ohio  . . 

Brier  Hill,  Ohio  . . 
Hocking  Valley,  Ohio  . 
Yanderpool,  Ky.  . . 
Muhlenberg  Co.,  Ky.  . 
Scott  Co.,  Tenn.  . . 

Jefferson  Co.,  Ala.  . . 

Big  Muddy,  111. . . • 

Mt.  Olive,  111 

Str^ator,  111 

Missouri  . . . . • • 

Lignite  and  Lignitic  Cot 

Iowa 

Wyoming 

Utah 

Oregon  lignite  . . . 


Moisture. 

Volatile  Matter. 

Fixed  Carbon. 

Ash. 

Sulphur. 

Heating  Value  per  Lb. 
Coal,  B.  T.  U. 

1 

Volatile  Matter  Per  Cent, 
of  Combustible. 

Fixed  Carbon. 

Per  Cent,  of  Combustible. 

Heating  Value  per  Lb. 
Combustible. 

1 Theoretical  Evaporation 

3.42 

4.38 

83.27 

8.20 

.73 

13,160 

5.00 

95.00 

14,900  1 

3.71 

3.08 

86.40 

6.22 

.58 

13,420 

3.44 

96.56 

14,900  1 

3.16 

3.72 

81.59 

10.65 

.50 

12,840 

4.36 

95.64 

14,900  1 

3.09 

4.28 

83.81 

8.18 

.64 

13,220 

4.85 

95.15 

14,900  1 

1.30 

8.10 

83.34 

6.23 

1.63 

13,920 

8.86 

91.14 

15,500  1 

.65 

9.40 

83.69 

5.34 

.91 

13,700 

10.98 

89.02 

15,500  1 

.79 

15.61 

77.30 

5.40 

.90 

14,820 

17.60 

82.40 

15,800  1 

.76 

22.52 

71.82 

3.99  ; 

.91 

14,950 

24.60 

75.40 

15,700  ] 

.94 

19.20 

71.12 

7.04 

1.70 

14,450 

22.71 

77.29 

15,700 

1.58 

16.42 

71.51 

8.62 

1.87 

14,200 

20.37 

79.63 

15,800  ’ 

1.09 

17.30 

73.12 

7.75 

.74 

14,400 

19.79 

80.21 

15,800 

1.00 

21.00 

74.39 

3.03 

.58 

15,070 

22.50 

77.50 

15,700 

.85 

17.88 

77.64 

3.36 

.27 

15,220 

18.95 

81.05 

15,800 

1.26 

30.12 

59.61 

8.23 

.78 

14,050 

34.03 

65.97 

15,300 

1.03 

36.50 

59.05 

2.61 

.81 

14,450 

38.73 

61.27 

15,000 

1.37 

35.90 

52.21 

8.02 

1.80 

13,410 

41.61 

58.39 

14,800 

1.21 

32.53 

60.99 

4.27 

1.00 

14,370 

35.47 

64.53 

15,200 

L.  1.81 

35.33 

53.70 

7.18 

1.98 

13,200 

40.27 

59.73 

14,500 

' 1.93 

35.90 

50.19 

9.10 

2.89 

13,170 

43.59 

56.41 

14,800  1 

1.38 

35.04 

56.03 

6.27 

1.28 

14,040 

39.33 

60.67 

15,200 

, 3.83 

32.07 

57.60 

6.50 

13,090 

35.76 

64.24 

14,600 

4.80 

34.60 

56.30 

4.30 

13,010 

38.20 

61.80 

14,300 

6.59 

34.97 

48.85 

8.00 

1.59 

12,130 

42.81 

57.19 

14,200 

4.00 

34.10 

54.60 

7.30 

12,770 

38.50 

61.50 

14.400 

4.33 

33.65 

55.50 

4.95 

1.57 

13,060 

38.86 

61.14 

' 14,400(?)  | 

1.26 

35.76 

53.14 

8.02 

1.80 

13,700 

34.17 

65.83 

1 15,100(?)  | 

1.55 

34.44 

59.77 

2.62 

1.42 

13,770 

37.63 

62.37 

14,400(?)  | 

7.50 

30.70 

53.80 

8.00 

12,420 

36.30 

63.70 

! 14,700 

. 11.00 

35.65 

37.10 

13.00 

10,490 

i 47.00 

53.00 

13,800 

12.00 

33.30 

40.70 

14.00 

10,580 

i 45.00 

55.00 

14,300 

. 6.44 

37.57 

47.94 

8.05 

12,230 

i 43.94 

56.06 

14,300(?) 

s. 

8.45 

37.09 

35.60 

18.86 

8,720 

) 51.03 

48.97 

! 12,000(?) 

8.19 

38.72 

41.83 

11.26 

10,390 

> 48.07 

51.93 

12,900(?) 

9.29 

41.97 

44.37 

3.20 

1 .18 

i 11,030 

) 48.60 

51.40 

1 ]2,600(?) 

. 15.25 

42.98 

33.32 

7.11 

1.6( 

5 8,540 

) 54.95 

45.05 

11,000(?) 

% I 


15.84 

15.53 

15.32 

15.74 

15.01 

15.32 

15.74 

15.11 


14.91 

14.91 

15.63 

14.91 

15.22 

14.29 

14.80 

14.80 

12.42 

13.35 

13.04 

11.39 


A British  therma  un  t (B.  T.  U.)  is  me  quantity  ui  neat  — v. 

temperature  ofl  lb.  of  water  1°  F.  at  or  near  the  temperature  of  maximum 
density,  89.1°  F.  _ , . , 

A calorie  is  the  quantity  of  heat  required  to  raise  the  temperature  of 
1 kilogram  of  water  1°  C.  at  or  about  4°  C. 

A pound  calorie  is  the  quantity  of  heat  necessary  to  raise  the  temperature 

of  1 lb.  of  water  1°  C.  . . . . . 

1 French  calorie  = 3.968  British  thermal  units. 

1 B T U.  = -252  calorie. 

lib.  calorie  = | B.  T.  U.  = .4536  calorie. 

The  heating  value  of  any  coal  may  be  calculated  from  its  ultimate 
analysis,  with  I probable  error  not  exceeding  by  Dulong  s formula: 

Heating  value  per  lb.  = 146  C + 620  ( H — — ^ , 
in  which  C ; H,  and  0 are,  respectively,  the  percentages  of  carbon,  hydrogen, 
and  oxygen. 


CLASSIFICATION  OF  COALS. 


169 


?>• 


in  which  C,  0,  H,  and  S represent  the  weights  of  carbon,  oxygen,  hydro- 
gen, and  sulphur  in  1 lb.  of  the  substance. 

Composition  of  Fuels. 

( Mechanical  Draft,  B.  F.  Sturtevant  Co.) 


Heat  in  pound  calorie  = 8,080  C + 34,462  (^H  — 
or  = 8,080  C + 34,462  ) + 2,250  S. 

T.  U.  — 14,650  C -f  62,100  (ll  — y ) 


Heat  in  B. 


Description. 

Carbon. 

Hydro- 

gen. 

Oxy- 

gen. 

Nitro- 

gen. 

Sul- 

phur. 

Ash. 

Anthracite. 

France  

90.9 

1.47 

1.53 

1.00 

.80 

4.3 

Wales  

91.7 

3.78 

1.30 

1.00 

.72 

1.5 

Rhode  Island  

85.0 

3.71 

2.39 

1.00 

.90 

7.0 

Pennsylvania 

78.6 

2.50 

1.70 

.80 

.40 

14.8 

Semibituminous. 

Maryland 

80.0 

5.00 

2.70 

1.10 

1.20 

8.3 

Wales 

88.3 

4.70 

.60 

1.40 

1.80 

3.2 

Bituminous. 

Pennsylvania 

75.5 

4.93 

12.35 

1.12 

1.10 

5.0 

Indiana 

69.7 

5.10 

19.17 

1.23 

1.30 

3.5 

Illinois  

61.4 

4.87 

35.42 

1.41 

1.20 

5.7 

Virginia 

57.0 

4.96 

26.44 

1.70 

1.50 

8.4 

Alabama  

53.2 

4.81 

32.37 

1.62 

1.30 

6.7 

Kentucky 

49.1 

4.95 

41.13 

1.70 

1.40 

7.2 

Cape  Breton 

67.2 

4.26 

20.16 

1.07 

1.21 

6.1 

Vancouver  Island 

66.9 

5.32 

8.76 

1.02 

2.20 

15.8 

Lancashire  gas  coal 

80.1 

5.50 

8.10 

2.10 

1.50 

2.7 

Boghead  cannel 

63.1 

8.90 

7.00 

.20 

1.00 

19.8 

Lignite. 

California  brown  

49.7 

3.78 

30.19 

1.00 

1.53 

13.8 

Australian  brown 

73.2 

4.71 

12.35 

1.11 

.63 

8.0 

Petroleum. 

Pennsvl vania  (crude) 

84.9 

13.70 

1.40 

Caucasian  (light)  

86.3 

13.60 

.10 

Caucasian  (heavy)  

86.6 

12.30 

1.10 

Refuse 

87.1 

11.70 

1.20 

CLASSIFICATION,  COM  POSITIO:  J,  AN  D PROPERTIES  OF  COALS. 

Coals  may  be  broadly  divided  into  two  classes:  Anthracite,  or  hard,  coal; 
and  bituminous,  or  soft,  coal. 

Anthracite,  or  Hard,  Coal.— Specific  gravity,  1.30  to  1.70.  This  is  the  densest, 
hardest,  and  most  lustrous  of  all  varieties.  It  burns  with  little  flame  and 
no  smoke,  but  gives  a great  heat.  Contains  very  little  volatile  combustible 
matter.  Color,  deep  black,  shining;  sometimes  iridescent.  Fracture, 
conchoidal. 

Semianthracite  coal  is  not  so  dense  nor  so  hard  as  the  true  anthracite. 
Its  percentage  of  volatile  combustible  matter  is  somewhat  greater,  and  it 
ignites  more  readily. 

Bituminous,  or  Soft,  Coal.— Specific  gravity,  1.25  to  1.40.  It  is  generally 
brittle;  has  a bright  pitchy  or  greasy  luster,  and  is  rather  fragile  as  compared 
with  anthracite.  It  burns  with  a yellow  smoky  flame,  and  gives,  on  distil- 
lation, hydrocarbon  oils  or  tar. 

Under  the  term  “bituminous”  are  included  a number  of  varieties  of  coal 
that  differ  materially  under  the  action  of  heat,  giving  rise  to  the  general 
classification:  Coking  or  caking  coals,  and  free-burning  coals. 

Semibituminous  coal  has  the  same  general  characteristics  as  the  bituminous, 
although  it  is  usually  not  so  hard,  and  its  fracture  is  more  cuboidal.  The 


170 


FUELS. 


nercentage  of  volatile  combustible  matter  is  less.  It  kindles  readily,  and 
burns  quickly  with  a steady  fire,  and  is  much  valued  as  a steam  coal. 

Coking  coals  are  those  that  become  pasty  or  semiviscid  in  the  fire,  and, 
when  heated  in  a close  vessel,  become  partially  fused  and  agglomerate  into  a 
mas? of ^coherent  coke.  This  property  of  coking  may,  however,  become 
Seatly  impaired,  if,  indeed,  not  entirely  destroyed,  by  weathering. 

Free-burning  coals  have  the  same  general  characteristics  as  the  cokm^ 
coals  but  they  burn  freely  without  softening,  and  do  not  fuse  or  cake 

t0Sslkl  o?arZaduUblacTcolor,  and  is  much  harder  and  less  frangible 
than  "he  coMng  coal.  It  is  readily  fissile,  like  slate,  but  breaks  with 
difficulty  on  cross-fracture.  It  ignites  less  readily,  but  makes  a hot  fire, 
constituting  a good  house  coal. 

Weights  and  Measurements  of  Coal. 

( Coxe  Bros.  & Co.,  Chicago , III.) 


Coal. 


Lehigh  lump 

Lehigh  cupola 

Lehigh  broken 

Lehigh  egg 

Lehigh  stove 

Lehigh  nut 

Lehigh  pea 

Lehigh  buckwheat... 
Lehigh  dust  


Weight  per 
Cubic  Foot. 
Pounds. 

Cubic  Feet 
per  Ton, 
2,000  Lb. 

55.26 

36.19 

55.52 

36.02 

56.85 

35.18 

57.74 

34.63 

58.15 

34.39 

58.26 

34.32 

53.18 

37.60 

54.04 

37.01 

57.25 

34.93 

Coal. 


Free-burning  egg... 
Free-burning  stove 
Free-burning  nut ... 

Pittsburg  

Illinois  ' - 

Connellsville  coke 

Hocking 

Indiana  block 

Erie 

Ohio  cannel 


*1.8 

US 

’S-Si 


A 2 


56.07 
56.33 
56.88 
46.48 
47.22 

26.30 

49.30 
43.85 

48.07 
49.18 


- . 

0^0 
f-i  o 
^ ®o 


35.67 

35.50 

35.16 

43.03 
42.35 

76.04 
40.56 

45.61 

41.61 
40.66 


Cannel  coal  differs  from  the  ordinary  bituminous  coal  in  its  texture.  It  is 
compact  with  little  or  no  luster  and  without  any  appearance  of  a banded 
structure.  It  breaks  with  a smooth  conchoidal  fracture,  kindles  readily,  and 
burns  with  a dense  smoky  flame.  It  is  rich  in  volatile  matter,  and  makes  an 
excellent  gas  coal.  Color,  dull  black  and  grayish  black. 

Uenffe  or  brown  coal,  often  has  a lamellar  or  woody  structure;  is  some- 
times pitch  black,  but  more  often  rather  dull  and  brownish  black.  It  kindles 
readily  and  burns  rather  freely  with  a yellow  flame  and  comparatively  little 
smoke  but  it  gives  only  a moderate  heat.  It  is  generally  non-coking.  The 
nercentage  of  moisture  present  is  invariably  high  from  10^  to  30/). 

The  subdivisions  given  above  are  entirely  arbitrary,  as  the  different 
varieties  of  coal  are  found  to  shade  insensibly  into  one  another.  The  follow- 
ing are  two  classifications  according  to  percentages  of  volatile  combustible 
matter:  „ 

Classification  of  Coal  According  to  Volatile  Combustible. 


Coal. 

Per  Cent. 

Kent. 
Per  Cent. 

2.5  to  6 

0 to  7 

An  till dci ic * 

7 to  10 

7.5  to  12 



12  to  20 

12.5  to  25 

oGiniulluiiLiiiuuo  

over  20 

25  to  50 

I)  1 LlIILLlllU  

over  50 

- 

_ . . 

The  ComDosition  of  Coals.-A  proximate  analysis  determines  tne  proport 
of  those  products  of  a coal  having  the  most  important  bearing  on  its  uses. 
Th^subsCces  as  usually  presented  are:  Moisture,  or  water,  volatile  com- 


PROPERTIES  OF  COALS . 


171 


bustible  matter,  fixed  carbon,  sulphur,  and  ash.  In  addition  to  these,  the 
following  physical  properties  are  generally  given:  Color  of  ash,  specific 
gravity,  and  strength  or  hardness.  The  determination  of  these  eight  factors 
gives  a fair  general  idea  of  the  adaptabilities  of  a coal. 

Moisture,  or  water,  in  coal,  has  no  fuel  value,  is  an  inert  constituent,  dug, 
handled,  and  hauled,  and  finally  expelled  at  a cost  of  fuel.  Each  per  cent, 
of  moisture  means  20  lb.  less  fuel  for  each  ton  of  coal. 

Volatile  combustible  matter  is  an  important  constituent  of  coal,  the  amount 
and  quality  deciding  whether  a coal  is  suitable  for  the  manufacture  of 
illuminating  gas.  The  coking  of  coal  also  is  largely  dependent  on  this 
constituent.  When  a large  percentage  of  volatile  combustible  matter  is 
present,  coals  ignite  easily  and  burn  with  a long  yellow  flame,  and,  in 
ordinary  combustion,  give  out  dense  smoke,  and  form  soot.  This  quality 
makes  a fuel  objectionable  for  railway  and  sometimes  for  naval  use. 

The  fixed  carbon  is  the  principal  combustible  constituent  in  coal,  and,  in 
bituminous  and  semibituminous  coals,  the  steaming  value  is  in  proportion  to 
the  percentage  of  fixed  carbon.  Though  the  fixed  carbon  of  a coal  evapo- 
rates much  less  water  than  an  equivalent  weight  of  the  volatile  combustible 
matter  when  properly  burnt,  in  practice,  so  much  of  the  latter  is  lost  through 
careless  firing,  or  improper  furnace  construction,  that  the  relative  steaming 
value  of  a coal  may  be  fairly  approximated  by  assuming  the  carbon  to  be 
the  only  useful  constituent. 

Sulphur  will  burn  and  develop  heat,  and  is  not  inert  like  moisture  and 
as}i.  But  it  corrodes  grates  and  boilers;  in  the  blast  furnace  it  injures  iron, 
and  produces  a hot  short  pig,  and  is  objectionable  in  coal  for  forge  use.  In 
gas  making,  the  sulphur  must  be  removed.  It  usually  occurs  in  coal  in  the 
form  of  iron  pyrites,  which,  oxidizing,  causes  disintegration,  and  sometimes 
spontaneous  combustion.  It  is  then  an  element  of  danger  and  loss. 

Ash  is  an  inert  constituent,  which  means  20  lb.  of  weight  to  be  handled 
and  20  lb.  loss  per  ton  of  coal  for  each  per  cent,  present.  Water  in  coal  is 
removed  at  the  cost  of  fuel,  while  ashes  are  removed  at  extra  cost  of  labor. 
It  is  estimated  that  if  the  cost  of  stoking  coal  is  6 f0  of  the  cost  of  coal  (coal 
at  $3.00  per  ton,  and  labor  at  $1.00  per  day),  and  with  cost  of  handling  ashes 
double  that  of  stoking  coal,  5$  of  ash  will  lessen  the  fuel  value  of  coal  over 
6$;  10 0 ash,  over  120;  and  so  on. 

The  color  of  the  ash  furnishes  a rough  estimate  of  the  amount  of  iron  con- 
tained in  a fuel.  Iron  in  an  ash  makes  it  more  fusible,  and  increases  its 
tendency  to  clinker.  In  domestic  consumption,  where  the  temperature  is 
low,  the  quantity  of  ash  is  of  more  importance  than  its  fusibility,  but  for 
steam  purposes,  where  an  excessive  heat  is  required,  ashes  of  a clinkering 
coal  will  fuse  into  a vitreous  mass  and  accumulate  upon  the  grate  bars  and 
exclude  the  passage  of  necessary  air.  The  practicability  of  employing  a coal 
will  often  be  determined  by  the  quality  of  the  clinkering  of  the  ashes. 
Under  such  conditions,  such  coals  are  best  whose  ashes  are  nearly  pure 
white  and  which  contain  little  or  no  alkali  nor  any  lime,  and  do  not  contain 
silica  and  alumina. 

The  specific  gravity  is  an  important  factor  when  there  is  restriction  of 
I space,  as  on  railway  cars  and  in  ship  bunkers.  A given  bulk  of  anthracite 
! coal  will  weigh  from  100  to  150  more  than  the  same  bulk  of  bituminous  coal, 
so  that  from  100  to  150  more  pounds  of  fuel  can  be  carried  in  the  same  place. 
The  average  specific  gravity  of  anthracite  coal  is  1.5,  and  a cubic  yard  weighs 
about  2,531  lb. 

The  average  specific  gravity  of  American  bituminous  coals,  and  of  grades 
intermediate  between  them  and  anthracite,  is  about  1.325,  and  1 cu.  yd. 
weighs  about  2,236  lb. 

Strength  or  hardness  is  valuable  in  preventing  waste.  In  soft  coal,  much  is 
ground  to  dust  in  mining  and  at  the  tipple.  In  railway  transportation,  soft 
coal  is  crushed,  which  further  increases  the  loss,  and  the  coal  reaches  market 
in  bad  condition.  A very  soft  coal  is  shipped  m lump,  and  is  not  in  so  wide 
demand.  For  marine  use,  a soft  coal  is  objectionable,  because  of  disintegra- 
tion by  the  motion  of  the  ship.  Strength  is  a requisite  for  the  use  of  raw 
coal  in  the  blast  furnace,  and  also  to  prevent  excessive  loss  of  coal  through 
the  grates  in  ordinary  furnaces. 

Steaming  Coals— For  steam  making,  the  superiority  of  coals  high  in  com- 
bustible constituents  is  admitted,  and  those  with  the  higher  percentage  of 
fixed  carbon  are  the  most  desirable.  But  the  consideration  of  the  steaming 
qualities  of  a coal  involves,  also,  a consideration  of  the  form  of  furnace  and 
of  all  the  conditions  of  combustion.  The  evaporative  power  of  a coal  in 


172 


FUELS. 


Dractice  cannot  be  stated  without  reference  to  the  conditions  of  combustion, 
and  every  practical  test  of  a coal,  to  be  thorough,  should  lead  to  ^determi- 
nation of  the  best  form  of  furnace  for  that  coal,  anu  slmuld  furnish  knowl- 
edge as  to  what  class  of  furnaces  in  actual  use  such  coal  is  specially  adapted. 

Tt  fs  not  sufficient  that  in  comparative  tests  of  coals  the  same  conditions 
should  ex?s?  w!?h  each,  but  there  should  also  be  determined  the  best 

co: Ofraals1 highain  fixed  carbon,  the  semianthracites  and  the  semibitumi- 
nous  rank  as  high  as  the  anthracites  in  meeting  the  various  requirements  of 

a ^Fo? railway  <use,t  these^co^ls'^ave  been  found  to  excel  anthracites  in 
evaporating  power.  The  comparative  absence,  m semibitummous  coals,  of 
smoke  which  means  loss  of  combustible  matter  as  well  as  discomfort  to  the 
traveler  is  sufficient  to  suggest  the  superiority  of  these  coals  over  bituminous 
coals  for  such  use  In  fact  the  high  rate  of  combustion  and  the  strong  drait 
necessary  ^n  locomotiv  e s is  particularly  unfavorable  to  the  economic  com- 
hnstTon  of  bituminous  coal.  Such  semibitummous  coals  are  also  specially 
well suited ^for^mall  tubular  boilers,  firebox  steam  boilers,  or  other  forms 
with  small  uifiined  combustion  chambers,  in  which  the  gases  from  bitumi- 
nous coals  become  cooled,  are  not  burnt,  and  deposit  soot m nT1(q 

Steaming  coal  should  kindle  readily  and  burn  quickly  but  steadily , and 
should  contain  only  enough  volatile  matter  to  insure  rapid  combustio n . I 
should  be  low  in  ash  and  sulphur,  should  not  clinker,  and  when  it  is  t 

traCoafsfo? Ircm 'Makfng^.— J th?manufarture^rf  iron  and  forme— cal 
•nnrrioses  coal  is  chiefly  used  after  being  converted  into  coke,  though  it  is 
alsoPused  to  a limited  extent  in  the  raw  state.  Coal  directly  used  must  be 
«tronp-  and  not  swell  nor  disintegrate  so  as  to  choke  the  furnace.  It  .hould 
be  cafable  of  producing  a high  heat  and  should  not  contain  a large  amount 

0f  SCo\Peh-Cok^s  tCfaed  carbon  of  a coal,  a.fused  and  porous  product  pro- 
duced by  the  distillation  of  the  gaseous  constituent.  For  metallurgical  use, 
t ^hoi  fl  be  firm  tough,  and  bright,  with  a sonorous  ring,  and  should 
InuSn  not  over  ’k  of  sulphur.  For  blast-furnace  use,  a dense  coke  is 
nhWtLable Ind  the  best  i^the  one  with  the  largest  cell  structure  and  the 
hardest  cell  wall.  A high  percentage  of  volatile  hydrocarbon  is,  as  a rule, 

neTMXfit?ofCtheincMboi;  the  amount  of  disposable  hydrogen,  the 
tenacftv  whh  wL?h  the  gaseous’  constituents  are  held,  all  affect  the  recite 

iected'^ the^nflue’neeaof^^e1S\^Sher”loses  its^apacityfor  coking.  The 

antH r^the 'prcsCTit^rajde^of  manufacture  the 
ccontial  mi a ii ties  of  a good  coking  coal  are:  that  it  shall  contain  not  less  than 

a manner  f to  form  {“T^ofTolaSfmatter^  it  will  not  fuse  properly 
wmmi^it  has more Ithan 3CH  the  porous  structure  will  be  unduly  developed 

Wsf S ail.^and0 therefOTe^ do* riot 
coke  whife  others  fuse  properly  but  give  off  their  gas  so  as  to  form  large 

“rSSIS  ffiSwaafK 

the  "lttsDurg  o+ntidard  coking  coal,  but  coals  whose  analysis  differ  very 
instance,  the  Pocahontas  coke,  Virginia. 


ANALYSIS  OF.  COAL. 


173 


Domestic  Coals. — In  domestic  use,  coal  is  burned  in  open  grates,  in  closed 
stoves  with  ordinary  fire  bowls  and  flat  grates,  or  with  basket  grates  in  small 
furnaces  for  hot-air  heating,  and  in  cooking  stoves.  In  all  these,  the  coal 
that  sustains  a mild,  steady  combustion,  and  remains  ignited  at  a low  tem- 
perature with  a comparatively  feeble  draft,  is  the  best.  A coal  burning  with 
a smoky  flame  is  objectionable  as  producing  much  soot  and  dirt,  especially 
for  open  grates  or  cooking  purposes.  For  self-feeding  stoves,  or  for  base 
burners,  a dry  non-coking  coal  is  necessary.  A very  free  and  fiercely  burn- 
ing coal  is  not  desirable,  particularly  in  stoves,  as  the  temperature  cannot  be 
easily  regulated.  A sulphurous  coal  is  also  bad,  as  it  produces  stifling  gases 
with  a defective  draft,  and  corrodes  the  grates  and  fire  bowls.  The  difficulty 
from  clinkering  is  not  so  great  in  domestic  uses,  as  the  temperature  is  not 
generally  high  enough  to  fuse  the  ash.  A stony,  hard  ash  that  will  not  pass 
between  the  grate  bars  is  bad,  and  light  pulverulent  ash  is  best. 

Gas  Coals.— Mr.  H.  C.  Adams,  of  The  American  Gas  Light  Association, 
says:  “ The  essentials  of  a good  gas  coal  are  a low  percentage  of  ash,  say  5 $, 
and  of  sulphur,  say  £ of  1$,  a generous  share,  say  37$  to  40$  of  volatile  matter, 
charged  with  rich  illuminating  hydrocarbons.  And  it  should  yield,  under 
present  retort  practice,  85  candle-feet  to  the  pound  carbonized.  It  should  be 
sufficiently  dense  to  bear  transportation  well,  so  that,  when  carried  long 
distances,  it  may  not  arrive  at  its  destination  largely  reduced  to  slack  or  fine 
coal  of  the  consistency  of  sand.  And  it  should  possess  coking  qualities  that 
will  bring  from  the  retorts,  after  carbonization,  about  60$  of  clean,  strong-, 
bright  coke.” 

Blacksmith  Coals.— A good  coal  for  blacksmith  purposes  should  have  a 
high  heating  power,  should  contain  a very  small  amount  of  sulphur,  if 
any,  should  coke  sufiflciently  to  form  an  arch  on  the  forge,  and  should 
also  be  low  in  ash. 

From  the  above,  it  is  readily  seen  that  the  analysis  of  a coal  does  not 
necessarily  determine  its  value  or  the  uses  to  which  it  can  be  put.  How- 
ever, by  examining  the  analyses  given  in  the  table  on  page  168,  certain 
standards  may  be  adopted  as  showing  in  a general  way  about  what  the 
analysis  of  coal  should  be  for  certain  purposes.  For  steam  purposes,  the 
semibituminous  coals  have  established  reputations.  For  gas  coals,  that 
from  Youghiogheny,  Pa.,  is  well  known.  For  blacksmiths,  Broad  Top  and 
Tioga  County,  Pennsylvania,  coals  are  standards;  while  for  coking,  Connells- 
ville  is  recognized  as  a standard. 

The  sizes  of  anthracite  coal  vary.  The  sizes  of  screen  mesh  and  bar  open- 
ings used  for  separating,  range  as  follows: 

Lump,  over  bars  placed  7 to  9 in.  apart. 

Steamboat,  over  bars  placed  3£  to  5 in.  apart  and  through  bars  7 in.  apart. 

Grate,  over  2£  in.  and  through  4£  in.  square  mesh. 

Egg,  over  2 in.  and  through  2£  in.  square  mesh. 

Stove,  over  If  in.  and  through  2 in.  square  mesh. 

Chestnut,  over  £ in.  and  through  If  in.  square  mesh. 

Pea,  over  £ in.  and  through  £ in.  square  mesh. 

Buckwheat,  over  £ in.  and  through  £ in.  square  mesh. 

No.  2 Buckwheat,  or  Bird’s-eye,  over  £ in.  and  through  x8ff  in.  square  mesh. 

The  sizes  of  bituminous  coal  are  Lump,  Nut,  and  Slack. 

All  coal  that  passes  over  bars  1£  in.  apart  is  called  Luw,p. 

All  coal  that  passes  through  bars  1£  in.  apart  and  over  bars  £ in.  apart  is 
called  Nut. 

All  coal  that  passes  through  bars  £ in.  apart  is  called  Slack. 


ANALYSIS  OF  COAL. 

The  following  is  the  outline  of  the  method  recommended  for  the 
analysis  of  coal  by  a committee  of  the  American  Chemical  Societv.  Messrs 
. VV.  F.  Hillebrand,  C.  B.  Dudley,  and  W.  A.  Noyes: 

Sampling.— At  least  5 lb.  of  coal  should  be  taken  for  the  original  sample, 
with  care  to  secure  pieces  that  represent  the  average.  These  should  be 
broken  up  and  quartered  down  to  obtain  the  smaller  sample,  which  is  to 
be  reduced  to  a fine  powder  for  analysis.  The  quartering  and  grinding 
should  be  carried  out  as  rapidly  as  possible,  and  immediately  after  the 
original  sample  is  taken,  to  prevent  gain  or  loss  of  moisture.  The  pow- 
dered coal  should  be  kept  in  a tightly  stoppered  tube,  or  bottle,  until 
analyzed.  Unless  the  coal  contains  less  than  2$  of  moisture,  the  shipment 
of  large  samples  in  wooden  boxes  should  be  avoided. 


174 


FUELS. 


In  boiler  tests  shovelfuls  of  coal  should  be  taken  at  regular  intervals  and 
out  in  a tight  covered  barrel,  or  some  air-tight  cbvered  receptacle,  and  the 
Fatter  sLufd  be  placed  whereit  is  protected  from  the  heat  of  the  furnace 
In  sampling  from  a mine , the  map  of  the  mine  should  be  carefully 
examined  and  points  for  sampling  located  m such  a manner  as  to  fairly 
rporesent  the  body  of  the  coal.  These  points  should  be  placed  close  to  the 
^kinS  facl  hefore  sampling,  make  a fresh  cut  of  the  face  from  top  to 
bottom^o  a depth  that  will  insure  the  absence  of  possible  changes  or  of 
sulphur  and  smoke  from  the  blasting  powders.  Clean  the  floor  and  spread 
Tmece  of  canvas  to  catch  the  cuttings.  Then,  with  a chisel,  make  a cutting 
from  floor  to  roof,  say  3 in.  wide  and  about  1 in.  deep.  Do  not  chisel  out 
the  shale  or  other  impurities  that  it  is  the  practice  at  that  flame  to  reject. 
Measure  the  length  of  the  cutting  made,  but  do  not  include  the  impurities 
^tMs  measurement?  With  a piece  of  flat  iron  and  a hammer  break  all 
nieces  to  quarter-inch  cubes  or  less,  without  removing  from  the  cloth. 
Quarter  down  and  transfer  to  a sealed  bottle  or  jar.  For  the  r\ 

samnle  samples  taken  at  several  points  in  this  manner  should  be  mixed 
and^iuartered  down.  If  the  vein  varies  in  thickness  at  different  points,  the 
^mnles  taken  at  each  point  should  correspond  in  amount  to  the  thickness 
vein  For  instance,  a small  measure  may  be  filled  as  many  times 
with  the  coal  of  the  sample  as  the  vein  is  feet  m thickness.  Should  the  e 
appear  differences  in  the  nature  of  the  coal,  it  will  be  more  satisfactory  to 
tekrfn  adSon  to  the  general  sample,  samples  of  such  portions  of  the 

V6i ■oK-Srlg’  ofthedcoal“  open  porcelain  or  platinum  crucible 
at  104°  to  107°  C.  for  1 hour,  best  in  a double-walled  bath  containing  pure 

t0lVolatile Combustible  ^ Matter.— Placelgfof  fresh,  undried  coal  in  a platinum 
crucible  weiehing  20  to  30  g„  and  haying  a tightly  fitting  coyer  Heat  over 
thpTll  flame  of  a Bunsen  burner  for  7 minutes.  The  crucible  should  be 
the  lull  name  o triangle  with  the  bottom  6 to  8 cm.  above  the  top 

n7t?1P  burner  %he  flame  use!  should  be  fully  20  cm.  high  when  burning 
free  Ind  the determinSfon  made  in  a place  free  from  drafte.  The  upper 
Jfrfkce  of  the  cover  should  burn  clear,  but  the  under  surface  should 
remain  covered  with  carbon.  To  find  “ volatile  combustible  matter, 
«nhtrnet  the  percentage  of  moisture  from  the  loss  found  here. 

SU^sh  — Burr^Se^ortfon  of  coal  used  for  the  determination  of  moisture  at 
first  over  a very  low  flame,  with  the  crucible  open  and  inclined,  untilfree 
from  carbon  If  properly  treated,  this  sample  can  be  burned  much  more 
quSkly  than  the  dJnse  carbon  left  from  the  determination  of  volatile 

maFixed  Carbon.-This  is  found  by  subtracting  the  percentage  of  ash  from 
the  percentage  of  coke.  _Mix  thoroughly  1 g.  of  the  finely  powdered 
coaSlwPhh  lg  of  magnesium  oxide  and.£  g.  of  dry  sodium  carbonateinathm 
7?toToOc  c platinum  dish  or  crucible.  The  magnesium  oxide  should  be 

triangle  ove^analcoho?  lT£pPheid KTS  affirsf)^  mu^not  be 

?nals  The  flame  is  kept  in  motion  and  barely  touching  the  dish,  at  first, 

fhen’lL  carbon 

60  c.  c.  oi  warer.  a™  ''  , . through  a filter,  boil  a second  and  third 

?iSenwUh  3o"oTwfter%nerlsh  unfil  the  filtrate  gives  only  a slight 
opalescence  with  Over  hydrochloric  acid 

Snl  SCfn^is^ 

especially  at^first,  ^ with  oonstant^irring,  10 

iS  lnr  the  case  of  coals  containing  much  pyrites  or  calcium  sulphate,  the 


STEAM. 


175 


> 


residue  of  magnesium  oxide  should  be  dissolved  in  hydrochloric  acid  and 
the  solution  tested  for  sulphuric  acid. 

When  the  sulphur  in  the  coal  is  in  the  form  of  pyrites,  that  compound  is 
converted  almost  entirely  into  ferric  oxide  in  the  determination  of  ash,  and, 
since  3 atoms  of  oxygen  replace  4 atoms  of  sulphur,  the  weight  of  the  ash 
is  less  than  the  weight  of  the  mineral  matter  in  the  coal  by  f the  weight  of 
the  sulphur.  While  the  error  from  this  source  is  sometimes  considerable, 
a correction  for  “proximate”  analyses  is  not  recommended.  When 
analyses  are  to  be  used  as  a basis  for  calculating  the  heating  effect  of  the 
coal,  a correction  should  be  made. 

The  analysis  of  a coal  may  be  reported  in  three  different  forms,  as  per- 
centages of  the  moist  coal,  of  the  dry  coal,  or  of  the  combustible.  Thus, 
suppose  1 g.  of  coal  is  analyzed,  and  the  first  heating  shows  a loss  of 
weight  of  .1  g.,  the  second  of  .3  g.,  the  third  .5  g.,  the  remainder,  or  ash, 
weighing  .1  g.,  the  complete  report  would  be  as  follows: 


Per  Cent. 

of  the 
Moist  Coal. 

Per  Cent. 

of  the 
Dry  Coal. 

Per  Cent, 
of  the 

Combustible. 

Moisture 

10 

Volatile  matter 

30 

33.33 

37.50 

Fixed  carbon  

50 

55.56 

62.50 

Ash  

10 

11.11 

Total  

100 

100.00 

100.00 

STEAM. 

A calculation  of  the  power  that  coal  possesses,  compared  with  the  useful 
work  which  steam  engines  exert,  shows  that  probably  in  the  very  best 
engines  not  one-tenth  of  the  power  is  converted  into  useful  work,  and  in 
some  very  bad  engines,  probably  not  one  one-hundredth.  There  are  many 
causes  for  this;  some  we  can  never  remedy,  because  to  do  so  it  would  be 
necessary  to  exhaust  the  steam  at  a lower  temperature  than  is  practical. 
There  are  other  causes  that  can  and  ought  to  be  removed.  We  want  good 
engines,  good  boilers,  high-pressure  steam,  expansive  working,  and  con- 
densing appliances. 

High-Pressure  Steam.— Why  should  we  use  high-pressure  steam?  There 
are  several  good  reasons.  Whatever  pressure  we  have  available  at  the 
steam  boiler,  a certain  amount  is  absorbed  in  overcoming  the  resistances  of 
the  engine  and  without  doing  any  useful  work.  Suppose  our  available 
steam  pressure  is  20  lb.,  and  10  lb.  are  so  absorbed;  that  leaves  us  only 
one-half;  but,  if  we  have  100  lb.  available,  it  would  leave  us  nine-tenths. 
High-pressure  steam  means  fewer  boilers  and  smaller  engines,  with  founda- 
tions and  houses  of  less  dimensions.  Then,  again,  the  amount  of  work  that 
it  is  possible  to  get  out  of  a given  quantity  of  steam  depends  on  the  differ- 
ence between  the  temperature  at  the  commencement  of  the  stroke  and  the 
temperature  at  the  end  of  the  stroke. 

Now,  there  is  a limit  as  to  how  low  the  temperature  can  be  at  the  end, 
and  as  we  raise  the  commencing  temperature,  we  enlarge  the  available 
difference.  We  may  put  the  advantages  of  high-pressure  steam  in  this  way. 
By  taking  a fixed  temperature  in  the  condenser  of,  say,  100°  F.,  and  initial 
temperatures  when  the  steam  enters  the  cylinder,  of  varying  amounts,  the 
theoretic  efficiency  of  that  steam  can  be  determined.  Commencing  with 
atmospheric  pressure,  we  have  an  efficiency  of  16.6$. 


Lb.  Per  Cent. 

10  20.0 

20  22.1 

30  23.7 

40  25.0 

50 26.1 

60  27 .0 

§0 28.6 


Lb.  Per  Cent 

100 29.8 

125 31.1 

150 32.2 

200 33.9 

250 35.3 

300 36.5 


176 


BOILERS. 


Wp  oan  only  get  in  practice  with  steam  a certain  proportion  of  the 
theoretic  power,  and  that  proportion  varies  with  the  pressure  of  the  steam. 

In  early  days  we  used  steam  at  atmospheric  pressure,  the  efficiency 
hpinp-  16  6 afterwards,  we  had,  in  compound  engines  of  two  cylinders, 
steam  of^Olb.,  the  efficiency  being  27/*.  we  have^  ^ 

pnp-irips  usine*  stG&in  £it  150  lb.,  ttiG  GflticiGiicy  being  32.2,0.  It 
observed  that  although  the  efficiency  increases  as  the  steam  pressure 
increases  the  amount  of  that  increase  is  a diminishing  quantity,  and  it 
becomes  so  small  at  and  beyond  150  lb.  pressure  that  probably  any  gain  m 
efficiency  is  not  a satisfactory  set-off  to  the  additional  expense  of  strength- 
eSng  the  parts  of  the  engine.  But  then,  how  very  few  of  our  engines  work 

n6¥he  advantages^ high-pressure  steam  are  not  yet  sufficiently  appreciated. 
Tt  S not  meVelf  t he  difference  between  60  lb.  and  120  lb.  Suppose  we  use 
steam  at  60  lb.f  probably  we  shall  get  50  lb.  at  engine,  and  ^sirtances  of 
enHne  will  absorb  10  lb.,  leaving  40  lb.  Now,  suppose  we  use  120  lb.,  we  can 
gefat  engine  110  lb.,  and  if  resistances  of  engine  absorb  10  lb.,  we  shall  have 

100EKoanSsro?lofsu0am.-By  “ expansion  of  steam  ” we  mean  that  at  a certain 
noint  of  the  stroke  we  shut  off  steam  supply  from  the  boiler  to  the 
Irnrl  the  steam  already  within  the  cylinder  performs  the  remainder  of  the 
s^ok^un^dedaiI^h)W,  Suppose  we  do  not  expand  at  all.  Suppose  we  allow 
fee ^^dmitsion' of  steam  into  the  cylinder  all  through  the  stroke;  we  shall 
have  at  the  end  of  the  stroke  pressure  exactly  similar  to  the  Pressure  with 
which  we  commenced.  Now,  we  cannot  work  a seam  of  coal  and  smi  nave 
the  coal  left*  we  cannot  get  work  out  of  steam  and  still  have  the  work  left 
in  it  and  so’,  if  our  steam  pressure  is  the  same  at  the  end  of  the  stroke  as  at 
the  beginning,  we  simply  discharge  twice  m each  revolution  a whole 
cylinder  full  of  steam  that  has  done  no  work  at  all,  and  waste  it  just  the 
same  as  if  we  had  discharged  it  from  the  boiler  without  passing  through  the 
SStafat  aTl?  But  some  one  mil  say,  work  has  been  done  upon  the  engine 
while  that  steam  was  in  the  cylinder.  True — and  the  explanation  is,  that 
while  the  steam  is  performing  work  its  heat  and  pressure  must  dimmish, 
and  so  long  as  the  communication  with  the  boiler  is  open,  fresh  heat  comes 
from  the  boiler  into  the  cylinder  to  take  its  place,  and  at  the  end  of  the 
strcSe  we  have  expended  heat  represented  by  the  capacity  of  two  cylinders, 
and  have  performed  work  as  represented  by  the  capacity  of  one  cylinder. 
Nffw  suppose  we  close  the  communication,  and  beyond  a certain  point  of 
the  stroke  allow  no  more  steam  to  enter,  we  get  an  amount  of  work  from 
the  steam  already  in  the  cylinder,  represented  by  the  diminishing  pressure 

°f  Condensers  —The  Effective  power  of  an  engine  does  not  depend  on,  and 
is  not  measured  by,  the  pressure  pushing  the  piston.  There] 
is  termed  a back  pressure  holding  the  piston  back,  and  the  real  effective 
nressure  is  evidently  the  difference  between  the  two.  Suppose  we  have  a 
locomotive  engine,  or  a winding  engine,  throwing  exhaust  into  the  open 
air  The  back  pressure  cannot  be  less  than  the  pressure  of  the  open  air, 
and  indeed  to  overcome  it,  it  must  be  something  more.  But  if  we  can 
d?scha?ge  our  exhaust  into  some  vessel  from  which  atmospheric  pressure 
and  all^ other  pressure  has  been  removed,  we  ku°w 

“ e amounts  to  about  15  lb.,  and  the  removal  of  that  from  the  front  of  the 
piston  is  as  good  as  adding  15  lb.  behind. 


BOILERS. 

The  steam  boiler  that  will  be  the  most  suitable  for  a certain  mine  will 
denend  on  the  nature  of  the  feedwater,  the  cost  of  fuel,  and  the  amount  of 
steam  required.  When  the  acid  water  from  the  mine  is  used  for  feedwater, 
and^uel  is  cheap  the  type  of  boiler  generally  used  is  either  the  plain 
rvllndrical  or  flue  boiled  because  it  is  simple  in  construction  and  can 
therefore  be  easily  cleaned  and  cheaply  replaced  when  eaten  by  the  mine 
water  The  tubular  or  locomotive  type  is  used  where  good  water  can  be 
offiffined1  except  in  the  best  equipped  plants,  where  the  water-tube  boiler  is 
used  Feedwater  taken  from  the  mine,  or  containing  acid,  should  be 
neutralized  by  lime  or  soda  before  being  used.  In  case  it  contains  minerals 
fn  solution,  a feedwater  separator  should  be  employed  to  Precipitate  the 
mineral  substance  before  the  water  is  allowed  to  enter  the  boiler. 


HORSEPOWER  OF  BOILERS. 


177 


We  always  calculate  the  strength  of  a boiler  in  the  direction  of  its 
diameter,  because,  theoretically,  a boiler  is  twice  as  strong  in  the  direction 
of  length  as  direction  of  diameter.  Many  causes  may  bring  about  boiler 
explosions.  First,  bad  materials;  second,  bad  workmanship;  third,  bad 
water,  which  eats  away  the  plates  by  internal  corrosion;  fourth,  water  lying 
upon  plates,  bringing  about  external  corrosion;  fifth,  overpressure:  sixth, 
safety  valves  sticking;  seventh,  water  getting  too  low;  eighth,  excessive 
tiring;  ninth,  hot  gases  acting  on  plates  above  water  level;  tenth,  choking  of 
feedpipes;  eleventh,  insufficient  provision  for  expansion  and  contraction: 
twelfth,  insufficient  steam  room  and  too  sudden  a withdrawal  of  a large 
quantity  of  steam;  thirteenth,  getting  up  steam,  or  knocking  off  a boiler 
too  suddenly;  fourteenth,  allowing  wet  ashes  to  lie  in  contact  with  plates. 
The  probable  causes  suggest  their  several  remedies. 

Wherever  possible  and  except  under  certain  circumstances,  stear^ 
engines  should  not  be  placed  in  the  mine,  and  certainly  steam  boilers 
should  be  in  all  cases  placed  upon  the  surface.  Steam  injures  the  ventiia* 
tion,  increasing  the  temperature  where  already  too  high,  doing  injury  and 
causing  inconvenience  by  condensation,  and  many  tires  in  mines  have  been 
caused  by  underground  boilers. 

The  Lancashire  Boiler.— The  colliery  boiler  that  finds  much  fa^or  m Eng- 
land is  that  class  of  Lancashire  boiler  which  is  28  or  30  ft.  long  ana  7 or  8 ft. 
in  diameter,  and  has  two  large  flues  running  through.  There  is  no  doubt 
that  the  marine  type  will  generate  more  steam  with  a given  amount  of 
coal,  and,  consequently,  is  gaining  ground,  and  will  gain  grouna  where 
coal  is  dear.  But  the  Lancashire  boiler  is  a good  steam  generator,  and  will 
not  only  work  longer  without  repairs,  but  is  less  troublesome  and  expensive 
to  repair.  The  favorite  construction  some  few  years  ago  was  wrought  iron 
with  double-riveted  horizontal  joints  and  Galloway  tubes  (Galloway 
tubes  are  simply  taper  tubes  running  across  the  flues  in  the  boiler),  and 
expansion  weldless  hoops  strengthening  the  flues  and  allowing  for  expan- 
sion and  contraction.  The  dimensions  were  7 ft.  diameter,  and  from 
28  to  30  ft.  long,  with  internal  flues  each  2 ft.  9 in.  diameter,  the  circular 
plates  being  about  i in.  and  the  end  plates  about  f in.  The  safe  working 
pressure  was  about  60  lb.  per  sq.  in.  Now  the  conditions  are  somewhat 
altered.  Steel  has  taken  the  place  of  iron,  giving  increased  strength,  and 
allowing  increased  diameter  and  increased  pressure.  Ring  plates  have  also 
abolished  a great  source  of  weakness  in  a boiler,  namely,  horizontally 
riveted  joints.  A good  Lancashire  boiler  now  will  measure  8 ft.  in 
diameter  and  30  ft.  long,  with  ring  plates  f in.  thick,  end  plates  probably 
£ in.,  and  will  work  very  well  at  120  lb.  pressure  per  sq.  in. 

Horsepower  of  Boilers.— The  horsepower  of  a boiler  is  a measure  of  its 
capacity  for  generating  steam.  Boilermakers  usually  rate  the  horsepower 
of  their  boilers  as  a certain  fraction  of  the  heating  surface;  but  this  is  a 
very  indefinite  method,  for  with  the  same  heating  surface,  different  boilers 
of  the  same  type  may,  under  different  circumstances,  generate  different 
quantities  of  steam. 

In  order  to  have  an  accurate  standard  of  boiler  power,  the  American 
Society  of  Mechanical  Engineers  has  adopted  as  a standard  horsepower 
an  evaporation  of  30  lb.  of  water  per  hour  from  a feedwater  temperature  of  100°  F. 
into  steam  at  70  lb.  gauge  pressure , which  is  considered  equivalent  to 
34.5  units  of  evaporation;  that  is,  to  34.5  lb.  of  water  evaporated  from  a 
feedwater  temperature  of  212°  F.  into  steam  at  the  same  temperature. 

Example.— A boiler  evaporates  per  hour  1,980  lb.  of  water  from  a feed 
temperature  of  100°  into  steam  at  70  lb.  gauge  pressure.  What  is  the 
horsepower  of  the  boiler? 

Since,  under  the  given  conditions,  an  evaporation  of  30  lb.  is  equivalent 
to  1 horsepower,  the  number  of  horsepower  is  1,980  -r-  30  = 66. 

In  the  various  types  of  boilers  there  is  a nearly  constant  ratio  between 
the  water-heating  surface  and  the  horsepower,  and  also  between  the  heating 
surface  and  the  grate  area.  These  ratios  are  given  in  the  table  on  page  178. 

If  the  heating  surface  of  a boiler  is  known,  the  horsepower  can  be  found 
roughly;  thus,  if  a return-tubular  boiler  has  a heating  surface  of  900  sq.  ft., 
its  horsepower  lies  between  -9T°g°-  = 50  H.  P.  and  9X°5°-  = 64.3  H.  P.,  say  about 
57  H.  P. 

The  heating  surface  of  a boiler  is  the  portion  of  the  surface  exposed  to  the 
action  of  flames  and  hot  gases.  This  includes,  in  the  case  of  the  multi- 
tubular boiler,  the  portions  of  the  shell  below  the  line  of  brickwork,  the 
exposed  heads  of  the  shell,  and  the  interior  surface  of  the  tubes.  In  the 


178 


BOILERS. 


case  of  a water-tube  boiler,  the  heating  surface  comprises  the  portion  ol 
the  shell  below  the  brickwork,  the  outer  surface  of  the  headers,  and  outer 
surface  of  tubes.  In  any  given  case,  the  heating  surface  may  be  calculated 

Ratio  of  Heating  Surface  to  Horsepower  and  of  Heating  Surface 

to  Grate  Area. 


Type  of  Boiler. 

_ A._  Heating  Surface 

Ratio  — Horsepower 

Heating  Surface 
Ratio  - Grate  Area 

Plain  cylindrical 
Elue  

6 to  10 
8 to  12 

12  to  15 
20  to  25 

Return  - tubular 
V ertical  

14  to  18 

15  to  20 

25  to  35 
25  to  30 

Water-tube 

Locomotive  

10  to  12 
1 to  2 

35  to  40 
50  to  100 

bv  the  rules  of  mensuration,  rne  ionowmg  ewimuc  

nf  calculating  the  heating  surface  of  a return-tubular  boiler. 

Example  — A horizontal  return-tubular  boiler  has  the  followmg  dimen- 
sion Diameter  60  in.;  length  of  tubes,  12  ft.;  internal  diameter  of  tubes^ 
3 iS  number  of  tubes  ’ 82.  Assume  that  f of  the  shell  is  in  contact  with 
hnt  or  flame  and  f of  the  two  heads  are  heating  surface.  _ . 

S fH'ofshe11  - - m5in"say' 

. 

Heating  surface  of  tubes  = v*  TOM  -4  2827  44  sq^n.  ^ 

Area  of  one  head  — ® X ™ h = V7fiq'92  sa  in 

thedhelds  mu^t  be  sSbtracted\wice  the  area  cut  out  by  the  tubes; 
this  is  82  X 32  X .7854  X 2.  = 1,159.26. 

Total  heating  surface  m square  feet  — 


18,096  + 111,290.4  + 3,769.92-1,159.26 


144 


= 916.64  sq.ft.  Ans. 


Pporarle  Maximum  Work  of  a Plain  Cylindrical  Boiler  of  120  Sq.Ft. 
^ ^HeaSw”  Bubfacb  and  12  Sq.  Ft.  Gbate  Surface,  at 

Different  Rates  of  Driving.  


Rate  of  driving;  lb. 

water  evaporated | 

per  sq.  ft.  of  heating 
surface  per  hour  .... 

2 

3 

3.5 

4 

4.5 

5 

6 

7 

8 

Total  water  evapora- 

ted by  120  sq.  ft. 

heating  surface  peri 
hour  lb 

240.00 

360.00 

420.00; 

o 

© 

oB 

540.00 

600.00 

720.00 

840.00 

960.00 

Horsepower;  34.5  lb. 
per  hour  = 1 H.  P. 

6.96 

10.43 

12.17 

13.91 

1 

15.65 

1 

17.39 

20.87 

24.35 

27.83 

Pounds  water  evapo- 

rated per  lb.  com- 

V^nctihlp  

10.88 

11.30 

11.36 

11.29 

11.20 

11.05 

10.48 

9.48 

i 

8.22 

Uuoiiuiv  ? 

Pounds  combustible 
burned  per  hour  ... 

22.10 

31.90 

37.00 

42.50 

48.20 

54.30 

68.70 

88.60 

116.80 

Pounds  combustible 

per  hour  per  sq.ft. 

nf  OTQt.P  

1.85 

2.65 

3.08 

3.55 

4.02 

4.52 

5.72 

7.38 

9.73 

Pounds  combustible 

per  hour  per  horse- 


3.17 

3.05 

i 3.04 

3.06 

3.08 

; 3.12 

3.30 

i 3.64 

4.16 

pu  w 

1 

urAm  fhh  fi mires  in  the  last  line,  we  see  that  the  amount  of  fuel  required 
for^given  horsepower  is  nearly  37^  greater  when  the  rate  of  evaporation  is 
8 lb.  Sian  when  it  is  3-5  lb. 


DANGER  OF  EXPLOSION. 


179 


The  figures  in  the  preceding  table  that  represent  the  economy  of  fuel,  viz., 
“Pounds  water  evaporated  per  lb.  combustible”  and  “Pounds  combustible 
per  hour  per  horsepower,”  are  what  may  be  called  “maximum”  results, 
and  they  are  the  highest  that  are  likely  to  be  obtained  with  anthracite  coal, 
with  the  most  skilful  tiring  and  with  every  other  condition  most  favorable. 
Unfavorable  conditions,  such  as  poor  tiring,  scale  on  the  inside  of  the 
heating  surface,  dust  or  soot  on  the  outside,  imperfect  protection  of  the  top 
of  the  boiler  from  radiation,  leaks  of  air  through  the  brickwork,  or  leaks  of 
water  through  the  blow-off  pipe,  may  greatly  reduce  these  figures. 

Choice  of  a Boiler.— Questions  that  arise  under  this  head  in  regard  to  any 
boiler  are: 

1.  Is  the  grate  surface  sufficient  for  burning  the  maximum  quantity  of 
coal  expected  to  be  used  at  any  time,  taking  into  consideration  the  availa- 
ble draft,  the  quality  of  the  coal,  its  percentage  of  ash,  whether  or  not  the 
ash  tends  to  run  into  clinker,  and  the  facilities,  such  as  shaking  grates,  for 
getting  rid  of  the  ash  or  clinker? 

2.  Is  the  furnace  of  a kind  adapted  to  burn  the  particular  kind  of  coal 
used? 

3.  Is  the  heating  surface  of  extent  sufficient  to  absorb  so  much  of  the 
heat  generated  that  the  gases  escaping  into  the  chimney  shall  be  reasonably 
low  in  temperature,  say  not  over  450°  F.  with  anthracite,  and  550°  F.  with 
bituminous  coal? 

4.  Are  the  gas  passages  so  designed  and  arranged  as  to  compel  the  gas 
to  traverse  at  a uniform  rate  the  whole  of  the  heating  surface,  being  not  so 
large  at  any  point  as  to  allow  of  the  gas  finding  a path  of  least  resistance,  or 
short-circuiting,  or,  on  the  other  hand,  so  contracted  at  any  point  as  to 
cause  an  obstruction  to  the  draft? 

These  questions  being  settled  in  favor  of  any  given  boiler — and  they  may 
be  answered  favorably  for  boilers  of  many  of  the  common  types — the 
relative  merits  of  the  different  types  may  now  be  considered  with  reference 
to  their  danger  of  explosion;  their  probable  durability;  the  character  and 
extent  of  repairs  that  may  be  needed  from  time  to  time,  and  the  difficulty, 
delay,  and  expense  that  these  may  entail;  the  accessibility  of  every  part  of 
the  boiler  to  inspection,  internal  and  external;  the  facility  for  removal 
of  mud  and  scale  from  every  portion  of  the  inner  surface,  and  of  dust  and 
soot  from  the  exterior;  the  water  and  steam  capacity;  the  steadiness  of 
water  level,  and  the  arrangements  for  securing  dry  steam. 

Each  one  of  the  points  referred  to  above  should  be  considered  carefully 
by  the  intending  purchaser  of  any  type  of  boiler  with  which  he  is  not 
familiar  by  experience.  The  several  points  may  be  considered  more  in 
detail. 

Danger  of  Explosion.— All  boilers  may  be  exploded  by  overpressure,  such  as 
might  be  caused  by  the  combination  of  an  inattentive  fireman  and  an 
inoperative  safety  valve,  or  by  corrosion  weakening  the  boiler  to  such 
an  extent  as  to  make  it  unable  to  resist  the  regular  working  pressure;  but 
some  boilers  are  much  more  liable  to  explosion  than  others.  In  consider- 
ing the  probability  of  explosion  of  any  boiler  of  recent  design,  it  is  well  to 
study  it  to  discover  whether  or  not  it  has  any  of  the  features  that  are  known 
to  be  dangerous  in  the  plain  cylinder,  the  horizontal  tubular,  the  vertical 
tubular,  and  the  locomotive  boilers.  The  plain  cylinder  boiler  is  liable  to 
explosion  from  strains  induced  by  its  method  of  suspension,  and  by  changes 
of  temperature.  Alternate  expansion  and  contraction  may  produce  a line 
of  weakness  in  one  of  the  rings,  which  may  finally  cause  an  explosion.  A 
boiler  should  be  so  suspended  that  all  its  parts  are  free  to  change  their  posi- 
tion under  changes  of  temperature  without  straining  any  part.  The 
circulation  of  water  in  the  boiler  should  be  sufficient  to  keep  all  parts 
at  nearly  the  same  temperature.  Cold  ffiedwater  should  not  be  allowed  to 
come  in  contact  with  the  shell,  as  this  will  cause  contraction  and  strain. 
The  horizontal  tubular  boiler,  and  all  externally-fired  shell  boilers,  are 
liable  to  explosion  from  overheating  of  the  shell,  due  to  accumulation  of 
mud,  scale,  or  grease,  on  the  portion  of  the  shell  lying  directly  over  the  fire, 
to  a double  thickness  of  iron  with  rivets,  together  with  some  scale,  over  the 
fire,  or  to  low  water  uncovering  and  exposing  an  unriveted  part  of  the  shell 
directly  to  the  hot  gases.  Vertical  tubular  boilers  are  liable  to  explosion 
from  deposit  of  mud,  scale,  or  grease,  upon  the  lower  tube-sheet,  and  from 
low  Water  allowing  the  upper  part  of  the  tubes  to  get  hot  and  cease  to  act 
as  stays  to  the  upper  tube-sheet.  Locomotive  boilers  may  explode  from 
deposits  On  the  crown  sheet,  from  low  water  exposing  the  dry  crown  sheet 


180 


BOILERS. 


to  the  hot  gases,  and  from  corrosion  of  the  staybolts.  Double-cylinder 
boilers,  such  as  the  French  elephant  boiler,  and  the  boilers  used  at  some 
American  blast  furnaces,  have  exploded  on  account  of  the  formation  oi  a 
“steam  pocket”  on  the  upper  portion  of  the  lower  drum,  the  steam  being 
prevented  from  escaping  from  out  of  the  rings  of  the  drum  by  the  lap  joint 
of  the  adjoining  ring,  thus  making  a layer  of  steam  about  4 inch  micx 
against  the  shell,  which  was  directly  exposed  to  the  hot  gases. 

Questions  to  Be  Asked  Concerning  New  Boilers. — The  causes  mentioned 
above  are  only  a few  of  the  causes  of  explosions,  but  they  are  the  principal 
ones  that  are  due  to  features  of  design.  These  features  should  be  looked  for 
in  any  new  style  of  boiler,  and  if  they  are  found  they  should  be  considered 
elements  of  danger.  Such  questions  as  the  following  may  be  asked:  is  tne 
method  of  suspension  of  the  boiler  such  as  to  allow  its  parts  to  be  tree  to 
move  under  changes  of  temperature?  Is  the  circulation  such  as  to  keep  all 
parts  at  practically  the  same  temperature?  Is  there  a shell  with  Riveted 
seams  exposed  to  the  fire?  Is  there  a shell  exposed  to  the  hre  that  may  at 
any  time  be  uncovered  by  water?  Is  there  a crown  sheet  on  which  scale 
mav  lodge?  Are  there  vertical  or  inclined  tubes  acting  as  stays  to  an  upper 
sheet,  the  upper  part  of  which  tubes  may  become  overheated  m case  01 
low  water?  Are  there  any  stayed  sheets,  the  stays  of  which  are  liable  to 
become  corroded?  Is  there  any  chance  for  a steam  pocket  to  be  formed  on  a 
sheet  that  is  exposed  to  the  fire?  _ _ , . , . 

In  addition  to  the  above-mentioned  features  of  design,  which  are 
elements  of  danger,  all  boilers,  as  already  stated,  are  liable 
to  corrosion.  Internal  corrosion  is  usually  due  to  acid  feedwater,  and  all 
boilers  are  equally  liable  to  it.  External  corrosion,  however,  is  more  liable 
to  take  place  in  some  designs  of  boilers  than  others,  and  m 
rather  than  others.  If  any  portion  of  a boiler  is  in  a cold  and  damp  place,  it 
is  liable  to  rust  out.  For  this  reason  the  mud-drums  of  many  modern  forms 
of  boilers  are  made  of  cast  iron,  and  resist  rusting  better  than  either  wrought 
iron  or  steel.  If  any  part  of  a boiler,  other  than  a part  made  of  cast  iron  is 
liable  to  be  exposed  to  a cold  and  damp  atmosphere,  or  covered  with  damp 
or  ashes  or  exposed  to  drip  from  ram  or  from  leaky  pipes,  and 
especially  if  such  part  is  hidden  by  brickwork  or  otherwise  so  that  it  can- 

“,:as  sasssa ssss: »,  w .x 

3—ed  by interi  or  external  corrosion,  but  they  may  also  be  burned 
nut  It  mav  “i e ded  ag  impossible  to  burn  a plate  or  tube  of  iron  or 
rin  matter  how  high  the  temperature  of  the  flame,  provided  one  side  of 
ft* Staffs ^cove?S  with  water.  If  a steam  pocket  is  formed,  so  that  the 
wntS  does  not*  touch  the  metal,  or  if  there  is  a layer  of  grease  or  hard  scale 
thpn  the  nlate  or  tube  may  be  burned.  In  a water  tube  that  is  horizontal,  o 
^trlv  so  and  in  which  the  circulation  of  water  is  defective,  it  is  Possible  to 
nearly  so,  anu  , . m drive  the  water  away  from  the  metal,  and 

fallow  the  tabe  to  ^ burn out  In  considering  the  probable  durability  of 
a Soiler  we  may  ask  the  same  questions  as  those  that  have  been  asked 
dimeer  of  explosion.  There  are,  however,  many  chances  of 
Wntn^  out  a mfnor  part  of  a boiler  without  serious  danger,  to  one  chance 
nf  ^difastrous  explomon.  Thus  the  tubes  of  a water-tube  boiler,  if  allowed 
£ thicklvcovered  with  scale,  might  be  burned  out  again  and  again 

without  causing  ^any  further  destruction  at  any  one  time  than  the  rupture 
Tnew  type  of  boiler  should  be  questioned  in  regard  to  the 

u4ohhnod  of  frequent  small  repairs  being  necessary,  as  well  as  in  regard  to 
likelihood  ot  irequein  ^ P We  ^ gk;  Is  the  circulation  through 

all  rnr’  S \he  ta  er  s4h  Sarthe  water  cannot  be  driven  out  of  any  tube 
anv  nortion  of  a plate,  so  as  to  form  a steam  pocket  exposed  to  high 
temperature?0  Are  thereproper  facilities  for  removing  the  scale  from  every 

P° oin?i«  thThiqutsat?onsUofedL  and  of  repairs  are,  in  some  respects, 

,*•£1 "to 7a  ch  other  The  more  infrequent  and  the  less  extensive  the 
relat>^  tb p6ffreater  the  durability.  The  tubes  of  a boiler,  where  corroded  or 
™Pa JZv  bt  replaced  and  made  as  good  as  new.  The  shell,  when  it 
burnt  out,  may  P tched  an(j  is  then  likely  to  be  far  from  as  good  as 
springs  a leak,  y P d badlv  it  must  be  replaced,  and  to  replace  the 
new  . When ^the ^shel oau  Herei^  is  the  advantage  of  the 

seclional  wX-Ue  toilerl  The  sections,  or  parts  of  a section,  may  be 


WATER  AND  STEAM  CAPACITY. 


181 


renewed  easily,  and  made  as  good  as  new  while  the  shell  being  far reared 
from  the  fire  and  easily  kept  dry  externally,  is: H J 
out  or  external  corrosion.  In  considering .the  merits  o a new; style  ol 
boiler  with  reference  to  repairs,  we  may  ask  what  parts  ot  tne  Doner  are 
most  likelv  to  give  out  and  need  to  be  repaired  or  replaced?  Are  these 
repairs  easily  effected,  how  long  will  they  require,  and,  after  they  are  made, 

iS  tF*eeHU»efof  Removal  ofYcale  and  for  Inspeotion.-These  questions  have 
already  lleen  discussed  to  some  extent  under  the  head  of  durability.  Some 
w«t2r-tube  boilers  now  dead  and  gone,  were  some  years  ago  put  on  the 
market  which  had  no  facilities  for  the  removal  of  scale.  It  was  claimed  by 
SeirproCtersthat  they  did  not  need  any,  because  th^utobonwMso 
raDid  Every  few  years  boilers  of  these  types  are  reinvented,  and  the  same 
claim  is  madl  for  them,  that  their  rapid  circulation  prevents  the  formation 
of  scale  The  fact  is  that  if  there  is  scale-forming  material  m the  water  it 
will  be  deposited  when  the  water  is  evaporated,  and  no  amount  or  kind  of 
circulation  will  keep  it  from  accumulating  on  every  part  of  the  boiler,  jmd 
in  every  kind  of  tubes,  vertical,  horizontal,  and  inclined.  I have  seen 
the  nearly  vertical  circulating  tubes  of  a water-tube  boiler, 
circulation  is  nine  times  as  fast  as  the  average  circulation  m the  inclined 
tubes!  nearly  full  of  scale;  that  is,  a 4"  tube  had  an  opening  m it  of  less  than 
1 in  in  diameter.  This  was  due  to  carelessness  m blowing  off  the  boiler,  or 
exceptionally  bad  feedwater,  or  both.  If  circulation  would  prevent  scaling 

at  Water^nd^tf^CaJadty^-B  is  claimed  for  some  forms  of  boilers  that 
they  are  better  than  others  because  they  have  a larger  water  or  steam 
capacity.  Great  water  capacity  is  useful  where  the  demands  for  steam  are 
extremely  fluctuating,  as  in  a rolling  mill  or  a sugar  refinery,  where  it  is 
desirable^to  store  up  heat  in  the  water  in  the  boilers  during  the  periods  of 
the  least  demand,  to  be  given  out  during  periods  of  greatest  demand.  Large 
water  capacity  is  obiectionable  in  boilers  for  factories,  usually,  especially  if 
?hev  do  not  run  at night,  and  the  boilers  are  cooled  down,  because  there  is  a 

lar  Je  Quantity  of  w|ter  to  be  heated  before  starting  each  morning.  If 
-mnid  steaming”  or  the  ability  to  get  up  steam  quickly  from  cold  water,  or 
to  rSse  the  pressure  quickly,  is  desired,  large  water  capacity  is  a.  detriment. 
Thl dSWe  steam  capacity  is  usually  overrated.  It  is  useful  to 
enable  the  steam  to  be  drained  from  water  before  it  escapes  into  the  steam 
r>i  ne  but  the  same  result  can  be  effected  by  means  of  a dry  Pipe,  as  m 
fo?omotive  and  SIrine  practice,  in  which  the  steam  space  m the  boiler  is 
very  small  hi  proportioS  to  the  horsepower.  Large  steam  space  in  the 
io  no  irrmortance  for  storing  energy  or  equalizing  the  pressure 
^irinVfhfstrokeXan^ enjine  The  water  in  the  boiler  is  the  place  to  store 
heat  and  if  the  steam  pipe  leading  to  an  engine  is  of  such  small  capacity 
that  it  reduces  the  pressure,  the  remedy  is  a steam  reservoir  close  to  the 

engStneldTn«saoTwate?Te«eL-This  requires  either  a large  area  of  water  sur- 
Steadiness  oTwaxer  Leve.  h slowiy  by  fluctuations  in  the  demand 

fofstlam  or  in the of  thffl-pumpT or  else  constant,  and  preferably 
a^itomaUc°  regulation 1 of  the  feedwater  supply  to  suit  the  steam  demand 
A ranidlv  lowering  water  level  is  apt  to  expose  dry  sheets  or  tubes  to  the 
^ctfon  of  thl  hot  gases,  and  thus  be  a source  of  danger  A rapidly  rising 
level  may  before  it  is  seen  by  the  fireman,  cause  water  to  be  carried  over 

°f f^ilfp'boifor 'of  a 

boiler  is  important  for  two  reasons:  (1)  To  keep  all  parts  of  the  toiler  of  a 
uniform  temperature,  and  (2)  to  prevent  the  adhesion  of  steam  bubbles  to 
ihe fSStee whfch  may  cause  overheating  of  the  metal  It  is  claimed  by 
some  manufacturers  that  the  rapid  circulation  of  water  m their  boilers 
tends  to  make  them  more  economical  than  others.  I have  as  yet,  however, 
to  findanv  proof  that  increased  rapidity  of  circulation  of  water  beyond 
t h at  usual  1 v found  in  any  boiler  will  give  increased  economy.  We  know 
that  increased  rate  of  flow  of  air  over  radiating  surfaces  increases  the 
amount  of  heat  transmitted  through  the  surface,  but 

increased  circulation,  cold  air  is  continually  brought  into  contact  with 
the  surface  making  an  increased  difference  of  temperature  on  the  two  sides, 
which  causes  increased  transmission.  But  by  increasing  the  rapidity  oi 
circulation^  a steam  boiler  we  cannot  vary  the  difference  of  temperature  to 
any  appreciable  extent,  for  the  water  and  the  steam  in  the  boiler  are  at 


182 


BOILERS . 


about  the  same  temperature  throughout.  The  ordinary  or  “Scotch”  form 
of  marine  boiler  shows  an  exception  to  the  general  rule  of  uniformity  of 
temperature  of  water  throughout  the  boiler,  but  the  temperature  above  the 
level  of  the  lower  fire  tubes  is  practically  uniform. 


INCRUSTATION  AND  SCALE. 

Nearly  all  waters  contain  foreign  substances  in  a greater  or  less  degree, 
and  though  this  may  be  a small  amount  in  each  gallon,  it  becomes  of 
importance  where  large  quantities  are  evaporated.  For  instance,  a 100  H.  P. 
boiler  evaporates  30,000  lb.  of  water  in  10  hours,  or  390  tons  per  month;  in 
comparatively  pure  water  there  would  be  88  lb.  of  solid  matter  in  that 
quantity,  and  in  many  kinds  of  spring  water  as  much  as  2,000  lb. 

The  nature  and  hardness  of  the  scale  formed  of  this  matter  will  depend 
on  the  kind  of  substances  held  in  solution  and  suspension.  Analyses  of  a 
great  variety  of  incrustations  show  that  carbonate  and  sulphate  of  lime 
form  the  larger  part  of  all  ordinary  scale,  that  from  carbonate  being  soft 
and  granular,  and  that  from  sulphate,  hard  and  crystalline.  Organic 
substances  in  connection  with  carbonate  of  lime  will  also  make  a hard  and 
troublesome  scale. 

The  presence  of  scale  or  sediment  in  a boiler  results  in  loss  of  fuel, 
burning  and  cracking  of  the  boiler,  predisposes  to  explosion,  and  leads  to 
extensive  repairs,  it  is  estimated  that  the  presence  of  in.  of  scale  causes 
a loss  of  13 $ of  fuel;  i in.,  38^;  and  ± in.,  60$.  The  Railway  Master 
Mechanics’  Association  of  the  United  States  estimates  that  the  loss  of  fuel, 
extra  repairs,  etc.,  due  to  incrustation,  amount  to  an  average  of  8750  per 
annum  for  every  locomotive  in  the  Middle  and  Western  States,  and  it  must 
be  nearly  the  same  for  the  same  power  in  stationary  boilers. 

Causes  of  Incrustation.— 

1.  Deposition  of  suspended  matter. 

2.  Deposition  of  salts  from  concentration. 

3.  Deposition  of  carbonates  of  lime  and  magnesia,  by  boiling  off  carbonic 
acid,  which  holds  them  in  solution. 

4.  Deposition  of  sulphates  of  lime,  because  sulphate  of  lime  is  soluble  in 
cold  water,  less  soluble  in  hot  water,  insoluble  above  270°  F. 

5.  Deposit  of  magnesia,  because  magnesium  salts  decompose  at  high 
temperatures. 

6.  Deposition  of  lime  soap,  iron  soap,  etc.,  formed  by  saponification  of 
grease. 

Method  of  Preventing  Incrustation.— 

1.  Filtration. 

2.  Blowing  off. 

3.  Use  of  internal  collecting  apparatus,  or  devices,  for  directing  the 
circulation. 

4.  Heating  feedwater. 

5.  Chemical  or  other  treatment  of  water  in  boiler. 

6.  Introduction  of  zinc  in  boiler. 

7.  Chemical  treatment  of  water  outside  of  boiler. 


Troublesome  Substance. 


Trouble. 


Remedy  or  Palliation. 


Sediment,  mud,  clay,  etc. 

Readily  soluble  salts. 

Bicarbonates  of  lime,  magnesia,  and  iron. 
Sulphate  of  lime. 

Chloride  and  sulphate  of  magnesium. 
Carbonate  of  soda  in  large  amounts. 
Acid  (in  mine  water). 

Dissolved  carbonic  acid  and  oxygen. 


Incrustation. 

Incrustation. 

Incrustation. 

Incrustation. 

Corrosion. 

Priming. 

Corrosion. 

Corrosion. 


Grease  (from  condensed  water). 


Corrosion. 


Organic  matter  (sewage). 


Priming. 


Organic  matter. 


Corrosion. 


Filtration;  blowing  off. 

Blowing  off. 

Heating  feed;  addition  of  caustic  soda, 
lime,  or  magnesia,  etc. 

Addition  of  carbonate  of  soda,  barium 
chloride,  etc. 

Addition  of  carbonate  soda,  etc. 

Addition  of  barium  chloride,  etc. 

Alkali.  , 

Heating  feed;  addition  of  caustic  soda, 
slaked  lime,  etc. 

Slaked  lime  and  filtering.  Substitute 
mineral  oil. 

Precipitate  with  alum  or  ferric  chloride, 
and  filter. 

Precipitate  with  alum  or  ferric  chloride, 
and  filter. 


PREVENTION  OF  SCALE. 


183 


Means  of  Prevention. — It  is  absolutely  essential  to  the  successful  use  of  any 
boiler  except  in  pure  water,  that  it  be  accessible  for  the  removal  of  scale, 
for  though  a rapid  circulation  of  water  will  delay  the  deposit,  and  certain 
chemicals  will  change  its  character,  yet  the  most  certain  cure  is  Periodical 
inspection  and  mechanical  cleaning.  This  may , however,  be  rendered  less 
frequently  necessary,  and  the  use  of  very  bad  water  more  practical  bv  the 
employment  of  some  preventives.  The  following  are  fair  samples  ol  those 

in  use.  with  their  results:  . . , ,,  , . . 

M Bidard’s  observations  show  that  “ anti-mcrustators  containing 
organic  matter  help  rather  than  hinder  incrustations,  and  are  therefore 

t0  Oak  hemlock,  and  other  barks  and  woods,  sumac,  catechu,  logwood,  etc. 
are  effective  in  waters  containing  carbonates  of  lime  or  magnesia,  by  reason 
of  their  tannic  acid,  but  are  injurious  to  the  iron  and  not  to  be  recom- 

meMo!asses,  cane  juice,  vinegar,  fruits,  distillery  slops  etc.  have  been  used 
With  success  so  far  as  scale  is  concerned,  by  reason  of  the  acetic  acid  that 
they  contain,  but  this  is  even  more  injurious  to  the  iron  than  tannic  acid, 
while  the  organic  matter  forms  a scale  with  sulphate  of  lime  when  it  is 

PreMUk  of  lime  and  metallic  zinc  have  been  used  with  success  in  waters 
charged  with  bicarbonate  of  lime,  reducing  the  bicarbonate  to  the  insoluble 

Ca  Barium  chloride  and  milk  of  lime  are  said  to  be  used  with  good  effect  at 
Krupp’s  works,  in  Prussia,  for  waters  impregnated  with  gypsum. 

Soda  ash  and  other  alkalies  are  very  useful  in  waters  containing  sulphate 
of  lime  bv  converting  it  into  a carbonate,  and  so  forming  a soft  scale 
easily  cleaned.  But  when  used  in  excess  they  cause  foaming,  particularly 
where  there  is  oil  coming  from  the  engine,  with  which  they  form  soap.  All 
soapv  substances  are  objectionable  for  the  same  reason. 

Petroleum  has  been  much  used  of  late  years.  It  acts  best  m waters  m 
which  sulphate  of  lime  predominates.  Sulphate  of  lime  is  the  injurious 
Stance  in  nearly  all  mine  waters,  and  petroleum  when  properly 
prepared,  is  a good  preventive  of  scale  and  pitting.  Crude  petroleum 
Should  not  be  used,  as  it  sometimes  helps  in  forming  a very  injurious  scale. 
Refined  petroleum,  on  the  other  hand,  is  useless,  as  it  vaporizes  at  a 
temperature  below  that  of  boiling  water.  Therefore,  only  such  prepara- 
tions should  be  used  as  will  not  vaporize  below  500°  F. 

Tannate  of  soda*  is  a good  preparation  for  general  use,  but  m waters  con- 
taining much  sulphate,  it  should  be  supplemented  by  a portion  of  carbonate 

of  ^rom  the  leaves  of  the  eucalyptus  is  found  to  work  well  in 

^^o^muddy1  water^^rticularly  if  it  contain  salts  ?f  lime,  no  preventive  of 
incrustation  will  prevail  except  filtration,  and  in  almost  every  instance  the 
use  of  a filter,  either  alone  or  in  connection  with  some  means  of  precipita- 
ting the  solid  matter  from  solution,  will  be  found  very  desirable.  . ,, 

In  all  cases  where  impure  or  hard  waters  are  used,  frequent  blowing 
from  the  mud-drum  is  necessary  to  carry  off  the  accumulated  matter, 
which  if  allowed  to  remain  would  form  scale.  ....... 

When  boilers  are  coated  with  a hard  scale,  difficult  to  remove,  it  will  be 
found  that  the  addition  of  i lb.  caustic  soda  per  horsepower,  and  steaming 
for  some  hours,  according  to  the  thickness  of  the  scale,  just  before  cleaning, 
will  ffreatlv  facilitate  that  operation,  rendering  the  scale  soft  and  loose. 
This  should  be  done,  if  possible,  when  the  boilers  are  not  otherwise  m use. 


COVERING  FOR  BOILERS,  STEAM  PIPES,  ETC. 

The  losses  by  radiation  from  unclothed  pipes  and  vessels  containing 
steam  are  considerable,  and  in  the  case  of  pipes  leading  to  steam  engines,  are 
magnified  by  the  action  of  the  condensed  water  m the  cylinder.  It  there- 
fore is  important  that  such  pipes  should  be  well  protected  The  following 
table  ffives  the  loss  of  heat  from  steam  pipes  naked,  and  clothed  with  wool  or 
hair  felt,  of  different  thickness,  the  steam  pressure  being  assumed  at  75  lb., 

There  is  a wide  difference  in  the  value  of  different  substances  for  protec- 
tion from  radiation,  their  values  varying  nearly  in  the  reverse  ratio  to  their 
conducting  power  for  heat,  up  to  their  ability  to  transmit  as  much  heat  as 


184 


BOILERS. 


the  surface  of  the  pipe  will  radiate,  after  which  they  become  detrimental, 
rather  than  useful,  as  covering.  This  point  is  reached  nearly  at  baked  clay 
or  brick. 

Table  of  Loss  of  Heat  From  Steam  Pipes. 


Outside  Diameter  of  Pipe,  Without  Felt 


Thickness  of  Covering.  In< 

2 In.  Diameter. 

4 In. 

Diameter. 

6 In.  Diameter. 

8 In.  Diameter. 

12  In.  Diameter. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

Ratio  of  Loss.  | 

• 1 

Feet  in  Length  per 
H.  P.  Lost. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

Ratio  of  Loss. 

Feet  in  Length  per 
H.  P.  Lost. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

Ratio  of  Loss. 

Feet  in  Length  per 
H.  P.  Lost. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

Ratio  of  Loss. 

Feet  in  Length  per 
H.  P.  Lost. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

| Ratio  of  Loss. 

Feet  in  Length  per 
H.  P.  Lost. 

0 

219.0 

1.00 

132 

390.8 

1.00 

75 

624.1 

1.000 

46 

729.8 

1.000 

40 

1,077.4 

1.000 

26 

i 

100.7 

.46 

288 

180.9 

.46 

160 

i 

65.7 

.30 

441 

117.2 

.30 

247 

187.2 

.300 

154 

219.6 

.301 

132 

301.7 

-.280 

92 

] 

43.8 

.20 

662 

73.9 

.18 

392 

111.0 

.178 

261 

128.3 

.176 

225 

185.3 

.172 

157 

2 

28.4 

.13 

1,020 

44.7 

.11 

648 

66.2 

.106 

438 

75.2 

.103 

385 

98.0 

.091 

294 

4 

19.8 

.09 

1,464 

28.1 

.07 

1,031 

41.2 

.066 

703 

46.0 

.063 

630 

60.3 

.056 

486 

6 

23.4 

.06 

1,238 

33.7 

.054 

860 

34.3 

.047 

845 

45.2 

.042 

642 

A smooth  or  polished  surface  is  of  itself  a good  protection,  polished  tin 
or  Russia  iron  having  a ratio,  for  radiation,  of  53  to  100  for  cast  iron.  Mere 
color  makes  but  little  difference. 


Table  of  Conducting  Power  of  Various  Substances. 


( From  Peclet.) 


Substance. 

Conducting 

Power. 

Substance. 

* 

Conducting 

Power. 

Blotting  paper 

.274 

Wood,  across  fiber 

.83 

Eiderdown  

.314 

Cork  

1.15 

Cotton  or  Wool,  | 

QOQ 

Coke,  pulverized  

1.29 

any  density  j 

.oZo 

India  rubber  

1.37 

Hemp,  canvas 

.418 

Wood,  with  fiber  

1.40 

Mahogany  dust  

.523 

Plaster  of  Paris 

3.86 

Wood  ashes  

.531 

Baked  clay 

4.83 

Straw  

.563 

Glass  

6.60 

Charcoal  powder  

.636 

Stone 

13.68 

Hair  or  wool  felt  has  the  disadvantage  of  becoming  soon  charred  from 
the  heat  of  steam  at  high  pressure,  and  sometimes  of  taking  fire  therefrom. 
This  has  led  to  a variety  of  “cements”  for  covering  pipes— composed  gen- 
erally of  clay  mixed  with  different  substances,  as  asbestos,  paper  fiber, 
charcoal,  etc.  A series  of  careful  experiments,  made  at  the  Massachusetts 
Institute  of  Technology  in  1871,  showed  the  condensation  of  steam  in  a pipe 
covered  by  one  of  them,  as  compared  with  a naked  pipe,  and  one  clothed 
with  hair  felt,  was  100  for  the  naked  pipe,  67  for  the  “cement”  covering, 
and  27  for  the  hair  felt.  . . . 

The  presence  of  sulphur  in  the  best  coverings  and  its  recognized  injurious 
effects  make  it  imperative  that  moisture  be  kept  from  the  coverings,  for, 
if  present,  it  will  surely  combine  with  the  sulphur,  thus  making  it  active. 
Stated  in  other  words,  keep  the  pipes  and  coverings  in  good  repair.  Much 
of  the  inefficiency  of  coverings  is  due  to  the  lack  of  attention  given  them; 
they  are  often  seen  hanging  loosely  from  the  pipe  which  they  are  supposed 
to  protect. 


CARE  OF  BOILERS. 


185 


Table  of  Relative  Value  of  Non-Conductors. 
( From  Chas.  E.  Emery,  Ph.  D.) 


Non-Conductor. 

Value. 

Non-Conductor. 

Value. 

Wnnl  felt  

1.000 

Loam,  dry  and  open  

.550 

Mineral  wool  No  2 

.832 

Slaked  lime  

.480 

lYllllvlcU  W wl  i’v.  ^ 

Mineral  with  tar  

.715 

Gas-house  carbon 

.470 

1VIII1CI cXA  W ini  

Qo  wflnat.  

.680 

Asbestos  

.363 

.345 

oaWUUSl 

Mineral  wool  No.  1 

PViotpaqI  

.676 

.632 

f'lnal  qkLpk  

Coke  in  lumps  

.277 

T)i  y-i  a q PTOSS  fiber 

.553 

Air  space  undivided  

.136 

JL  111“  W UUU  dblvoo  AX  MUX 

Carbonate  of  magnesia,  as  compared  with  wool  felt  at  1.000,  has  a rela- 
tive value  of  472.  This  is  determined  from  tests  by  Prof.  Ordway,  of  Boston, 

an'^^  ^g,  - a 

^°^rk°clSps,ncementedCtogether  with  water  glass,  make  one  of  the  best 
eoverin^s  known  but  a very  efficient  one,  may  be 

annlied  as  ^follows  First,  wrap  the  pipe  in  asbestos  paper,  though  this  may 
be  dispenLd  wUh;  then  lay  slips  of  wood  lengthways  from  6 to  12,  accord- 
ino-  to  size  of  pipe,  binding  them  in  position  with  wire  or  cord,  and 
around  the  framework  thus  constructed  wrap  roofing  paper,  fastening  it 
bv  naste  or  twine.  For  flanged  pipe,  space  may  be  left  for  access  to  the 
bolts  which  space  should  be  filled  with  felt.  If  exposed  to  weather,  use 
tkrrld  naper  T paint  the  exterior.  A French  plan  is  to  cover  the  surface 
with  a rough  flour  paste,  mixed  with  sawdust  until  it  forms  a nmderately 
stiff  dough  Apply  with  a trowel  in  layers  of  about  4 in.  thick,  give  4 or  5 
layers  iifall.  IfPiron  surfaces  are  well  cleaned  from  grease,  the  adhesion  is 
perfect.  For  copper,  first  apply  a hot  solution  of  clay  m water.  A coating 
of  tar  renders  the  composition  impervious  to  the  weather. 

DATA  FOR  PROPORTIONING  AN  ECONOMIZER. 

( The  Green  Fuel  Economizer  Co.,  Matteawan,  N.  Y.) 

The  following  estimate  is  given  for  the  amount  of  heating  surface  to  be 
provided  in  an  Iconomizer  to  be  used  in  connection  with  a given  amount  of 

b01Bv  allowing  4 sq.  ft.  of  heating  surface  per  boiler  horsepower  (Centennial 
rating^W  lb  of  water  evaporated  from  and  at  212°  = I E P.),  we  are  able 
to  raise  the  feedwater  60°  for  every  100°  reduction  m the  temperature  enter- 
ing the  economizer  with  gases  from  450°  to  600°.  These  results  are  cor- 

r°bWH^?lm^t^p?ratureSo?the  gases  entering  the  economizer  at  600°  to  700°, 
we  have  allowed  4£  to  5 sq.  ft.  of  heating  surface  per  boiler  horsepower, 
and  for  every  100°  reduction  of  gases  we  have  obtained  about  65  rise  m 
temperature  of  the  water;  the  temperature  of  the  feedwater  entering  aver- 

aglw1thToOO° sq°ft.2of  ’ boiler  heating  surface  (plain  cylinder  boilers)  develop- 
ing 1 000  H.  P.,  we  should  recommend  using  5 sq.  ft  of  economizer  heating 
surface  per  B.  H.  P.,  or  an  economizer  of  about  500  tubes,  and  it  should  heat 
the  feedwater  about  300°.  

CARE  OF  BOILERS. 

1 Safetv  Valves  —Great  care  should  be  exercised  to  see  that  these  valves 
are  ample  in  size  and  in  working  order.  Overloading  or  neglect  frequently 
leads  to  the  most  disastrous  results.  Safety  valves  should  be  tried  at  least 
once  every  day,  to  see  that  they  act  freely. 

2 Pressure  Gauge.-The  steam  gauge  should  stand  at  zero  when  the 
pressure  is  off,  and  it  should  show  same  pressure  as  the  safety  valve  when 
that  is  blowing  off.  If  not,  then  one  is  wrong,  and  the  gauge  should  be 
tested  by  one  known  to  be  correct. 


186 


BOILERS. 


3.  Water  Level.— The  first  duty  of  an  engineer  before  starting,  or  at  the 
beginning  of  his  watch,  is  to  see  that  the  water  is  at  the  proper  height.  Do 
not  rely  on  glass  gauges,  floats,  or  water  alarms,  but  try  the  gauge-cocks. 
If  they  do  not  agree  with  water  gauge,  learn  the  cause  and  correct  it. 

4.  Gauge-cocks  and  water  gauges  must  be  kept  clean.  Water  gauges  should 
be  blown  out  frequently,  and  the  glasses  and  passages  to  them  kept  clean. 
The  Manchester,  England,  Boiler  Association  attributes  more  accidents  to 
inattention  to  water  gauges  than  to  all  other  causes  put  together. 

5.  Feed-Pump  or  Injector. — These  should  be  kept  in  perfect  order,  and  be 
of  ample  size.  No  make  of  pump  can  be  expected  to  be  continuously 
reliable  without  regular  and  careful  attention.  It  is  always  safe  to  have  two 
means  of  feeding  a boiler.  Check-valves  and  self-acting  feed-valves  should 
be  frequently  examined  and  cleaned.  Satisfy  yourself  frequently  that  the 
valve  is  acting  when  the  feed-pump  is  at  work. 

6.  Low  Water.— In  case  of  low  water,  immediately  cover  the  fire  with 
ashes  (wet  if  possible)  or  any  earth  that  may  be  at  hand.  If  nothing  else  is 
handy,  use  fresh  coal.  Draw  fire  as  soon  as  it  can  be  done  without  increas- 
ing the  heat.  Neither  turn  on  the  feed,  start  nor  stop  engine,  nor  lift  safety 
valve  until  fires  are  out  and  the  boiler  cooled  down. 

7.  Blisters  and  Cracks.— These  are  liable  to  occur  in  the  best  plate  iron. 
When  the  first  indication  appears,  there  must  be  no  delay  in  having  it 
carefully  examined  and  properly  cared  for. 

8.  Fusible  plugs,  when  used,  must  be  examined  when  the  boiler  is  cleaned, 
and  carefully  scraped  clean  on  both  the  water  and  fire  sides,  or  they  are 
liable  not  to  act. 

9.  Firing.— Fire  evenly  and  regularly,  a little  at  a time.  Moderately 
thick  fires  are  most  economical,  but  thin  firing  must  be  used  where  the 
draft  is  poor.  Take  care  to  keep  grates  evenly  covered,  and  allow  no  air 
holes  in  the  fire.  Do  not  “ clean”  fires  oftener  than  necessary.  With 
bituminous  coal,  a “coking  fire,”  i.  e.,  firing  in  front  and  shoving  back 
when  coked,  gives  best  results  if  properly  managed. 

10.  Cleaning.— All  heating  surfaces  must  be  kept  clean  outside  and  in,  or 
there  will  be  a serious  waste  of  fuel.  The  frequency  of  cleaning  will  depend 
on  the  nature  of  fuel  and  water.  When  a new  feedwater  supply  is 
introduced,  its  effect  upon  the  boiler  should  be  closely  observed,  as  this  new 
supply  may  be  either  an  advantage  or  a detriment  as  compared  with  the 
working  of  the  boiler  previous  to  its  introduction.  As  a rule,  never  allow 
over  Tyr  scale  or  soot  to  collect  on  surfaces  between  cleanings.  Handholes 
should  be  frequently  removed  and  surfaces  examined,  particularly  in 
case  of  a new  boiler,  until  proper  intervals  have  been  established  by 
experience. 

The  exterior  of  tubes  can  be  kept  clean  by  the  use  of  blowing  pipe  and 
hose  through  openings  provided  for  that  purpose.  In  using  smoky  fuel,  it  is 
best  to  occasionally  brush  the  surfaces  when  steam  is  off. 

11.  Hot  Feedwater.— Cold  water  should  never  be  fed  into  any  boiler  when 
it  can  be  avoided,  but  when  necessary  it  should  be  caused  to  mix  with  the 
heated  water  before  coming  in  contact  with  any  portion  of  the  boiler. 

12  Foaming.— When  foaming  occurs  in  a boiler,  checking  the  outflow  of 
steam  will  usually  stop  it.  If  caused  by  dirty  water,  blowing  down  and 
pumping  up  will  generally  cure  it.  In  cases  of  violent  foaming,  check  the 
draft  and  fires. 

13  Air  Leaks.— Be  sure  that  all  openings  for  admission  of  air  to  boiler  or 
flues,  except  through  the  fire,  are  carefully  stopped.  This  is  frequently  an 
unsuspected  cause  of  serious  waste. 

14  Blowing  Off.— If  feedwater  is  muddy  or  salt,  blow  off  a portion  fre- 
quentlv,  according  to  condition  of  water.  Empty  the  boiler  every  week  or 
two  and  fill  up  afresh.  When  surface  blow  cocks  are  used,  they  should  be 
often  opened  for  a few  minutes  at  a time.  Make  sure  no  water  is  escaping 
from  the  blow-off  cock  when  it  is  supposed  to  be  closed.  Blow-off  cocks  and 
check-valves  should  b'e  examined  every  time  the  boiler  is  cleaned.  Never 
empty  the  boiler  while  the  brickwork  is  hot. 

15.  Leaks.— When  leaks  are  discovered,  they  should  be  repaired  as  soon 
as  possible. 

16  Filling  Up.— Never  pump  cold  water  into  a hot  boiler.  Many  times 
leaks,  and,  in  shell  boilers,  serious  weaknesses,  and  sometimes  explosions 
are  the  result  of  such  an  action. 


THICKNESS  OF  BOILER  IRON. 


187 


\ 


17  Dampness.— Take  care  that  no  water  comes  in  contact  with  the 
exterior  of  Pthe  boiler  from  any  cause,  as  it  tends  to  corrode  and  weaken 
the  boiler.  Beware  of  all  dampness  in  seatmgs  and  coverings. 

18  Galvanic  Action.— Examine  frequently  parts  in  contact  with  copper  or 

brass  where  water  is  present,  for  signs  of  corrosion.  If  water  is  salt  or  acid, 
some’ metallic  zinc  placed  in  the  boiler  will  usually  prevent  corrosion,  but  it 
will  need  attention  and  renewal  from  time  to  time.  , 

19  Rapid  Firing.— In  boilers  with  thick  plates  or  seams  exposed  to  the 
fire  steam  should8  be  raised  slowly,  and  rapid  or  intense  firing  avoided. 
With  thin  water  tubes,  however,  and  adequate  water  circulation,  no  dam- 

ag^ 0 anstand?ngrUnu sel— If  a boiler  is  not  required  for  some  time,  empty  and 
dry  it  thoroughly*  If this  is  impracticable,  fill  it  quite  full  of  water  and  put 
in  a quantity  of  common  washing  soda.  External  parts  exposed  to  damp- 

ne?lSXda  Aould  be  looked  after  at  least  once 

a vear  given  necessary  repairs,  refitted  to  the  pipe,  and  the  spaces  due  to 
ffiLfe  taken  up  Little  can  be  expected  from  the  best  non-conductors  if 
they  are  allowed  to  become  saturated  with  water,  or  if  air-currents  are 
nermitted  to  circulate  between  them  and  the  pipe.  . i_,vrvf 

P 22.  General  Cleanliness.— All  things  about  the  boiler  room  should  be  kept 
clean  and  in  good  order.  Negligence  tends  to  waste  and  decay. 


THICKNESS  OF  BOILER  IRON  REQUIRED  AND  PRESSURE 
ALLOWED  BY  THE  LAWS  OF  THE  UNITED  STATES. 


Pressure  Equivalent  to  the  Standard  for  a Boiler  42  In.  in  Diam- 
eter and  £ In.  Thick. 


Thickness. 
16ths.  • 


5 

4* 

4 

3» 

3£ 

3 


Diameter. 


34  In. 
Lb. 

36  In. 
Lb. 

38  In. 
Lb. 

40  In. 
Lb. 

42  In. 
Lb. 

44  In. 
Lb. 

46  In. 
Lb. 

169.9 

158.5 

135.9 

124.5 
113.2 

101.9 

160.4 

149.7 

128.3 

117.6 

106.9 

96.2 

152.0 

141.8 

121.6 

111.4 

101.3 

91.2 

144.4 
134.7 

115.5 
105.9 

96.2 

82.6 

137.5 

128.3 

110.0 

100.8 

91.7 

82.5 

131.2 

122.5 

105.0 

96.2 

87.5 

78.7 

125.5 

117.2 

100.0 

92.0 

83.0 

75.1 

The  rule  for  finding  the  proper  sectional  area  for  the  narrowest  part  of 
the  nozzle  is  given  by  Rankine,  S.  E.,  page  477,  as  follows: 

cubic  feet  per  hour  gross  feedwater 
Area  in  square  inches  — 800 V pressure  in  atmospheres 


Diameter  of 
Throat.  Decimals 
of  an  Inch. 


.10 

.15 

.20 

.25 

.30 


Delivery  in  Gallons  per  Hour  with  a Pressure 
per  Square  Inch  of 


30  Lb. 

45  Lb. 

60  Lb. 

75  Lb. 

56 

69 

80 

89 

127 

156 

180 

201 

226 

278 

321 

360 

354 

434 

502 

561 

505 

624 

722 

807 

90  Lb. 


98 

221 

393 

615 

884 


188 


BOILERS. 


Pressure  of  Steam  at  Different  Temperatures. 


( Results  of  Experiments  Made  by  the  Franklin  Institute.) 


Pressure. 
Inches  of 
Mercury. 

Tempera- 

ture. 

Degrees  F. 

Pressure. 
Inches  of 
Mercury. 

Tempera- 

ture. 

Degrees  F. 

Pressure. 
Inches  of 
Mercury. 

Tempera- 

ture. 

Degrees  F. 

30 

212.0 

135 

298.5 

225 

. 331.0 

45 

235.0 

150 

304.5 

240 

336.0 

60 

250.0 

165 

310.0 

255 

340.5 

75 

264.0 

180 

315.5 

270 

345.0 

90 

275.0 

195 

321.0 

285 

349.0 

105 

284.0 

| 210 

326.0 

300 

352.5 

120 

291.5 

Maximum  Economy  of  Plain  Cylinder  Boilers. 


Pounds  of  Water  Evaporated  From  and  at  212°. 


Per  sq.  ft.  heating 
surface  per  hour 

1.70 

2.00 

2.60 

3.50 

4.00 

4.50 

5.00 

6.00 

7.00 

8.00 

Per  lb.  combustible, 
maximum  of  other 
boilers,  Centennial 
tests 

11.90 

12.00 

12.10 

12.05 

12.00 

11.85 

11.70 

11.50 

10.85 

9.80 

8.50 

Subtract  extra  radia- 
tion loss  for  cylin- 
der boilers 

1.32 

1.12 

.87 

.75 

.64 

.56 

.50 

.45 

.37 

.32 

.28 

Probable  maximum 
per  lb.  combus- 
tible, cylinder 
boilprs 

10.58 

10.88 

11.23 

11.30 

11.36 

i 

11.29 

11.20 

11.05 

10.48 

9.48 

8.22 

1 

1 

■ 

Scheme  for  Boiler  Test. 


1 

Mn  mhpr  nf  t 

1 

o 

Mn/lp  hv  

Z 

Q 

Tvnp  nf*  Vinllpr  - 

O 

A 

Tjotp  of  t,pst,  - 

1 

Rnratinn  of  t,PSt  

Hr. 

O 

6 

n 

Dimensions  and  Proportions. 

Number  of  boilers  tested  

In. 

/ 

Q 

E/laLllclCi,  uuiici  -------- 

Ft.  In. 

O 

Q 

Ft.  In. 

V 

in 

T.PnO’th  orrc itP  

Ft.  In. 

1U 

JUCllgUl)  g 1 

No. 

1 9 

T^iorYidtpr  nf  tllhps  

In. 

1Z 

IQ 

Ft.  In. 

lo 

1 A 

T'rfctcil  wqIpt1  Y\ pn t i n p*  siirfn op  

Sq.  Ft. 

1 Utdl  Wdtt/l  llucttiiig  

Tnfol  ctoom  liPQtiTiO'  cn T*"fVl  PP  

Sq.  Ft. 
Sq.  Ft. 

* 1> 

ID 
1 A 

1 Utdl  otCdlll  DUlldvv  

turfopp  t\ot  hnilpp  

lo 

1 7 

Ijrldtv  0U.1  idCv  uui  1 vi  

Par  norit  air  C'AQPP  1TI  OTQtp  

1 / 
18 
1 Q 

it/l  belli,  dll  opdbe  111  gicite  

Ratio  water  heating  to  grate  surface  - 

Sq.  Ft. 

on 

Ft. 

ZU 

21 

09 

ilGlglll  SlaUi.  dUUYc  UedU  piaieo 

Ratio  stack  area  to  grate  surface  - 

Average  Pressures. 

A irw aotvVi orn  Taxt  Kq vayyi ptpp  

In. 

zz 

9Q 

A Lino s pile i c uy  udi  uiiiei^i  

GtooTYi  nroccnrh  hv  o*Q  11 o*P  - 

Lb. 

Zo 

OXalll  pieooUlG  uy  gdUge  

24 

25 


26 

27 

28 

29 

30 

31 


32 

33 

34 

35 

36 

37 

38 


45 

46 

47 


48 

49 

50 


CHIMNEYS. 


Scheme  for  Boiler  Test— ( Continued). 


Force  chimney  draft,  inches  water 

Force  blast  in  ash  pit,  inches  water •--- 

Average  Temperatures. 

Of  external  air 

Oftireroom  

Of  steam  

Of  feedwater  before  heater 

Of  feedwater  after  heater 

Of  stack  gases ••  •••: 

Fuel. 


Kind  of  coal  

Total  coal  consumed  

Moisture  in  coal 

Total  dry  coal  consumed  - 

Total  ash  and  refuse  - 

Per  cent,  ash  and  refuse  in  dry  coal  

Total  combustible  consumed - 

Calorimetric  Tests. 

Per  cent,  moisture  in  steam 

Degrees  superheat  in  steam 

"Water . 

Total  water  pumped  into  boiler ----- 

Water  evaporated  corrected  for  quality  of  steam 

Equiv.  water  evap.  to  dry  steam  from  and  at  212  - 

Equiv.  water  evap.  to  dry  steam  from  and  at  212°  per  hour 
Economic  Evaporation. 

Water  evap.  per  lb.  dry  coal  actual  pressures  and  temp 

Equiv.  water  evap.  lb.  dry  coal  from  and  at  212  

Equiv.  water  evap.  lb.  combustible  from  and  at  212  

Rate  of  Combustion. 

Dry  coal  burned  per  hr.  per  sq.  ft.  grate  surface  

Combustible  burned  per  hr.  per  sq.  ft.  grate  surface  

Dry  coal  per  hour  per  H.  P.  developed  

Rate  of  Evaporation. 

Water  evap.  from  and  f Per  sq.  ft.  grate  surface  

at  212°  per  hour j Per  sq.  ft.  heating  surface 

Commercial  Horsepower. 

Basis  20  lb.  water  from  100°  feed  to  70  lb.  steam  per  hour.... 

Horsepower  builders  rating - - 

Heating  surface  to  one  horsepower  developed  

Per  cent,  total  horsepower  d ^e  to  feed  heater 


189 


\ 


In. 

In. 


°F. 

°f" 

°F. 

°f’ 

°F. 

°f! 


Lb. 


Lb. 

Lb. 

i 

Lb. 


°F. 


Lb. 

Lb. 

Lb. 

Lb. 


Lb. 

Lb. 

Lb. 


Lb. 

Lb. 

Lb. 


Lb. 

Lb. 


H.  P. 
H.  P. 
Sq.  It. 

]o 


CHIMNEYS. 

Chimneys  have  two  important  duties  to  perform,  the  first  being  to  carry 
off  the  waste  furnace  gases,  which  requires  size,  and  the  second  to  produce 
a draft  sufficient  to  insure  the  complete  combustion  of  the  ^uei,  which 
requires  height.  The  area  of  a chimney  is  usually  made  from  -f  to  is  as  large 
as  the  area  of  the  furnace  grates,  or  of  about  the  same  cross-section  as  the 
cross-sectional  area  of  the  flues  or  tubes;  we  have,  therefore ^ a comparaUvely 
simple  method  of  determining  one  of  the  required  dimensioi^  of  a ch^ 
and,  when  this  is  known,  it  becomes  an  easy  matter  to  determine  the  height 
of  the  chimney  when  the  horsepower  of  the  boiler  has  been  ascertained. 

The  horsepower  of  a boiler  being  given  and  the  necessary  chimney  area 
having  been  determined,  the  following  rule  gives  the  required  height  that 

the  chimney  must  be  to  produce  the  necessary  draft:  , 

Rule  —From  3.33  times  the  area  of  the  chimney  in  square  feet,  subtract  twice  the 
rxfvho  nron  nffhfi  nbim/npn  in.  Ran, are  feet,  and  divide  the  given  horsepower 


Ru|e  —From  3.33  times  the  area  oj  me  chimney  in  squuicjv », 
square  root  of  the  area  of  the  chimney  in  square  feet,  and  divide  the  given  hoi  sepower 
by  the  remainder.  The  square  of  the  quotient  will  be  the  height  of  the  chimney  in  feet. 
A — area  of  chimney; 
horsepower  of  boil 
height  of  chimney 

/ x— Jy 

\3.33  A — 2]/  A/ 


Then, 


190 


STEAM  ENGINES. 


Example. — What  must  be  the  height  of  a chimney  that  is  to  have  a cross- 
sectional  area  of  7 sq.  ft.,  and  to  supply  the  draft  for  a 141-horsepower  boiler? 

h = \3.33  X 7 — 2]/  7 ) =-  (.3.33  X 7 - (2  X 2.65) ) = 613  ft  AnS- 

Forced  Draft.— The  use  of  forced  draft  as  a substitute  for,  or  as  an  aid  to, 
natural  chimney  draft  is  becoming  quite  common  in  large  boiler  plants. 
Its  advantages  are  that  it  enables  a boiler  to  be  driven  to  its  maximum 
capacity  to  meet  emergencies  without  reference  to  the  state  of  the  weather 
or  to  the  character  of  the  coal;  that  the  draft  is  independent  of  the  tempera- 
ture of  the  chimney  gases,  and  that  therefore  lower  flue  temperatures  may 
be  used  than  with  natural  draft;  and  in  many  cases  that  it  enables  a poorer 
quality  of  coal  to  be  used  than  is  required  with  natural  draft.  Forced  draft 
may  be  obtained:  First,  by  a steam  jet  in  the  chimney,  as  in  locomotives  and 
steam  fire-engines;  second,  by  a steam-jet  blower  under  the  grate  bars; 
third,  by  a fan  blower  delivering  air  under  the  grate  bars,  the  ash-pit  doors 
being  closed;  fourth,  by  a fan  blower  delivering  air  into  a closed  fireroom, 
as  in  the  “ closed  stoke-hold  ” system  used  in  some  ocean-going  vessels;  and 
fifth,  by  a fan  placed  in  the  flue  or  chimney  drawing  the  gases  of  combustion 
from  the  boilers,  commonly  called  the  induced-draft  system.  Which  one  of 
these  several  systems  should  be  adopted  in  any  special  case  will  usually 
depend  on  local  conditions.  The  steam  jet  has  the  advantage  of  lightness 
and  compactness  of  apparatus,  and  is  therefore  most  suitable  for  locomotives 
and  steam  fire-engines,  but  it  also  is  the  most  wasteful  of  steam,  and  there- 
fore should  not  be  used  when  one  of  the  fan-blower  systems  is  available, 
except  for  occasional  or  temporary  use,  or  when  very  cheap  fuel,  such  as 
anthracite  culm  at  the  coal  mines,  is  used. 


STEAM  ENGINES. 


What  Is  a Good  Steam  Engine?— It  should  be  as  direct  acting  as  possible; 
that  is,  the  connecting  parts  between  the  piston  and  the  crank-shaft  should 
be  few  in  number,  as  each  part  wastes  some  power.  Formerly,  beam 
engines  were  all  the  rage.  They  were  well  enough  in  their  time  for  pump- 
ing, when  the  pump  was  at  one  end  of  the  beam  and  the  piston  at  the  other. 
Few  of  our  modern  colliery  engines  have  such  an  appendage,  except  in 
some  instances  for  pumping,  and  even  for  that  kind  of  work  the  better 
engines  have  no  beams.  The  moving  parts  of  an  engine  should  be  strong,  to 
resist  strains,  and  light,  so  as  to  offer  no  undue  resistance  to  motion;  parts 
moving  upon  each  other  should  be  well  and  truly  and  smoothly  finished,  to 
reduce  resistances  to  a minimum;  the  steam  should  get  into  the  cylinder 
easily  at  the  proper  time,  and  the  exhaust  should  leave  the  cylinder  as 
exactly  and  as  easily.  The  steam  pipes  supplying  steam  should  have 
an  area  one-tenth  the  combined  areas  of  the  cylinders  they  supply,  and 
exhaust  pipes  should  be  somewhat  larger.  The  cylinder  and  the  steam  pipes 
and  the  boiler  should  be  well  protected.  The  engine  should  be  capable  of 
being  started  and  stopped  and  reversed  easily  and  quickly. 

Rule. — To  find  the  indicated  horsepower  developed  by  an  engine , multiply 
together  the  M.  E.  P.  per  square  inch , the  area  of  the  piston,  the  length  of  stroke, 
and  the  number  of  strokes  per  minute.  This  gives  the  work  per  minute  in  foot- 
pounds. Divide  the  product  by  33,000;  the  result  wiU  be  the  indicated  horse- 
power of  the  engine. 

Let  I.  H.  P.  = indicated  horsepower  of  engine; 

P = M.  E.  P.  in  pounds  per  square  inch; 

A = area  of  piston  in  square  inches; 

L = length  of  stroke  in  feet; 

N = number  of  strokes  per  minute. 

Then,  the  above  rule  may  be  expressed  thus: 


I.  H.  P.  = 


PLAN 
33,000  * 


The  number  of  strokes  per  minute  is  twice  the  number  of  revolutions  per 
minute.  For  example,  if  an  engine  runs  at  a speed  of  210  revolutions  per 
minute,  it  makes  420  strokes  per  minute.  A few  types  of  engines,  however, 
are  single  acting;  that  is,  the  steam  acts  on  only  one  side  of  the  piston. 
In  this  case,  only  1 stroke  per  revolution  does  work,  and,  consequently,  the 


RULES  FOR  ENGINE  DRIVERS. 


191 


number  of  strokes  per  minute  to  be  used  in  the  above  rule  is  the  same  as  the 

number  of  revolutions  per  minute.  . 

Example— The  diameter  of  the  piston  of  an  engine  is  10  in.  and  the 
length  of  stroke  15  in.  It  makes  250  revolutions  per  minute,  with  a M.  E.  P. 
of  40  lb  ner  sa  in.  What  is  the  horsepower? 
f As  it  £ not  stated  whether  the  engine  is  single  or  double  acting,  assume 
that  it  is  double  acting.  Then,  the  number  of  strokes  is  250  X 2 — 500  per 
minute.  Hence, 


I.  H.  P.  = 


PLAN  40  X if  X (10^  X .7854)  X 500 


= 59.5  H.  P. 


33,000  33,000 

Approximate  Determination  of  M.  E.  P.-To  approximately  determine  the 
M.  E.  P.  of  an  engine,  when  the  point  of  apparent  cut-off  is  known  and  the 
boiler  pressure,  or  the  pressure  per  square  inch  m the  boiler  from  which 
the  supplv  of  steam  is  obtained,  is  given:  . , ..  . 

Rule.—  Add  U.7  to  the  gauge  pressure,  and  multiply  the  result  by  the  number 
ovvosite  the  fraction  indicating  the  point  of  cut-off  in  the  following  table.  Subtract 
17  from  the  product , and  multiply  by  .9.  The  result  is  the  M.  E.  P.  for  good , 
simple  non-condensing  engines. 

Or,  letting 

p gauge  pressure; 
k -=  a constant  (see  following  table); 

M.  E.  P.  = mean  effective  pressure. 


Then, 


M.  E.  P.  = .9[k(p  14.7)  -17]. 


Table. 


Cut-Off. 

Constant. 

Cut-Off. 

Constant. 

Cut-Off. 

Constant. 

b 

I 

£ 

.566 

f 

.771 

2 

3 

.917 

.603 

.4 

.789 

.7 

.926 

.659 

£ 

.847 

I 

.937 

.3 

.708 

.6 

.895 

.8 

.944 

h 

.743 

5 

5 

.904 

7 

5 

.951 

If  the  engine  is  a simple  condensing  one,  subtract  the  pressure  in  the 
condenser  instead  of  17.  * The  fraction  indicating  the  point  of  cut-off  is 
obtained  by  dividing  the  distance  that  the  piston  has.  traveled  when  the 
steam  is  cut  off  by  the  whole  length  of  the  stroke.  For  a f cut-off,  and  92  lb. 
gauge  pressure  in  the  boiler,  the  M.  E.  P.  is,  by  the  formula  just  given, 
.9 [.917(92  4-  14.7)  — 17]  = 72.6  lb.  per  sq.  in.  a . . 

Example.— Find  the  approximate  1.  H.  P.  of  a 9"  X 12"  non-condensmg 
engine,  cutting  off  at  £ stroke,  and  making  240  revolutions  per  minute.  The 
boiler  pressure  is  80  lb.  gauge.  7 _ ... 

80  4-  14.7  = 94.7.  The  constant  for  £ cut-off  is  .847,  and  .847  X boiler 
pressure  = .847  X 94.7  = 80.21.  M.  E.  P.  = (80.21  - 17)  X .9  = 56.89  lb.  per 
sq.  in.  Then, 


P L A N _ 56.89  X if  X (.7854  X 92)  X 240  X 2 
33,000  _ 33,000 


52.64  H.  P.  Ans. 


RULES  FOR  ENGINE  DRIVERS. 

If  a gauge  glass  breaks,  turn  off  the  water  first  and  then  the  steam,  to 
avoid  scalding  yourself. 

Don’t  buy  oil  or  waste  simply  because  it  is  very  cheap;  it  will  cost  more 
than  a good  article  in  the  end. 


192 


STEAM  ENGINES. 


In  cutting  rubber  for  gaskets,  etc.,  have  a dish  of  water  handy,  and  keep 
wetting  the  knife  blade;  it  makes  the  work  much  easier. 

Don’t  forget  that  there  is  no  economy  in  employing  a poor  fireman.  He 
can,  and  probably  will,  waste  more  coal  than  would  pay  the  wages  of  a first- 
class  man. 

An  ordinary  steam  engine  having  two  cylinders  connected  at  right  angles 
on  the  same  shaft  consumes  one-third  more  steam  than  a single-cylinder 
engine,  while  developing  only  the  same  amount  of  power. 

A fusible  plug  ought  to  be  renewed  every  three  months,  bv  removing  the 
old  metal  and  refilling  the  case;  and  it  should  be  scraped  clean  and  bright 
on  both  ends  every  time  that  the  boiler  is  washed  out,  to  keep  it  in  good 
working  order. 

When  you  try  a gauge-cock,  don’t  jerk  it  open  suddenly,  for  if  the  water 
happens  to  be  a trifle  below  the  cock,  the  sudden  relief  from  pressure  at  that 
point  may  cause  it  to  lift  and  flow  out,  deceiving  you  in  regard  to  its  height. 
Whereas,  if  you  open  it  quietly,  no  lift  will  occur,  and  you  ascertain  surely 
whether  there  is  water  or  steam  at  that  level. 

Always  open  steam  stop-valves  between  boilers  very  gently,  that  they 
may  heat  and  expand  gradually.  By  suddenly  turning  on  steam  a stop- 
valve  chest  was  burst,  due  to  the  expansive  power  of  heat  unequally 
applied.  The  same  care  is  also  recommended  when  shutting  off  stop- valves. 
A fearful  explosion  once  occurred  by  shutting  a communicating  stop-valve 
too  suddenly— due  to  the  recoil. 

In  order  to  obtain  the  driest  possible  steam  from  a boiler,  there  should  be 
an  internal  perforated  pipe  (dry  pipe,  so  called)  fixed  near  the  top  of  the 
boiler,  and  suitably  connected  to  the  steam  pipe.  The  perforations  in  this 
pipe  should  be  from  one-quarter  to  one-half  greater  in  area  than  that  of  the 
steam  pipe.  Domes  are  of  no  use  as  steam  driers;  they  only  add  a very  little 
to  the  steam  space  of  a boiler,  and  are  often  a source  of  loss  by  radiation. 

if  a glass  gauge  tube  is  too  long,  take  a triangular  file  ana  wet,  11  with 
turpentine;  hold  the  tube  in  the  left  hand,  with  the  thumb  and  forefinger  at 
the  place  where  you  wish  to  cut  it,  saw  it  quickly  and  lightly  two  or  three 
times  with  the  edge  of  the  file,  and  it  will  mark  the  glass.  Now  take  the 
tube  in  both  hands,  both  thumbs  being  on  the  side  opposite  the  mark,  and 
an  inch  or  so  apart,  and  then  try  to  bend  the  glass,  using  your  thumbs  as 
ful crums,  and  it  will  break  at  the  mark,  wrhich  has  weakened  the  tube. 

A stiff  charge  of  coal  all  over  a furnace  will  lower  the  temperature  200° 
or  300°  in  a very  short  time.  After  the  coal  is  well  ignited  the  temperature 
will  rise  about  500°,  and  as  it  continues  burning  will  gradually  drop  about 
200°,  until  the  fireman  puts  in  another  charge,  when  the  sudden  fall  before 
mentioned  takes  place  again.  This  sudden  contraction  and  expansion 
frequently  causes  the  bursting  of  a boiler,  and  it  is  for  this  reason  that  light 
and  frequent  charges  of  coal,  or  else  firing  only  one-half  of  the  furnace  at  a 
time,  should  be  always  insisted  on. 

Be  careful  when  using  a wrench  on  hexagonal  nuts  that  it  fits  snugly,  or 
the  edges  of  the  nut  will  soon  become  rounded. 

Be  careful  how  you  use  a monkeywrench,  for  if  it  is  not  placed  on  the  nut 
properly  the  strain  will  often  bend  or  fracture  the  wrench. 

The  area  of  grate  for  a boiler  should  never  be  less  than  | sq.  ft.  per  I.  H.  P. 
of  the  engine,  and  it  is  seldom  advisable  to  increase  this  allowance  beyond 
I sq . ft.  per  I.  H.  P. 

The  area  of  tube  surface  for  a boiler  should  not  be  less  than  2£  sq.  ft.  per 
I.  H.  P.  of  the  engine. 

The  ratio  of  heating  surface  to  grate  area  in  a boiler  should  be  30  to  1 as  a 
minimum,  and  may  often  be  increased  to  40  to  1,  or  even  more,  with 
advantage. 

Lap-welded  pipe  of  the  same  rated  size  has  always  the  same  outside 
diameter,  whether  common,  extra,  or  double  extra,  but  the  internal  diame- 
ter is  of  course  decreased  with  the  increased  thickness. 

A good  cement  for  steam  and  water  joints  is  made  by  taking  10  parts,  by 
weight,  of  white  lead,  3 parts  of  black  oxide  of  manganese,  1 part  of  litharge, 
and  mixing  them  to  the  proper  consistency  with  boiled  linseed  oil. 

To  harden  a cutting  tool,  heat  it  in  a coke  fire  to  a blood-red  heat  and 
plunge  it  into  a solution  of  salt  and  water  (1  lb.  of  salt  to  1 gal.  of  water), 
then  polish  the  tool,  heat  it  over  gas,  or  otherwise,  until  a dark  straw  and 
purple  mixed  color  shows  on  the  polish,  and  cool  it  in  the  salt  water. 

Small  articles  can  be  plated  with  brass  by  dipping  them  in  a solution  of 
9£  gr.  each  of  sulphate  of  copper  and  chloride  of  tin,  in  If  pt.  of  water. 


BELTING  AND  VELOCITY  OF  PULLEYS. 


193 


Don’t  be  eternally  tinkering  about  your  engine,  but  let  well  enough 

al°Don’t  forget  that  with  a copper  hammer  you  can  drive  a key  just  as  well 
as  with  a steel  one,  and  that  it  doesn’t  leave  any  marks. 

Keep  on  hand  slips  of  thin  sheet  copper,  brass,  and  tin,  to  use  as  liners, 
and  if  you  shape  some  of  them  properly,  much  time  will  be  saved  when  you 

netA  few  wooden  skewer  pins,  such  as  butchers  use,  are  very  useful  for 
many  purposes  in  an  engine  room.  Try  them.  . . , 

In  running  a line  of  steam  pipe  where  there  are  certain  rigid  points, 
make  arrangements  for  expansion  on  the  line  between  those  points,  or  you 

will  come  to  grief.  ' „ , , . , 

Arrange  the  usual  work  of  the  engine  and  firerooms  systematically,  and 

adhere  to  it.  It  pays  well. 

Don’t  forget  that  cleanliness  is  next  to  godliness.  , ._ 

Rubber  cloth  kept  on  hand  for  joints  should  be  rolled  up  and  laid  away 
by  itself,  as  any  oil  or  grease  coming  in  contact  with  it  will  cause  it  to  soften 
aiid  give  out  when  put  to  use.  , 

When  using  a jet  condenser,  let  the  engine  make  three  or  four  revolutions 
before  opening  the  injection  valve,  and  then  open  it  gradually,  letting  the 
engine  make  several  more  revolutions  before  it  is  opened  to  the  full  amount 

reuuired.  * 

Open  the  main  stop-valve  before  you  start  the  fires  under  the  boilers. 
When  starting  fires,  don’t  forget  to  close  the  gauge-cocks  and  safety  valve 
as  soon  as  steam  begins  to  form.  . 

An  old  "Turkish  towel,  cut  in  two  lengthwise,  is  better  than  cotton  waste 
for  cleaning  brass  work.  , 

Always  connect  your  steam  valves  m such  a manner  that  the  valve 
closes  against  the  constant  steam  pressure.  , , . - . 

Turpentine  well  mixed  with  black  varnish  makes  a good  coating  for  iron 
smoke  T)it)6S 

Ordinary  lubricating  oils  are  not  suitable  for  use  in  preventing  rust. 

You  can  make  a hole  through  glass  by  covering  it  with  a thm  coating  of 
wax,  warming  the  glass  and  spreading  the  wax  on  it.  Scrape  off  the  wax 
where  you  want  the  hole,  and  drop  a little  fluoric  acid  on  the  spot  with  a 
wire.  The  acid  will  cut  a hole  through  the  glass,  and  you  can  shape  the 
hole  with  a copper  wire  covered  with  oil  and  rottenstone. 

A mixture  of  1 oz.  of  sulphate  of  copper,  j oz.  of  alum,  ^ teaspoonful  of 
powdered  salt,  1 gill  of  vinegar  and  20  drops  of  nitric  acid  will  max®  a hole 
in  steel  that  is  too  hard  to  cut  or  file  easily.  Also,  if  applied  to  steel  and 
washed  off  quickly,  it  will  give  the  metal  a beautiful  frosted  appearance. 

BELTING  AND  VELOCITY  OF  PULLEYS. 

Belts  should  not  be  made  tighter  than  necessary.  Over  half  the  trouble 
from  broken  pulleys,  hot  boxes,  etc.  can  be  traced  to  the  fault  of  tight  belts, 
while  the  machinery  wears  much  more  rapidly  than  when  loose  belts  are 

emThespeed  of  belts  should  not  be  more  than  3,000  or  3,750  ft.  per  minute 
The  motion  of  driving  should  run  with  and  not  against  the  laps  of  the 

^Leather  belts  should  be  run  with  the  stronger  or  flesh  side  on  the  outside 
and  the  grain  (hair)  side  on  the  inside,  nearest  the  pulley,  so  that  the 
stronger  plirt  of  the  belt  may  be  subject  to  the  least  wear.  It  will  also  drive 
30$  more  than  if  run  with  the  flesh  side  nearest  the  pulley.  The  grain  side 
adheres  better  because  it  is  smooth.  Do  not  expose  leather  belts  to  the 

WeWh!n  the  length  of  a belt  cannot  be  conveniently . ascertained  by 
measuring  around  the  pulleys  with  a tape  line,  the  following  rule  will  be 

semceabTe:  diameterg  of  the  2 pulleys  together  and  divide  by  2;  multiply 
this  quotient  by  3i,  and  to  the  product  add  twice  the  distance  between  the 
centers  of  the  shafts;  the  sum  will  be  the  length  required. 


194 


COMPRESSED  AIR. 


COMPRESSED  AIR.* 

By  Prof.  Robert  Peele. 


An  air  compressor  consists  essentially  of  a cylinder  in  which  atmospheric 
air  is  compressed  by  a piston,  the  driving  power  being  steam  or  water. 

Classification  of  Compressors.— Steam-driven  compressors  in  ordinary  use 
may  be  classed  as  follows:  . , , . A , . ..  , 

(a)  Straight-line  type,  in  which  a single  horizontal  air  cylinder  is  set 

tandem  with  its  steam  cylinder,  and  provided  with  two  flywheels.  This 
pattern  is  generally  adapted  for  compressors  of  small  size.  . 

( b ) Duplex  type,  in  which  there  are  two  steam  cylinders,  each  driving  an 
air  cylinder,  and  coupled  at  90°  to  a crank-shaft  carrying  a fly  wheel. 

(c)  Horizontal , cross-compound  engines,  each  steam  cylinder  set  tandem 

with  an  air  cylinder,  as  in  (b).  . , 

( d ) Vertical , simple , or  compound  engines,  with  the  air  cylinders  set 

above  the  steam  cylinders.  . . ..  , ,,  , 

(e)  Compound  or  stage  compressors , m which  the  air  cylinders  themselves 

are  compounded.  The  compression  is  carried  to  a certain  point  in  one 
cylinder  and  successively  raised  and  finally  completed  to  the  desired  pres- 
sure in  the  others.  They  may  be  either  of  the  straight-line  or  duplex  form, 
with  simple  or  compound  steam  cylinders.  , _ _ 

Classes  (a),  ( b ),  (c),  and  (e)  are  those  commonly  employed  for  mine 
service  The  principle  of  compound,  or  two-srage,  air  compression  is 
recognized  as  applicable  for  even  the  moderate  pressures  required  in 
mining,  and  the  compressors  of  class  (e)  are  frequently  employed. 

Construction  of  Compressors.— Compressors  are  usually  built  with  a short 
stroke  as  this  is  conducive  to  economy  in  compression  as  well  as  the  attain- 
ment of  a proper  rotative  speed.  In  ordinary  single-stage  compressors,  the 
usual  ratio  of  length  of  stroke  to  diameter  of  steam  cylinders  is  U to  1 or  1£ 
to  1.  In  some  makes,  such  as  the  Rand,  the  ratio  is  considerably  greater, 
varying  from  H to  If  to  1,  as  in  several  large  plants  built  for  the  Calumet 
& Hecla  Mining  Co.  Many  compressors  have  length  and  diameter  of  steam 
cylinders  equal.  The  relative  diameters  of  the  air  and  steam  cylinders 
depend  on  the  steam  pressure  carried,  and  the  air  pressure  to  be  produced. 
In  mining  operations,  there  is  usually  but  little  variation  in  these  con- 
ditions. For  rock-drill  work,  the  air  pressure  is  generally  from  60  to  80  lb. 

In  using  water-power,  a compressor  is  driven  most  conveniently  by  a 
bucket  impact  wheel,  such  as  the  Pelton  or  Knight.  The  waterwheel  is 
generally  mounted  directly  on  the  crank-shaft,  without  the  use  of  gearing. 
Since  the  power  developed  is  uniform  throughout  the  revolution  of  the 
wheel,  the  compressor  should  be  of  duplex  form,  in  order  to  equalize  the 
resistance  so  far  as  possible.  The  rim  of  the  wheel  is  made  extra  heavy,  to 
supply  the  place  of  a flywheel.  When  direct-connected,  the  wheel  is  of 
relatively  large  diameter,  as  its  speed  of  rotation  must  of  necessity  be  slow. 
With  small  high-speed  wheels,  the  compressor  cylinders  may  be  operated 
through  belting  or  gearing.  In  most  cases,  however,  the  waterwheel  may 
be  large  enough  to  render  gearing  unnecessary.  Impact  wheels  may  be 
employed  with  quite  small  heads  of  water,  by  introducing  multiple  nozzles. 
To  prevent  the  water  from  splashing  over  the  compressor,  the  wheel  is 
enclosed  in  a tight  iron  or  wooden  casing.  The  force  of  the  water  is  regu- 
lated usually  by  an  ordinary  gate  valve.  If  the  head  be  great,  it  may  be 
necessary  to  introduce  means  for  deflecting  the  nozzle,  so  that,  wnen  the 
compressor  is  to  be  stopped  suddenly,  danger  of  rupturing  the  water 
main  will  be  avoided.  . _ 

Theory  of  Air  Compression.— The  useful  effect  or  efficiency  of  a compressor  is 
the  ratio  of  the  force  stored  in  the  compressed  air  to  the  work  that  has  been 
expended  in  compressing  it.  This  probably  never  reaches  80$,  and  often 
falls  below  60$. 


# gee  “Mines  and  Minerals,"  Vols.  XIX  and  XX,  for  complete  discussion  of  this  subject  by  the 
same  author. 


RATING  OF  COMPRESSORS. 


195 


Free  air  is  air  at  ordinary  atmospheric  pressure  as  taken  into  the  com- 
pressor cylinder.  As  commonly  used,  this  means  air  at  sea-level  pressure 
(14.7  lb.  per  sq.  in.)  at  60°  F. 

The  absolute  pressure  of  air  is  measured  from  zero,  and  is  equal  to  the 
assumed  atmospheric  pressure  plus  gauge  pressure.  Air-compression  calcu- 
lations depend  on  the  two  well-known  laws: 

1.  Boyle's  Law—  The  temperature  being  constant,  the  volume  varies 
inversely  as  the  pressure;  or  P V = P'  V'  — a constant;  in  which  V equals 
volume  of  given  weight  of  air  at  the  freezing  point,  and  the  pressure  P;  V' 
equals  the  volume  of  the  same  weight  of  air  at  the  same  temperature  and 
under  the  pressure  P'. 

2.  Gay-Lussac's  Law.  —The  volume  of  a gas  under  constant  pressure,  when 
heated,  expands,  for  each  degree  of  rise  in  temperature,  by  a constant  pro- 
portional part  of  the  volume  that  it  occupied  at  the  freezing  point;  or, 
V’  = V (1  + a £°),  in  which  a equals  for  centigrade  degrees,  or  5^T  for 
Fahrenheit  degrees. 

Theoretically,  air  may  be  compressed  in  two  ways,  as  follows: 

1.  Isothermally , when  the  temperature  is  kept  constant  during  compres- 
sion, and  in  this  case,  the  formula  P V = Pr  V'  is  true. 

2.  Adiabatically,  when  the  temperature  is  allowed  to  rise  withdut  check 
during  the  compression. 

Since  the  pressure  rises  faster  than  the  volume  diminishes,  the  equation 

pr  / y\n 

P V — P'  V'  no  longer  holds,  and  we  have  -p-  = ( -yj  ) > in  which  n equals 

1.406.  The  specific  heat  of  air  at  constant  pressure  is  .2375,  and  at  constant 
2375 

volume  .1689,  and  n = = 1.406. 

In  practice,  compression  is  neither  isothermal  nor  adiabatic,  but  inter- 
mediate between  the  two.  The  values  of  n for  different  conditions  in 
practice  are  as  follows,  as  determined  from  a 2,000-horsepower  stage  com- 
pressor at  Q,uai  de  la  Gare,  Paris. 

For  purely  adiabatic  compression,  with  no  cooling  arrangements, 
n = 1.406;  in  ordinary  single-cylinder  dry  compressors,  provided  with  a 
water-jacket,  n is  roughly  1.3;  while  in  the  best  wet  compressors  (with  spray 
injection),  n becomes  1.2  to  1.25.  In  the  poorest  forms  of  compressor,  the 
value  n = 1.4  is  closely  approached.  For  large,  well-designed  compressors 
with  compound  air  cylinders,  the  exponent  n may  be  as  small  as  1.15. 


Rating  of  Compressors. — Compressors  are  rated  as  follows:  (1)  In  terms  of 
the  horsenower  developed  by  the  steam  end  of  the  compressor,  as  shown  bv 
indicator  cards  taken  when  running  at  full  speed,  and  when  the  usual 
volume  of  air  is  being  consumed.  (2)  Compressors  for  mines  are  often 
rated  roughly  as  furnishing  sufficient  air  to  operate  a certain  number  of  rock 
drills;  a 3"  drill  requires  a volume  of  air  at  60  lb.  pressure,  equal  to  100  or 
110  cu.  ft.  of  free  atmospheric  air  per  minute.  (3)  In  terms  of  cubic  feet  of 
free  air  compressed  per  minute  to  a given  pressure. 

As  the  actual  capacity  of  a compressor  depends  on  the  density  of  the 
intake  air,  it  will  obviously  be  reduced  in  working  at  an  altitude  above  sea 
level,  because  of  the  diminished  density  of  the  atmosphere.  The  following 
table  gives  the  percentages  of  output  at  different  elevations:  , 

Example.— Calculate  the  volume  of  air 
furnished  by  an  18"  X 24"  compressor  work- 
ing at  an  elevation  of  5,000  ft.  above  sea 
level,  revolving  95  times  per  minute,  and 
having  a piston  speed  of  380  ft.  per  minute. 
92  x 3.14  = 254.3  sq.  in.  = piston  area. 
254  3 

-tttt  X 380  = 668.8  cu.  ft.  = volume  dis- 
144 

placed  per  minute  by  the  piston;  deducting 
10$  for  loss  gives  602  cu.  ft.  At  sea  level  at 

15 

80  lb.  gauge  pressure,  this  equals  ^ ^ X 

602  = 95  cu.  ft.  At  an  elevation  of  5,000 
ft.,  the  output  of  a compressor  would  be 
95  X 85$  — 80.7  cu.  ft.  per  minute. 

Cooling.— Compressor  cylinders  may  be 
cooled  by  either  of  the  following  methods: 


Altitude. 

Feet. 

Atmospheric 

Pressure. 

Pounds. 

Percentages 
of  Output 
at  Sea  Level. 

0 

14.7 

100.0 

1,000 

14.2 

97.2 

2,000 

13.6 

93.5 

3,000 

13.1 

90.8 

4,000 

12.7 

88.4 

5,000 

12.2 

85.0 

6,000 

11.7 

82.0 

7,000 

11.3 

79.3 

8,000 

10.9 

77.0 

9,000 

10.5 

75.0 

10,000 

10.1 

72.0 

196 


COMPRESSED  AIR. 


(1)  by  injecting  water  into  the  cylinder,  known  as  wet  compressors;  or  (2)  by 
jacketing  the  cylinder  in  water,  known  as  dry  compressors. 

Dry  Versus  Wet  Compressors.— Up  to  about  the  year  1885  there  seemed  to 
be  little  doubt  among  mechanical  engineers  that  wet  compressors  were,  on 
the  whole,  superior  to  dry,  because,  by  bringing  the  air  into  direct  contact 
with  water,  the  heat  is  most  effectually  absorbed.  This  view  is  correct,  so 
far  as  heat  loss  alone  is  concerned,  presided  the  water  in  the  cylinder  is 
properly  applied.  But  the  question  of  heat  loss  is  not  the  only  consideration. 
Low  first  cost  and  simplicity  of  construction  are  often  more  advantageous 
than  a close  approximation  to  isothermal  compression.  Latterly,  the  wet 
system  has  lost  ground,  owing  to  the  fact  that  moisture  is  objectionable  in 
the  air,  as  it  forms  frost  in  the  exhaust  ports  of  the  drills,  and  stops  them  up, 
and  probably  no  wet  compressors  are  now  being  built  in  the  United  States. 
In  Europe,  also,  dry  compressors  have  grown  in  favor,  at  least  for  mining 
plants  and  others  of  moderate  size. 


c = 


TRANSMISSION  OF  AIR  IN  PIPES. 

The  actual  discharge  capacity  of  piping  is  not  proportional  to  the  cross- 
sectional  area  alone,  that  is,  to  the  square  of  the  diameter.  Although  the 
periphery  is  directly  proportional  to  the  diameter,  the  interior  surface 
resistance  is  much  greater  in  a small  pipe  than  in  a large  one,  because,  as 
the  pipe  becomes  smaller,  the  ratio  of  perimeter  to  area  increases. 

To  pass  a given  volume  of  compressed  air,  a 1"  pipe  of  given  length  re- 
quires over  three  times  as  much  head  as  a 2"  pipe  of  the  same  length. 
The  character  of  the  pipe,  also,  and  the  condition  of  its  inner  surface,  have 
much  to  do  with  the  friction  developed  by  the  flow  of  air.  Besides  imper- 
fections in  the  surface  of  the  metal,  the  irregularities  incident  on  coupling 
together  the  lengths  of  pipe  must  increase  friction.  There  are  so  few  relia- 
ble data  that  the  influences  by  which  the  values  of  some  of  the  factors  may 
be  modified  are  not  fully  understood;  and,  owing  to  these  uncertain  condi- 
tions the  results  obtained  from  formulas  are  only  approximately  correct. 

Among  the  formulas  in  common  use,  perhaps  the  most  satisfactory  is  that 
of  D’Arcy.  As  adopted  for  compressed-air  transmission,  it  takes  the  form: 

jd5(pi  — p2j 
D ” \ Wi  l 

in  which  D = volume  of  compressed  air  in  cubic  feet  per  minute  discharged 
at  final  pressure;  „ . A . 

coefficient  varying  with  diameter  of  pipe,  as  determined  by 

d — dTameter^f  pipe  in  inches  (the  actual  diameters  of  If" 
and  pipe  are  1.38"  and  1.61",  respectively;  the  nomi- 
nal diameters  of  all  other  sizes  may  be  taken  for  calcu- 
lations); 

l = length  of  pipe  in  feet;  . 

pi  = initial  gauge  pressure  in  pounds  per  square  inch; 
p,  = final  gauge  pressure  in  pounds  per  square  inch; 
w[  = density  of  air,  or  its  weight  in  pounds  per  cubic  foot,  at 
initiar pressure  pi.  . . , 

The  values  of  the  coefficients  c for  sizes  of  piping  up  to  12  are: 

1"  4 45.3  5" 59.0  9" 

2"  52.6  6" 59.8  10" 

3"" 56.5  7" 60.3  11" 

4 //  58.0  8" 60.7  12" v 

Some  apparent  discrepancies  exist  for  sizes  larger  than  9",  but  they  cause 
no  very  'material  differences  in  the  results.  . 

Another  formula,  published  by  Mr.  Frank  Richards,  is  as  follows: 

H = V*L 

10,000  IP  a 

in  which  H = head  or  difference  of  pressure  required  to  overcome  friction 

and  maintain  the  flow  of  air; 

y _ ydume  of  compressed  air  delivered  in  cubic  feet  per 
minute; 

L = length  of  pipe  in  feet; 

D = diameter  of  pipe  in  inches;  . 

a = coefficient,  depending  on  the  size  of  pipe. 


.61.0 

.61.2 

.61.8 

.62.0 


TRANSMISSION  OF  AIR  IN  PIPES. 


197 


Values  of  a for  nominal  diameters  of  wrought-iron  pipe: 


1" 

.350 

3"  

730 

8"  

1.125 

1±// 

500 

34/' 

787 

10" 

1.200 

-1-4  

H" 

662 

4"  

.840 

12" 

1.260 

2"  

565 

5"  

.934 

2£" 

650 

6"  

1.000 

The  values  of  a fur  l\"  and  1\"  pipe  are  not  consistent  with  those  for 
other  sizes,  for  the  reason  stated  above.  In  using  this  formula  with  its 
constants,  the  calculated  losses  of  pressure  are  found  to  be  smaller,  and, 
conversely,  the  volumes  of  air  discharged  are  larger,  under  the  same  condi- 
tions, than  those  obtained  from  D’Arcy’s  formula. 

It  must  be  remembered  that,  within  certain  limits,  the  loss  of  head  or 
pressure  increases  with  the  square  of  the  velocity.  To  obtain  the  best  results, 
it  is  found  in  practice  that  the  velocity  of  flow  in  the  main  air  pipes  should 
not  exceed  20  or  25  ft.  per  second.  When  the  initial  velocity  much  exceeds 
50  ft.  per  second,  the  percentage  loss  becomes  very  large;  and,  conversely, 
by  using  piping  large  enough  to  keep  down  the  velocity,  the  friction  loss 
may  be  almost  eliminated.  For  example,  at  the  Hoosac  tunnel,  in  transmit- 
ting 875  cu.  ft.  of  free  air  per  minute,  at  an  initial  pressure  of  60  lb.,  through 
an  8"  pipe,  7,150  ft.  long,  the  average  loss  including  leakage  was  only  2 lb. 
A volume  of  500  cu.  ft.  of  free  air  per  minute,  at  75  lb.,  can  be  transmitted 
through  1,000  ft.  of  3"  pipe  with  a loss  of  4.1  lb.,  while  if  a 5"  pipe  were  used 
the  loss  would  be  reduced  to  .24  lb.  The  velocity  of  flow  in  the  latter  case 
is  only  10  ft.  per  second. 

In  driving  the  Jeddo  mining  tunnel,  at  Ebervale,  Pa.,  two  34"  drills  were 
used  in  each  heading,  with  a 6"  main,  the  maximum  transmission  distance 
being  10,800  ft.  This  pipe  was  so  large  in  proportion  to  the  volume  of  air 
required  fur  the  drills  (230  cu.  ft.  free  air  per  minute)  that  the  loss  was 
reduced  to  an  extremely  small  quantity.  A calculation  shows  a loss  of 
.002  lb.,  and  the  gauges  at  each  end  of  the  main  were  found  to  record 
practically  the  same  pressure. 

A due  regard  for  economy  in  installation,  however,  must  limit  the  use  ot 
very  large  piping,  the  cost  of  which  should  be  considered  in  relation  to  the 
cost  of  air  compression  in  any  given  case.  Diameters  of  from  4 to  6 in.  for 
the  mains  are  large  enough  for  any  ordinary  mining  practice.  Up  to  a 
length  of  3,000  ft.,  a 4"  pipe  will  carry,  per  minute,  480  cu.  ft.  of  free  air 
compressed  to  82  lb.,  with  a loss  of  2 lb.  pressure.  This  volume  of  air  will 
run  four  3"  drills.  Under  the  same  conditions,  a 6"  pipe,  5,000  ft.  long,  will 
carry  1,100  cu.  ft.  of  free  air  per  minute,  or  enough  for  10  drills. 

A mistake  is  often  made  in  putting  in  branch  pipes  of  too  small  a diam- 
eter. For  a distance  of,  say,  100  ft.,  a 1£"  pipe  is  small  enough  for  a single 
drill,  though  a 1"  pipe  is  frequently  used.  While  it  is,  of  course,  admissible 
to  increase  the  velocity  of  flow  in  short  branches  considerably  beyond  20  ft. 
per  second,  extremes  should  be  avoided.  To  run  a 3"  drill  from  a 1"  pipe 
100  ft.  long,  would  require  a velocity  of  flow  of  about  55  ft.  per  second, 
causing  a loss  of  10  lb.  pressure.  . 

The  piping  for  conveying  compressed  air  may  be  of  cast  or  wrought  iron. 
If  of  wrought  iron,  as  is  customary,  the  lengths  are  connected  either  by 
sleeve  couplings  or  by  cast-iron  flanges  into  which  the  ends  of  the  pipe 
are  screwed  or  expanded.  Sleeve  couplings  are  used  for  all  except  the 
large  sizes.  The  smaller  sizes,  up  to  1£  in.,  are  butt-welded,  while  all  from 
li  in.  up  are  lap-welded,  to  insure  the  necessary  strength.  Wrought-iron 
spiral-seam  riveted  or  spiral-weld  steel  tubing  is  sometimes  used.  It  is 
made  in  lengths  of  20  ft.,  or  less.  For  convenience  of  transport  in  remote 
regions,  rolled  sheets  in  short  lengths  may  be  had.  They  are  punched 
around  the  edges,  ready  for  riveting,  and  are  packed  closely — 4,  6,  or  more 
sheets  in  a bundle.  . . _ _ 

All  joints  in  air  mains  and  branches  should  be  carefully  made.  Air  leaks 
are  more  expensive  than  steam  leaks  because  of  the  losses  already  suffered 
in  compressing  the  air.  The  pipe  may  be  tested  from  time  to  time  by  allow- 
ing the  air  at  full  pressure  to  remain  in  the  pipe  long  enough  to  observe  the 
gauge.  In  case  a leak  is  indicated,  it  should  be  traced  and  stopped  imme- 
diately. In  putting  together  screw  joints,  care  should  be  taken  that  none  of 
the  white  lead  or  other  cementing  material  is  forced  into  the  pipe.  This 
would  cause  obstruction  and  increase  the  friction  loss.  Also,  each  length  as 
put  in  place  should  be  cleaned  thoroughly  of  all  foreign  substances  that  may 
have  lodged  inside.  To  render  the  piping  readily  accessible  for  inspection 


198 


COMPRESSED  AIR. 


and  stoppage  of  leaks,  it  should,  if  buried,  be  carried  in  boxes  sunk  just 
below  the  surface  of  the  ground;  or,  if  underground,  it  should  be  supported 
upon  brackets  along  the  sides  of  the  mine  workings.  Low  points  in  pipe 
lines,  which  would  form  “pockets”  for  the  accumulation  of  entrained 
water,  should  be  avoided,  as  they  obstruct  the  passage  of  the  air.  In  long 
pipe  lines,  where  a uniform  grade  is  impracticable,  provision  may  be  made 
near  the  end  for  blowing  out  the  water  at  intervals,  when  the  air  is  to  be 
used  for  pumps,  hoists,  or  other  stationary  engines. 

For  long  lengths  of  piping,  expansion  joints  are  required,  particularly 
when  on  the  surface.  They  are  not  often  necessary  underground,  as  the 
temperature  is  usually  nearly  constant,  except  in  shafts,  or  where  there  may 
be  considerable  variations  of  temperature  between  summer  and  winter. 

LOSSES  IN  THE  TRANSMISSION  OF  COMPRESSED  AIR. 

By  E.  Hill,  Norwalk  Iron  Works  Co. 

The  increasing  use  that  is  being  made  of  compressed-air  engines  for  mine 
and  underground  work  stimulates  the  inquiry  regarding  their  efficiency. 

The  situation  is  apparently  very  simple.  An  engine  drives  an  air  com- 
pressor, which  forces  air  into  a reservoir.  The  air  under  pressure  is  led 
through  pipes  to  the  air  engine,  and  is  there  used  after  the  manner  of  steam. 

The  resulting  power  is  frequently  a small  percentage  of  the  power 
expended.  In  a large  number  of  cases  the  losses  are  due  to  poor  designing, 
and  are  not  chargeable  as  faults  of  the  system  or  even  to  poor  workmanship. 

The  losses  are  chargeable,  first,  to  friction  of  the  compressor.  This  will 
amount  ordinarily  to  15#  or  20 #,  and  can  be  helped  by  good  workmanship, 
but  cannot  probably  be  reduced  below  10#.  Second,  we  have  the  loss 
occasioned  by  pumping  the  air  of  the  engine  room,  rather  than  air  drawn 
from  a cooler  place.  This  loss  varies  with  the  season,  and  amounts  to  from 
3#  to  10#.  This  can  all  be  saved.  The  third  loss  or  series  of  losses  arises  in 
the  compressing  cylinder.  Insufficient  supply,  difficult  discharge,  defective 
cooling  arrangements,  poor  lubrication,  and  a host  of  other  causes,  perplex 
the  designer  and  rob  the  owner  of  power.  The  fourth  loss  is  found  in  the 
pipe.  This  has  heretofore  received  by  no  means  the  consideration  that  the 
subject  demands.  The  loss  varies  with  every  different  situation,  and  is  sub- 
ject to  somewhat  complex  influences.  The  fifth  loss  is  chargeable  to  fall  of 
temperature  in  the  cylinder  of  the  air  engine.  Losses  arising  from  leaks  are 
often  serious,  but  the  remedy  is  too  evident  to  require  demonstration.  No 
leak  can  be  too  small  to  require  immediate  attention.  An  attendant  who 
is  careless  about  packings  and  hose  couplings  will  permit  losses  for  which 
no  amount  of  engineering  skill  can  compensate. 

We  can  only  realize  100#  efficiency  in  the  air  engine,  leaving  friction  out 
of  our  consideration,  when  the  expansion  of  the  air  and  the  changes  of  its 
temperature  in  the  expanding  or  air-engine  cylinder  are  precisely  the 
reverse  of  the  changes  that  have  taken  place  during  the  compression  of  the 
air  in  the  compressing  cylinder.  But  these  conditions  can  never  be  realized. 
The  air  during  compression  becomes  heated,  and  during  expansion  it 
becomes  cold.  If  the  air  immediately  after  compression,  before  the  loss  of 
any  heat,  was  used  in  an  air  engine  and  there  perfectly  expanded  back  to 
atmospheric  pressure,  it  would,  on  being  exhausted,  have  the  same  tem- 
perature it  had  before  compression,  and  its  efficiency  would  be  100#. 

But  the  loss  of  heat  after  compression  and  before  use  cannot  be  pre- 
vented, as  the  air  is  exposed  to  such  very  large  radiating  surfaces  in  the 
reservoir  and  pipes,  on  its  passage  to  the  air  engine.  The  heat,  which 
escapes  in  this  way,  did,  while  in  the  compressing  cylinder,  add  much  to 
the  resistance  of  the  air  to  compression,  and  since  it  is  sure  to  escape,  at 
some  time,  either  in  reservoir  or  pipes,  it  is  evidently  the  best  plan  to 
remove  it  as  fast  as  possible  from  the  cylinder,  and  thus  remove  one  element 
of  resistance.  Hence,  we  find  compressors  are  almost  universally  provided 
with  cooling  attachments  more  or  less  perfect  in  their  action,  the  aim  being 
to  secure  isothermal  compression,  or  compression  having  equal  temperature 
throughout.  Where  the  temperature  rises,  without  check,  during  com- 
pression, the  term  adiabatic  compression  is  employed. 

If  air  compressed  isothermaliy  is  used  with  perfect  expansion  and  the 
fall  of  temperature  during  expansion  be  prevented,  then  we  will  have  100# 
efficiency.  But  air  will  grow  cold  on  being  expanded  in  an  engine,  and 
hence  we  conclude  that  warming  attachments  have  the  same  economic 
place  on  an  air  engine  that  cooling  attachments  have  on  an  air  compressor. 
In  fact,  we  find  attachments  of  this  kind  more  particularly  in  large  and 


TRANSMISSION  OF  COMPRESSED  AIR. 


199 


permanently  located  engines,  but,  for  practical  reasons,  their  use  on  most  of 
the  engines  for  mine  work  is  dispensed  with,  and  the  engines  expand  the 
air  adiabaticallv,  or  without  receiving  heat.  _ . ,,  . 

The  practical  engineer,  therefore,  has. to  deal  with  nearly  isothermal 
compression,  and  nearly  adiabatic  expansion,  and  must  also  consider  that 
thfair  in  reservoirs  and  pipes  becomes  of  the  same  temperature  as  surround- 
ing objects.  Consideration  must  also  be  had  for  the  friction  of  the  com- 
prlssor  and  the  air  engine.  For  the  pressure  of  60  lb.,  which  is  that  most 
commonly  used,  the  decrease  in  resistance  to  compression  secured  by  the 
cooling  attachments,  is  almost  exactly  equaled  by  the  friction  of  the  com- 
pressor. Hence  it  is  safe,  in  calculating  the  efficiency  of  the  air  engine,  to 
consider  the  compressor  as  being  without  cooling*  attachments,  and  also  as 
working  without  friction.  The  results  of  such  calculations  will  be  too  high 
efficiencies  for  light  pressures,  which  are  little  used;  about  correct  for  medium 
pressures,  which ; are  commonly  employed;  and  too  low  for  higher  pressures 
and  will  thus  have  the  advantage  of  not  being  overestimated.  This  result 
is  occasioned  by  the  fact  that,  owing  to  the  slight  heat  m compressing  low 
pressures  of  air,  the  saving  of  power  by  the  cooling  attachments  is  not 
equal  to  the  friction  of  the  machine,  but  at  high  pressures  on  account  of  the 
great  heat,  the  cooling  attachments  are  of  great  value  and  save  very  much 

more  power  than  friction  consumes.  . , „r  QO 

In  the  expanding  engines,  the  expansion  never  falls  as  low  as  the 
adiabatic  law  would  indicate,  owing  to  a number  of  reasons,  but  w e will 
consider  the  expansion  as  being  adiabatic,  as  an  error  m calculations 
caused  thereby  will  be  on  the  “ safe  side  ’’  and  the  actual  power  will  exceed 
the  calculated  power.  We  therefore  consider  the  compressor  and  engine  as 
following  the  adiabatic  law  of  compression  and  expansion,  and  as  working 

Wiwnh  ttoview  of  the  case,  the  efficiency  of  an  air  engine,  working  with 
perfect  expansion,  stated  in  percentages  of  the  power  required  to  operate 
the  compressor,  can  be  placed  as  below  for  the  various  pressures  above  the 

atmosphere.  , < , ftn1. 

Pressure  above  the  atmosphere,  2.9  lb. 

Pressure  above  the  atmosphere,  14.7  lb. 

Pressure  above  the  atmosphere,  29.4  lb. 

Pressure  above  the  atmosphere,  44.1  lb. 

Pressure  above  the  atmosphere,  58.8 
Pressure  above  the  atmosphere,  73.5  lb. 

Pressure  above  the  atmosphere,  88.2  lb. 

Wc  observe  that  the  efficiencies  for  the  lower  pressures  are  very  much 
..reYfer  iffian  for  the  high  pressures,  and  the  conclusion  is  almost  irresistible 
fhsf  to  secure  economical  results  we  must  design  our  air  engines  to  run 
“St  lhrht  measures  And,  in  fact,  the  consideration  of  tables  similar  to  the 
above ?gheretXe  published  by  writers  on  this  subject,  has  led  many 

en^heeffinehas?een  entirely  neglected.  We  notice  that  a pressure  of  2.9  lb. 

• Sh  i efficiency  of  94.85$.  It  is  clear  that  if  the  air  were 

is  credited  with  an  length  of  the  pipe  and  the  velocity  of  flow 

conveyed  through  a P P , | . friction,  then  its  efficiency,  instead 

zero  It  is,’  therefore  the  power  that 
leSttom  the  air,  after  it  has  passed  the  pipe  and  lost  a part  of  its 
pressure* by  friction,  which  we  must  consider  when  we  state  the  efficiency 

of  Ctor  table  of  eSencies  with  a loss  of  2,9  lb.  in  the  pipe,  now  gives  us  dif- 
ferent values  for  the  efficiencies  at  the  various  pressures. 


94.85$  efficiency. 
81.79$  efficiency. 
72.72$  efficiency. 
66.90  $ efficiency. 
62.70$  efficiency. 
59.48$  efficiency. 
56.88$  efficiency. 


Pressure  above  the  atmosphere,  2.9  lb. 

Pressure  above  the  atmosphere,  14.7  lb. 

Pressure  above  the  atmosphere, 

Pressure  above  the  atmosphere, 

Pressure  above  the  atmosphere, 

Pressure  above  the  atmosphere, 

Pressure  above  the  atmosphere, 

Tt  will  hP  noticed  that  the  light  pressures  have  lost  most  by  the  pipe 
friction  2 9 lb  having  lost W:  14.7  lb.  11*  and  88.2  lb.  9nly  a trifle  over  - of 
w We’  see  that  now  14.7  lb.  is  apparently  the  economical  pressure  to  use 
Put  a further  careful  analysis  of  the  subject  shows,  that  when  the  loss  m the 
pi^e  is  2.9  lb.,  then  20.5  lb.  is  the  most  economical  pressure  to  use,  and  that 


29.4  lb. 
44.1  lb. 
58.8  lb. 

73.5  lb. 
5.2  lb. 


00.00$  efficiency. 
70.44$  efficiency. 
68.81$  efficiency. 
64.87$  efficiency. 
61.48$  efficiency. 
58.62$  efficiency. 
56.23$  efficiency. 


200 


COMPRESSED  AIR. 


the  efficiency  is  71#.  But  2.9  lb.  is  a very  small  loss  between  compressor  and 
air  engine,  and  cases  are  extremely  exceptional  where  the  friction  of  valves, 
pipes,  elbows,  ports,  etc.  does  not  far  exceed  this.  Yet,  with  these  con- 
ditions, which  are  very  difficult  to  fill,  we  see  that  20.5  lb.  is  the  lightest 
pressure  that  should  probably  ever  be  used  for  conveying  power,  and  that 
71#  is  an  efficiency  scarcely  to  be  obtained.  . . 

Continuing  our  investigation  and  taking  examples  where  the  pipe  friction 
amounts  to  5.8  lb.,  we  find  the  following  efficiencies  to  correspond  to  the 


stated  pressure: 

Pressure  above  the  atmosphere,  14.7  lb. 
Pressure  above  the  atmosphere,  29.4  lb. 
Pressure  above  the  atmosphere,  44.1  lb. 
Pressure  above  the  atmosphere,  58.8  lb. 
Pressure  above  the  atmosphere,  73.5  lb. 
Pressure  above  the  atmosphere,  88.2  lb. 


57.14#  efficiency. 
64.49#  efficiency. 
62.71#  efficiency. 
60.12#  efficiency. 
57.73#  efficiency. 
55.59#  efficiency. 


We  again  notice  that  as  friction  increases,  or  in  other  words,  when  we 
beffin  to  use  more  air  and  make  greater  demands  on  the  carrying  capacity 
of  the  pipe,  then  we  must  increase  pressure  very  considerably  to  attain  the 
most  economical  results.  If  the  demands  are  such  as  to  increase  the  friction 
and  loss  in  pipe  to  14.7  lb.,  the  air  of  14.7  lb.  pressure  at  the  compressor  is 
entirelv  useless  at  the  air  engine. 

The* table  will  stand  thus: 


Pressure  above  the  atmosphere,  14.7  lb.  00.00^  efficiency. 

Pressure  above  the  atmosphere,  29.4  lb.  48.53#  efficiency. 

Pressure  above  the  atmosphere,  44.11b.  55.13#  efficiency. 

Pressure  above  the  atmosphere,  58.8  lb.  55.64#  efficiency. 

Pressure  above  the  atmosphere,  73.5  lb.  54.74#  efficiency. 

Pressure  above  the  atmosphere,  88.2  lb.  53.44#  efficiency. 

It  is  to  be  noticed  that  88.2  lb.  pressure  has  lost  only  about  3f#  of  its 
efficiency  by  reason  of  as  high  a friction  as  14.7  lb.,  while  the  efficiency  of 
the  lower  pressures  has  been  greatly  affected. 

As  the  friction  increases  we  see  that  the  most  efficient,  and,  consequently , 
most  economical,  pressure  increases.  In  fact,  for  any  given  friction  in  a 
pipe,  the  pressure  at  the  compressor  must  not  be  carried  below  a certain 
limit.  The  following  table  gives  the  lowest  pressures  that  should  be  used  at 
the  compressor,  with  varying  amounts  of  friction  in  the  pipe: 

2.9  lb.  friction.  20.5  lb.  at  compressor.  70.92#  efficiency. 

5.8  lb.  friction.  29.4  lb.  at  compressor.  64.49#  efficiency. 

8.8  lb.  friction.  38.2  lb.  at  compressor.  60.64#  efficiency. 

11.7  lb.  friction.  47.0  lb.  at  compressor.  57.87#  efficiency. 

14.7  lb.  friction.  52.8  lb.  at  compressor.  55.73#  efficiency. 

17.6  lb.  friction.  61.7  lb.  at  compressor.  53.98#  efficiency. 

20.5  lb.  friction.  70.5  lb.  at  compressor.  52.52#  efficiency. 

23.5  lb.  friction.  76.4  lb.  at  compressor.  51.26#  efficiency. 

26.4  lb.  friction.  82.3  lb.  at  compressor.  50.17#  efficiency. 

29.4  lb.  friction.  88.2  lb.  at  compressor.  49.19#  efficiency. 

So  long  as  the  friction  of  the  pipe  equals  the  amounts  given  above,  an 

efficiency  greater  than  the  corresponding  sums  stated  in  the  table  cannot  be 
expected.  If  we  should  have  a case  that  corresponded  to  any  of  these  cited 
in  the  table,  we  could  only  increase  efficiency  by  reducing  the  friction. 

An  increase  in  the  size  of  pipe  will  reduce  friction  by  reason  of  the  lower 
velocity  of  flow  required  for  the  same  amount  of  air.  But  many  situations 
will  not  admit  of  large  pipes  being  employed,  owing  to  considerations  of 
economy  outside  of  the  question  of  fuel  or  prime  motor  capacity. 

An  increase  of  pressure  will  decrease  the  bulk  of  air  passing  the  pipe,  and 
in  that  proportion  will  decrease  its  velocity.  This  will  decrease  the  loss  by 
friction,  and,  as  far  as  that  goes,  we  have  a gain.  But  we  subject  ourselves 
to  a new  loss,  and  that  is  the  diminishing  efficiencies  of  increasing  pressures. 
Yet  as  each  cubic  foot  of  air  is  at  a higher  pressure,  and.  therefore,  carries 
more  power,  we  will  not  need  as  many  cubic  feet  as  before  for  the  same 
work.  It  is  obvious  that  with  so  many  sources  of  gain  or  loss  the  question 
of  selecting  the  proper  pressure  is  not  to  be  decided  hastily . 

As  an  illustration  of  the  combined  effect  of  these  different  elements,  we 
will  suppose  a very  common  case.  

Compressor  102  revolutions,  pressure  52.8  lb.,  loss  in  pipe  14.7  lb.,  machine 
in  mine  running  at  38.2  lb.,  efficiency  55.73#. 


FRICTION  OF  AIR  IN  PIPES, 


201 


So  Ions1  as  the  friction  of  the  pipe  amounts  to  14.7  lb.,  we  have  seen  that 
52  8 lb.  is  the  best  pressure  and  55.73$  the  greatest  efficiency.  We  will 
reduce  the  friction  by  reducing  the  bulk  of  air  passing  through  the  pipe.  We 
reduce  the  cylinder  of  the  air  engine  so  that  it  requires  47  lb.  pressure  to  do 
the  same  work  as  before.  We  find  now  that  the  inction  of  pipe  drops  to 
11  7 lb.  The  pressure  on  the  compressor  rises  to  58.8  lb.,  its  number  of  revolu- 
tions falls  to  100,  and  the  resulting  efficiency  is  57.22$. 

Another  change  of  pressure  on  compresscir  to  64.7  lb.  would  decrease  its 
revolutions  to  93,  friction  to  8.8  lb.,  and  efficiency  would  rise  to  57.94$.  Still 
again  increasing  the  pressure  to  73.5  lb.,  we  have  only  84  revolutions  of  com- 
pressor, 5.8  lb.  loss  in  pipe,  and  efficiency  of  57./ 3$.  In  this  last  case  the 
efficiency  begins  to  fall  off  a little,  and  higher  pressures  would  now 
show  less  efficiency;  but,  in  comparison  with  the  first  example,  we  find  we 
are  doing  the  same  work  in  the  mine  with  a trifle  less  power  and  with  a 
decrease  of  nearly  20$  in  the  speed  oi  the  compressor. 

Other  common  examples  can  be  shown  where  an  increase  of  pressure 
would  result  in  wonderful  increase  in  efficiency  and  economy.  There  are 
many  cases  where  light  pressures  and  high  velocity  in  the  pipe  will  convey 
a given  power  with  greater  economy  than  higher  air  pressures  and  lower 
speed  of  flow  through  the  pipe.  But  these  cases  arise  mostly  when  the 
higher  air  pressures  become  very  much  greater  than  are  at  present  m com- 

m°Therefore,  in  estimating  the  efficiency  of  the  complete  outfit,  we  find  that 
the  pipe  and  the  pressure  are  very  important  elements,  and  must  be  deter- 
mined with  care  and  skill  to  secure  the  most  satisfactwy  results.  As  the 
volume  and  power  of  air  vary  with  its  pressure,  the  size  and  consequent 
cost  of  compressor  for  a certain  work  would  also  be  affected  by  the  pressure. 
To  plan  an  outfit  for  a mine,  due  regard  must  be  had  to  cost  of  fuel  or  prime 
motor  power,  and  also  to  cost  of  compressor,  pipes,  and  machinery,  as  the 
saving  in  one  is  often  secured  by  a sacrifice  in  the  other.  . 

Next  to  determining  the  size  of  pipe,  the  skilful  engineer  has  need  of 
further  care  in  the  proper  position  of  reservoirs,  branches,  drains,  and  other 
attachments,  as  only  by  the  exercise  of  good  judgment  m this  can  satis- 
factory working  be  secured.  • 

The  fact  that,  on  account  of  the  diminished  density  of  the  atmosphere  at 
high  altitudes,  air  compressors  do  not  give  the  same  results  as  at  sea  level, 
should  also  be  taken  into  consideration  when  a compressor  is  to  be  installed 
in  a mountainous  region.  . . . . 

Friction  of  Air  in  Pipes.— Air  in  its  passage  through  pipes  is  subject  to 
friction  in  the  same  manner  as  water  or  any  other  fluid.  Tim  pressure  at 
the  compressor  must  be  greater  than  at  the  point  of  consumption  m order 
to  overcome  this  resistance.  The  power  that  is  needed  to  produce  the  extra 
pressure  representing  the  friction  of  the  pipe  is  lost,  as  there  can  be  no  use- 
ful return  for  it.  The  friction  is  affected  by  very  many  circumstances,  but 
chiefly  to  be  noted  is  the  fact  that  it  increases  in  direct  proportion  to  the 
length  of  the  pipe  and  also  as  the  square  of  the  velocity  of  the  flow  of  air. 
The  pressure  of  the  air  does  not  affect  it.  . 

The  losses  bv  friction  may  be  quite  serious  if  the  piping  system  -is  poorly 
designed,  and,  on  the  other  hand,  extravagant  expenditure  in  pipe  may 
result  from  a timid  overrating  of  the  evils  of  friction.  A thorough  knowl- 
edge of  the  laws  governing  the  whole  matter,  as  well  as  a ripe  experience,  is 
necessary  to  secure  true  economy  and  mechanical  success. 

The  loss  of  power  in  pipe  friction  is  not  always  the  most  serious  result. 
When  a number  of  machines  are  in  use  in  a mine,  and  the  pipes  are  so  small 
as  to  cause  a considerable  loss  of  pressure  by  friction,  then  there  will  be 
sudden  and  violent  fluctuations  in  pressure  whenever  a machine  is  started 
or  stopped.  Breakages  will  be  of  common  occurrence,  as  the  changes  are  too 
quick  to  be  entirely  guarded  against  by  the  attendant.  Perfectly  even  pres- 
sure at  the  compressor  is  no  safeguard  against  this  class  of  accidents.  The 
trouble  arises  in  the  pipe,  and  the  remedy  must  be  applied  there.  A system 
of  reservoirs  and  governing  valves  will  regulate  these  matters  and  allow 
successful  work  to  be  done  with  pipes,  which  would  otherwise  be  entirely 

i n aTh e Sordin ary  formulas  for  calculating  the  volume  of  air  transmitted 
through  a pipe  do  not  take  into  account  the  increase  of  volume  due  to 
reduction  of  pressure,  i.  e.,  loss  of  head.  To  transmit  a given  volume  of  air 
at  a uniform  velocity  and  loss  of  pressure,  it  would  be  necessary  to  construct 
the  pipe  with  a gradually  increasing  area.  This,  of  course,  is  impracticable, 


202 


COMPRESSED  AIR. 


and  in  pipe  of  uniform  section  both  volume  and  velocity  must  increase  as 
the  pressure  is  reduced  by  friction.  The  loss  of  head  in  properly  propor- 
tioned pipes  is  so  small,  however,  that  in  practice  the  increase  in  volume  is 
usually  neglected. 

Loss  of  Pressure  in  Pounds  per  Square  Inch,  by  Flow  of  Air  in  Pipes. 


Calculated  for  pipes  1,000  ft.  long;  for  other  lengths,  the  loss  varies  directly 
as  the  length. 


Velocity  of  Air 
at  Entrance 
to  Pipe. 

1"  Pipe. 

2" 

' Pipe. 

2h"  Pipe 

L 

Meters  per  Second. 

Feet  per  Second. 

Loss  of  Pressure. 
Pounds. 

Cubic  Feet  of  Free  Air 
Passed  per  Minute  When 
Compressed  to  60  Lb. 
Above  the  Atmosphere. 

Cubic  Feet  of  Free  Air 
Passed  per  Minute  When 
Compressed  to  80  Lb. 
Above  the  Atmosphere. 

Loss  of  Pressure. 
Pounds. 

Cubic  Feet  of  Free  Air 
Compressed  to  60  Lb. 

Cubic  Feet  of  Free  Air 
Compressed  to  80  Lb. 

Loss  of  Pressure. 
Pounds. 

Cubic  Feet  of  Free  Air 
Compressed  to  60  Lb. 

Cubic  Feet  of  Free  Air 
Compressed  to  80  Lb. 

1 

3.28 

.1435 

6 

7 

.0794 

23 

29 

.0574 

32 

41 

2 

6.56 

.6405 

12 

15 

.3050 

46 

59 

.2562 

65 

82. 

3 

9.84 

1.4545 

18 

22 

.7216 

69 

88 

.5818 

97 

124 

4 

13.12 

2.5620 

24 

29 

1.2566 

93 

117 

1.0248 

130 

165 

5 

16.40 

3.9345 

29 

37 

1.9642 

116- 

146 

1.5738 

163 

207 

6 

19.68 

5.4225 

35 

44 

2.7120 

139 

175 

2.1690 

195 

247 

8 

26.24 

10.2480 

47 

59 

5.0264 

185 

234 

4.0992 

260 

330 

10 

32.80 

15.7380 

59 

74 

7.8568 

232 

294 

6.2952 

326 

413 

3"  Pipe. 

4"  Pipe. 

5"  Pipe. 

1 

3.28 

.0463 

48 

60 

.0347 

86 

109 

.0287 

134 

169 

2 

6.56 

.2092 

96 

121 

.1525 

172 

217 

.1281 

268 

239 

3 

9.84 

.4880 

144 

182 

.3608 

258 

326 

.2909 

402 

509 

4 

13.12 

.8381 

193 

243 

.6283 

343 

436 

.5124 

537 

678 

5 

16.40 

1.3176 

241 

304 

.9821 

429 

544 

.7869 

671 

844 

6 

19.68 

1.8080 

289 

364 

1.3560 

515 

653 

1.0845 

805 

1,017 

8 

26.24 

3.3525 

386 

486 

2.5132 

687 

871 

2.0496 

1,073 

1,357 

10 

32.80 

5.2704 

480 

607 

3.9284 

859 

1,088 

3.1476 

1,342 

1,696 

6"  Pipe. 

8"  Pipe. 

10"  Pipe. 

3.28 

.0232 

193 

244 

.0173 

343 

434 

.0143 

537 

680 

2 

6^56 

.1046 

386 

488 

.0762 

687 

864 

.0640 

1,073 

1,359 

3 

9.84 

.2440 

579 

633 

.1805 

1,030 

1,303 

.1455 

1,610 

2,039 

4 

13.12 

.4190 

772 

977 

.3141 

1,373 

1,736 

.2562 

2,146 

2,719 

5 

16.40 

.6588 

965 

1,221 

.4910 

1,717 

2,171 

.3934 

2,683 

3,399 

5 

19.68 

.9040 

1,158 

1,466 

.6780 

2,060 

2,605 

.5423 

3,220 

4,079 

8 

26.24 

1.6762 

1,544 

1,954 

1.2556 

2,747 

3,473 

1.0248 

4,293 

5,438 

10 

32.80 

.2.6352 

1,931 

2,443 

1.9642 

3,434 

4,342 

1.5738 

5,367 

6,798 

The  resistance  is  not  varied  by  the  pressure,  only  so  fer  as  changes  in 
pressure  vary  the  velocity.  It  increases  about  as  the  square  of  the  velocity , 

an E^ows^ho^  leaks  in  pipes  all  tend  to  reduce  the  pressure  in 

addition  to  the  losses  given  in  the  table. 


ELECTRICITY. 


203 


Table  of  Loss  by  Friction  in  Elbows. 


An  elbow  with  a radius 
as  can  be  made. 

Radius  of  elbow,  5 diams. 
Radius  of  elbow,  3 diams. 
Radius  of  elbow,  2 diams. 
Radius  of  elbow,  H diams. 
Radius  of  elbow,  H diams. 
Radius  of  elbow,  1 diam. 
Radius  of  elbow,  f diam. 
Radius  of  elbow,  £ diam. 


of  one-half  the  diameter  of  the  pipe  is  as  short 

Equivalent  length  of  straight  pipe,  7.85  diams. 
Equivalent  length  of  straight  pipe,  8.24  diams. 
Equivalent  length  of  straight  pipe,  9.03  diams. 
Equivalent  length  of  straight  pipe,  10.36  diams. 
Equivalent  length  of  straight  pipe,  12.72  diams. 
Equivalent  length  of  straight  pipe,  17.51  diams. 
Equivalent  length  of  straight  pipe,  35.09  diams. 
Equivalent  length  of  straight  pipe,  121.20  diams. 


ELECTRICITY. 


. PRACTICAL  UNITS. 

In  electrical  work  it  is  necessary  to  have  units  in  terms  of  which  to 
express  the  different  quantities  entering  into  calculations.  The  four  most 
important  of  these  are  used  to  express  strength  of  current;  electrical  pressure , 
or  electromotive  force;  resistance;  power.  . 

The  strength  of  current  bowing  in  a wire  may  be  measured  in  several 
wavs.  If  a compass  needle  be  held  under  or  over  a wire,  it  will  be  deflected 
and  will  tend  to  stand  at  right  angles  to  the  wire.  The  stronger  the  current, 
the  greater  the  deflection  of  the  needle.  If  the  wire  carrying  the  current  be 
cut  and  the  ends  dipped  into  a solution  of  silver  nitrate,  silver  will  be 
deposited  on  the  end  of  the  wire  toward  which  the  current  is  flowing,  and 
the  amount  of  silver  deposited  in  a given  time  will  be  directly  proportional 
to  the  average  strength  of  current  flowing  during  that  time.  When  the 
current  flowing  in  a wire  is  spoken  of,  the  strength  of  the  current  is  meant. 

Unit  Strength  of  Current.— The  unit  used  to  express  the  strength  of  a cur- 
rent is  called  the  ampere.  If  a current  of  1 ampere  be  sent  through  a bath 
of  silver  nitrate,  .001118  gram  of  silver  will  be  deposited  per  second.  The 
expression  of  the  flow  of  current  through  a wire  as  so  many  amperes  is 
analogous  to  the  expression  of  the  flow  of  water  through  a pipe  as  so  many 
gallons  per  second. 

Electromotive  Force.— In  order  that  a current  may  flow  through  a wire, 
there  must  be  an  electrical  pressure  of  some  kind  to  cause  the  flow.  In 
hydraulics,  there  must  always  be  a head  or  pressure  before  water  can  be 
made  to  flow  through  a pipe.  It  is  also  evident  that  there  may  be  a pressure 
or  head  without  there  being  any  flow  of  water,  because  the  opening  in  the 
pipe  might  be  closed;  the  pressure  would,  however,  exist,  and,  as  soon  as 
the  valve  closing  the  pipe  was  opened,  the  current  would  flow.  In  the 
same  way,  an  electrical  pressure  or  electromotive  force  (usually  written 
E.  M.  F.)  may  exist  in  a circuit,  but  no  current  can  flow  until  the  circuit  is 
closed  or  until  the  wire  is  connected  so  that  there  will  be  a path  for  the 
current. 

Unit  Electromotive  Force  (E.  M.  F.).— The  practical  unit  of  electromotive 
force  is  the  volt.  It  is  the  unit  of  electrical  pressure,  and  fulfils  somewhat 
the  same  purpose  as  “pounds  per  square  inch”  in  hydraulic  and  steam 
engineering.  The  E.  M.  F.  furnished  by  an  ordinary  cell  of  a battery  usually 
varies  from  .7  to  2 volts.  A Daniell  cell  gives  an  E.  M.  F.  of  1.072  volts.  A 
pressure  of  500  volts  is  generally  used  for  street-railway  work,  and,  for  incan- 
descent lighting,  1 10  volts  is  common. 

Resistance.— All  conductors  offer  more  or  less  resistance  to  the  flow  of  a 
current  of  electricity,  just  as  water  encounters  friction  in  passing  through  a 
pipe.  The  amount  of  this  resistance  depends  on  the  length  of  the  wire,  the 
diameter  of  the  wire,  and  the  material  of  which  the  wire  is  composed.  The 
resistance  Of  all  metals  also  increases  with  the  temperature. 

Unit  of  Resistance  — The  practical  unit  of  resistance  is  the  ohm.  A con- 
ductor has  a resistance  of  1 ohm  when  the  pressure  required  to  set  up 
1 ampere  through  it  is  1 volt.  In  other  words,  the  drop , or  fall,  in  pressure 
through  a resistance  of  1 ohm,  when  a current  of  1 ampere  is  flowing, 
is  1 volt.  1,000  ft.  of  copper  wire  .1  in.  in  diameter  has  a resistance  ot 
nearly  1 ohm  at  ordinary  temperatures- 


204 


ELECTRICITY. 


Ohm’s  Law.— The  law  governing  the  flow  of  current  in  an  electric  circuit 
was  first  stated  by  Dr.  G.  S.  Ohm,  and  is  known  as  Ohm's  law.  This  law  has 
since  stood  the  test  of  exhaustive  experiment,  and  has  been  found  correct. 
Ohm’s  law  may  be  briefly  stated  as  follows:  The  strength  of  the  current  in 

any  circuit  is  directly  proportional  to  the  electromotive  force  in  the  circuit , and 
inversely  proportional  to  the  resistance  of  the  circuit. 

This  means  that  if  the  resistance  of  a circuit  were  fixed,  and  the  E.  M.  F, 
varied,  the  current  would  be  doubled  if  the  E.  M.F.  were  doubled.  Also,  if 
the  E.  M.  F.  were  fixed,  and  the  resistance  doubled,  the  current  would  be 
halved. 

Let  E = electromotive  force  in  volts; 

R = resistance  in  ohms; 

C = current  in  amperes. 


Then,  C = -=,  or  R = — , or  E = C R. 

R C 

The  last  two  forms  are  useful  in  many  cases  where  the  usual  form 
E 

C — -==  is  not  directly  applicable. 

R 

Example. — A dynamo  D which  generates  110  volts,  is  connected  to  a coil 
of  wire  C,  Fig.  1,  which  has  a resistance  of  20  ohms;  what  current  will 
flow,  supposing  the  resistance  of  the  rest  of  the  circuit  to  be  negligible  ? 

We  have  E = 110  volts;  R — 20  ohms;  hence,  C = ^ = 5.5  amperes. 


were  8 amperes  and  the  E.  M.  F.  of  the  dynamo  110  volts,  the  resistance  of 
the  circuit  must  be 


Tf  lift 

R = ^;  R = ~ = 13.75  ohms. 
C o 


Electrical  Power.— The  electrical  power  expended  in  any  circuit  is  found 
by  multiplying  the  current  flowing  in  the  circuit  by  the  pressure  required 
to  force  the  current  through  the  circuit.  In  other  words,  W = E C;  where 
W is  the  power  expended,  E is  the  E.  M.  F.,  and  C is  the  current.  When  E 
is  expressed  in  volts  and  C in  amperes,  then  W is  expressed  in  watts.  The 
watt  is  the  unit  of  electrical  power,  and  is  equal  to  the  power  developed 
wThen  1 ampere  flows  under  a pressure  of  1 volt.  The  watt  is  equal  to 
horsepower.  We  have,  then,  the  following  general  relations: 

Let  E = electromotive  force  in  volts; 

C = current  in  amperes; 

R = resistance  in  ohms; 

W — power  in  watts; 

H.  P.  = horsepower. 

Then,  W = E C,  but  E = C R;  hence,  W = C2  R.  That  is,  the  power  in 
watts  expended  in  any  conductor  of  which  the  resistance  is  R,  and  through 
which  a current  C is  flowing,  is  equal  to  the  product  of  the  squares  of  the 
current  and  the  resistance.  The  energy  used  in  forcing  a current  through 
the  wire  reappears  in  the  form  of  heat;  hence,  we  may  say  that  the  heating 
effect  of  a current  flowing  in  a conductor  is  proportional  to  the  square  of  the 
current.  From  the  preceding,  we  also  have 


np_!i  = I 
I 746  746' 

This  relation  is  very  useful  for  calculating  power  in  terms  of  electrical 
units  The  watt  is  too  small  a unit  for  convenient  use  in  many  cases,  so 
that  the  kilowatt,  or  1,000  watts,  is  frequently  used.  This  is  sometimes 
abbreviated  to  K.W, 


CIRCUlfS. 


205 


The  Unit  of  Work  Is  the  Watt-Hour.— This  is  the  total  work  done  when  1 watt 
is  expended  for  1 hour.  For  example,  if  a current  of  1 ampere  were  made  flow 
for  1 hour  through  a resistance  of  1 ohm,  the  total  amount  of  work  done  would 
be  1 watt-hour.  A kilowatt-hour  is  the  total  work  done  when  1 kilowatt  is 
expended  for  1 hour.  It  is  about  equivalent  to  1}  horsepower  for  1 hour. 

ELECTRICAL  EXPRESSIONS  AND  THEIR  EQUIVALENTS. 

{Arranged  for  Convenient  Reference  by  C.  W.  Hunt.) 


One 

Watt 


f A rate  of  doing  work. 

1.  ampere  per  sec.  at  one  volt. 
.7373  foot-pound  per  second. 
44.238  foot-pounds  per  minute. 

^ 2,654.28  foot-pounds  per  hour. 
.5027  mile-pound  per  hour. 
.00134  horsepower. 

755  horsepower. 


One 

Kilowatt 


A rate  of  doing  work. 

737.3  foot-pounds  per  second. 
44,238.  foot-pounds  per  minute. 
502.7  mile-pounds  per  hour. 
1.34  horsepower. 


One 

Horse- 

power 


r A rate  of  doing  work. 

I 550.  foot-pounds  per  second. 

! 33,000.  foot-pounds  per  minute. 

\ 375.  mile-pounds  per  hour, 

i 746.  watts. 

L .746  kilowatt. 


One 

Watt- 

Hour 


One 

Horse- 

POWKR- 

Hour 


1A  quantity  of  work. 

2,654.28  foot-pounds. 

503  mile-pound. 

1.  ampere  hour  X one  volt. 

.00134  horsepower-hour, 
horsepower-hour. 

r A quantity  of  work. 

I 1,980,000.  foot-pounds. 

375.  mile-pounds. 

! 746.  watt-hour. 

I .746  kilowatt-hour. 


One 

Ampere- 

Hour 


A quantity  of  current. 

One  ampere  flowing  for  one  hour, 
irrespective  of  the  voltage. 
Watt-hour  -5-  volts. 


r Force  moving  in  a circle. 

Torque  ^ A force  of  one  pound  at  a radius  of 
t one  foot. 


CIRCUITS. 

The  path  through  which  a current  flows  is  generally  spoken  of  as  an 
electric  circuit.  This  path  may  be  made  up  of  a number  of  different  parts. 
For  example,  the  line  wires  may  constitute  part  of  the  circuit,  and  the 
remainder  may  be  composed  of  lamps,  motors,  resistances,  etc.  In  practice, 


the  two  kinds  of  circuits  most  commonly  met  with  are  (1)  those  in  which  the 
different  parts  of  the  circuit  are  connected  in  series;  (2)  those  in  which 
the  different  parts  of  the  circuit  are  connected  in  multiple  or  parallel. 

1.  Series  Circuits.— In  this  kind  of  circuit,  all  the  component  parts  are  con- 
nected in  tandem,  so  that  the  current  flowing  through  one  part  also  flows 


206 


ELECTRICITY. 


through  the  other  parts.  Fig.  2(a)  represents  such  a circuit  made  up  of  a 
different  number  of  parts.  The  current  leaves  the  dynamo  D at  the  + side 
and  flows  through  the  arc  lamps  aaaa , thence  through  the  incandescent 
lamps  1 1 1,  thence  through  the  motor  m and  resistance  r,  back  to  the  dynamo, 
thus  making  a complete  circuit.  All  these  different  parts  are  here  connected 
in  series,  so  that  the  current  flowing  through  each  of  the  parts  #nust  be  the 
same  unless  leakage  takes  place  across  from  one  side  of  the  circuit  to  the 
other,  and  this  would  be  impossible  if  the  lines  were  properly  insulated. 
The  pressure  furnished  by  the  dynamo  must  evidently  be  the  sum  of  the 
pressures  required  to  force  the  current  through  the  different  parts,  /the 
most  common  use  of  this  system  is  in  connection  with  arc  lamps.  These 
lamps  are  usually  connected  in  series,  as  shown  in  Fig.  2 (&).  The  objections 
to  this  system  of  distribution  for  general  work  are  that  the  breaking  of  the 
circuit  at  any  point  cuts  off  the  current  from  all  parts  of  the  circuit;  also 
the  pressure  generated  by  the  dynamo  has  to  be  very  high  if  many  pieces  of 
apparatus  are  connected  in  series.  In  such  a system,  the  dynamo  is  pro- 
vided with  an  automatic  regulator  that  increases  or  decreases  the  voltage : of 
the  machine,  so  that  the  current  in  the  circuit  is  kept  constant,  no  matter 
how  many  lamps  or  other  devices  are  in  operation.  For  this  reason,  such 
circuits  are  often  spoken  of  as  constant-current  circuits.  . 

2 Parallel  Circuits.— In  this  type  of  circuit,  the  different  pieces  of  appa- 
ratus are  connected  side  by  side,  or  in  parallel,  across  the  mam  wires  from 
the  dynamo,  as  shown  in  Fig.  2 (c).  In  this  case,  the  dynamo  D supplies 
current  through  the  mains  to  the  arc  lamps  a,  incandescent  lamps  J and 
motor  m.  This  system  is  more  widely  used,  and  it  will  be  seen  at  once  from 
the  figure  that  the  breaking  of  the  circuit  through  any  one  piece  of  apparatus 
will  not  prevent  the  current  from  flowing  through  the  other  parts.  Incan- 
descent lamps  are  connected  in  this  way  almost  exclusively.  The  lamps  are 
connected  directly  across  the  mains,  as  shown  in  Fig.  2 (d).  Street  cars  and 
mining  locomotives  are  operated  in  the  same  way,  the  trolley  wire  consti- 
tuting one  main  and  the  track  the  other,  as  shown  in  Fig.  2(e).  By  adopting 
this  system,  any  car  can  move  independently  of  the  others,  and  the  current 
mav  be  turned  off  and  on  at  will.  In  all  these  systems  of  parallel  distribu- 
tion the  pressure  generated  by  the  dynamo  is  maintained  constant,  no  matter 
what  current  the  dynamo  may  be  delivering.  For  example,  m the  lamp 
svstem  Fig-  2 (d).  the  dynamo  would  maintain  a constant  E.  M.  J?.  ot  110 
volts.  ’Each  lamp  has  a fixed  resistance,  and  will  take  a certain  current 

amperes^  when  connected  across  the  mains.  As  the  lamps  are  turned 

on  the  current  delivered  by  the  dynamo  increases,  the  pressure  remaining 
constant.  In  street-railway  work,  the  pressure  between  trolley  and  track  is 
kept  in  the  neighborhood  of  500  volts,  the  current  varying  with  the  number 
of  cars  in  operation.  In  mine-haulage  plants,  the  pressure  is  usually  250  or 
500  volts,  the  former  being  generally  preferred  as  being  less  dangerous. 
Lamps  may  also  be  connected  in  series  multiple,  as  shown  in  Fig  2 (c). 
Here  the  two  125-volt  lamps  1 1 are  connected  m series  across  the  250-volt 
circuit.  Such  an  arrangement  is  frequently  used  in  mines  when  lamps  are 

circuits1  a s those  just  described  are  called  constant-potential  or  con- 
stant-pressure circuits,  to  distinguish  them  from  the  constant-current  circuit 
mentioned  previously.  

RESISTANCES  IN  SERIES  AND  MULTIPLE. 

Resistances  in  Lines.— If  two  or  more  resistances  are  connected  in  series, 
Fiff  2 ( f ) their  total  combined  resistance  is  equal  to  the  sum  of  their  sepa- 
rate resistances.  If  R equal  total  combined  resistance,  and  RUR>,  Rs  are  the 
separate  resistances  connected  in  series,  then,  R = -Ri  + ^ . nhTT1 

Example.— If  the  separate  resistances  were  Ri  = 10  ohms,  i?2  — 1 ohm, 
and  = 30  ohms,  then  these  three  combined  would  be  equivalent  to  a 

^"Rlthtancerin  “pVralleK-lf  a=numbeTof  resistances  are . connected  in 
parallel  the  reciprocal  of  their  total  combined  resistance  is  equal  to  the 
sum  of  the  reciprocals  of  the  separate  resistances.  In  Fig.  2 (g),  three  resist- 
ances are  shown  connected  in  parallel.  It  is  evident  that  the  total  resistance 
of  such a Combination  must  be  lower  than  that  of  the  lowest  resistance 
entering  into  the  combination.  If  the  resistances  m this  case  were  all  equal, 


ELECTRIC  WIRING. 


207 


the  resistance  of  the  three  combined  would  be  one-third  the  resistance  of 
one  of  them,  because  a current  passing  through  the  three  combined  could 
split  up  between  three  equal  paths,  instead  of  having  only  one  path  to  pass 
through.  If  R represents  the  combined  resistance,  and  Ru  R2 , and  R3  the 
separate  resistances,  the  following  relation  is  true: 

+ -L  + JL 

R Ri  R2  R& 


from  which 


R = 


R\  Ro  R$ 


R2  Rz  + Lti  R,i  + Ri  R-z  13  R 

If  the  three  resistances  were  all  equal,  we  would  have  or  R = 

Example.— Three  resistances  of  3,  10,  and  5 ohms  are  connected  in  par- 
allel. What  is  their  combined  resistance?  We  have 


l = i+s  + i-orie  = 


150 


50  + 15  + 30 


150 

95 


1.58  ohms. 


Shunt.— When  one  circuit  B,  Fig.  2(h),  is  connected  across  another  A,  so 
as  to  form,  as  it  were,  a by-pass,  or  side  track,  for  the  current,  such  a circuit 
is  called  a shunt,  or  it  is  said  to  be  in  shunt  with  the  other  circuit. 


ELECTRIC  WIRING  (CONDUCTORS). 

Materials.— Practically  all  conductors  used  in  electric  lighting  or  power 
work  are  of  copper,  this  metal  being  used  on  account  of  its  low  resistance. 
Iron  wire  is  used  to  some  extent  for  conductors  in  telegraph  lines,  and  steel 
is  largely  used  as  the  return  conductor  in  electric-railway  or  haulage  plants 
wherti  the  current  is  led  back  to  the  power  station  through  the  rails.  The 
resistance  of  iron  or  steel  varies  from  six  to  seven  times  that  of  copper, 
depending  on  the  quality  of  the  metal.  Aluminum  is  coming  into  use  as  a 
material  for  conductors,  and  in  future  may  play  an  important  part  in  electric 
transmission.  It  is  so  much  lighter  than  copper  that  it  is  able  to  compete 
with  it  as  a conductor,  even  though  its  cost  per  pound  is  higher  and  its 

conductivity  only  about  6(K  that  of  copper. 

Forms  of  Conductors.— Most  of  the  conductors  used  are  m the  form  of 
copper  wire  of  circular  cross-section.  Conductors  of  large  cross-section  are 
made  up  of  a number  of  strands  of  smaller  wire  twisted  together.  For 
electrolytic  plants,  copper-refining  plants,  etc.,  copper  bars  of  rectangular 
cross-section  are  frequently  used.  . A . . , . 

Wire  Gauge.— The  gauge  most  generally  used  in  America  to  designate 
the  different  sizes  of  copper  wire  is  the  American,  or  Brown  & Sharpe 
(B  & S.).  The  sizes  as  given  by  this  gauge  range  from  No.  0000,  the 
largest  460  in.  diameter,  to  No.  40,  the  finest,  .003  in.  diameter.  Wire 
drawn ’to  the  sizes  given  by  this  gauge  is  always  more  readily  obtained 
than  sizes  according  to  other  gauges;  hence,  in  selecting  line  wire  for 
anv  purpose  it  is  always  desirable,  if  possible,  to  give  the  size  required  as 
a wire  of  the  B.  & S.  gauge.  A wire  can  usually  be  selected  from  this  gauge, 
which  will  be  verv  nearly  that  required  for  any  specified  case.  . 

Estimation  of  Cross-Section  of  Wires.— The  diameter  of  round  wires  is 
usually  given  in  the  tables  in  decimals  of  an  inch,  and  the  area  of  cross- 
section  is  given  in  terms  of  a unit  called  a circular  mil.  This  is  done  simply 
for  convenience  in  calculation,  as  it  makes  calculations  of  the  cross-section 
much  simpler  than  if  the  square  inch  were  used  as  the  unit  area.  A mil 
is  i of  an  inch,  or  .001  in.  A circular  mil  is  the  area  (in  decimals  of  a 
square  inch)  of  a circle,  the  diameter  of  which  is  in.,  or  1 mil.  The 

circular  mil  is  therefore  equal  to  (.001)2  = .0000007854  sq.  in. 

If  the  diameter  of  the  conductor  were  1 in.,  its  area  would  be  .7854  sq.  in.,. 

and  the  number  of  circular  mils  in  its  area  would  -be  0000007^54  = 1,000,000; 

but  1 in.  = 1,000  mils,  and  (1,000)2  = 1,000,000;  hence  the  following  is  true: 
CM  — d-\  or  the  area  of  cross-section  of  a wire  in  circular  mils  is  equal  to  the 

square  of  its  diameter  expressed  in  mils.  . . 

Example.— A wire  has  a diameter  of  .101  in.  What  is  its  area  in  circular 
^llOlin.  = 101  mils.  Hence,  CM  = (101)2  = 10,201. 


vide 

imbt 

>lum 

R0P1 

cj 

be 

u 3 

<V  <3 

|qd 

PQ 

0000 

000 

00 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 


ELECTRICITY. 


table  gives  the  dimensions,  weight,  and  resistance  of  pure 
6 weights  given  are,  of  course,  for  bare  wire.  The  first 
B.  & S.  gauge  number,  the  second  the  diameter  in  mils, 
inches  would  be  the  number  as  given  in  this  column, 
The  third  column  gives  the  area  in  circular  mils,  the 
olumn  being  equal  to  the  squares  of  those  in  the  second 
e carrying  capacity  is  also  given. 

Iopper  Wire.  American,  or  Brown  & Sharpe,  Gauge. 


Area  in  Circular 
Mils.  C.  M.  - d2. 

Weight. 

Pounds. 

Resistance  per 
1,000  Ft. 
International 
Ohms.  68°  F. 

Current  Capacity 
(Amperes). 
National  Board 
Fire  Underwriters. 

Per 

1,000  Ft. 

Per 

Mile. 

Weath- 

er-Proof. 

Rubber- 

Covered. 

211,600.0 

640.50 

3,381.4 

.0489 

312 

210 

167,805.0 

508.00 

2,682.2 

.0617 

262 

177 

133^079.4 

402.80 

2,126.8 

.0778 

220 

150 

105,534.5 

319.50 

1,686.9 

.0981 

185 

127 

83,694.2 

253.30 

1,337.2 

.1237 

156 

107 

66,373.0 

200.90 

1,060.6 

.1560 

131 

90 

52;  634.0 

159.30 

841.1 

.1967 

110 

76 

41,742.0 

126.40 

667.4 

.2480 

92 

65 

33,102.0 

100.20 

529.1 

.3128 

77 

54 

26,250.5 

79.46  I 

419.5 

.3944  j 

65 

46 

20,816.0 

63.02  1 

332.7 

.4973  1 

46 

33 

16,509.0 

49.98 

263.9 

.6271  1 

13.094.0 

39.63 

209.2 

• .7908 

32 

24 

10,381.0 

31.43 

165.9 

.9972 

8,234.0 

24.93 

131.6 

1.257 

23 

6,529.9 

19.77 

104.4 

1.586 

17 

5,178.4 

15.68 

82.8 

1.999 

12 

4,106.8 

12.43 

76.2 

2.521 

16 

3,256.7 

9.86 

52.0 

3.179 

8 

2,582.9 

7.82 

41.3 

4.009 

6 

2,048.2 

6.20 

32.7 

5.055 

1,624.3 

4.92 

25.9 

6.374 

5 

3 

1,288.1 

3.90 

20.6 

8.038 

1,021.5 

3.09 

16.3 

10.14 

810.1 

2.45 

12.9 

12.78 

642.4 

1.94 

10.3 

16.12 

509.4 

1.54 

8.1 

20.32 

404.0 

1.22 

6.4 

25.63 

320.4 

.96 

5.1 

32.31 

254.1 

.76 

4.0 

40.75 

201.5 

.61 

3.2 

51.38 

159.7 

.48 

2.5 

64.79 

126.7 

.38 

2.0 

81.7 

100.5 

.30 

1.6 

103.0 

79.70 

.24 

1.27 

129.9 

63.21 

.19 

1.01 

163.8 

50.13 

.15 

.801 

206.6 

39.75 

.12 

.635 

1 260.5 

31.52 

.095 

.504 

328.4 

25.00 

.075 

.400 

1 414.2 

19.83 

.060 

.317 

' 522.2 

15.72 

.047 

.251 

658.5 

12.47 

.038 

.190 

► 830.4 

9.89 

.030 

.15£ 

1 

; 1,047.0 

ELECTRIC  WIRING . 


209 


The  following  table  gives  a comparison  of  the  properties  of  aluminum 
and  copper: 

Comparison  of  Properties  of  Aluminum  and  Copper. 


Aluminum. 

Copper. 

Conductivity  (for  equal  sizes) 

Weight  (for  equal  sizes) - 

Weight  (for  equal  length  and  resistance).... 
Price  (per  pound)  aluminum,  29  cents;  cop- 

per,  16  cents  (bare  wire) 

Price  (equal  length  and  resistance,  bare 

.54  to  .63 
.33 
.48 

1.81 

.868 

.002138 

18.73 

2.5  to  2.68 

1 

1 

1 

1 

1 

1 

.002155 

10.5 

8.89  to  8.93 
1 

Temperature  coefficient  per  degree  F 

Resistance  of  mil-foot  (20°  C.) 

Cnnnififi  crfiivitv  

opt3CXX10  gXdVXl^ 

Breaking  strength  (equal  sizes) 

In  case  a conductor  larger  man  uuu  given  m ^ A 

stranded  cables  are  used.  These  are  made  m various  sizes.  The  table 
below  gives  some  of  the  more  common  sizes,  with  their  allowable  current 
capacity. 

Carrying  Capacity  of  Cables. 


I 

Area. 

Current. 

Amperes. 

Area. 

Circular 

Mils. 

Current. 

Amperes. 

Circular 

Mils. 

Exposed. 

Concealed. 

Exposed. 

Concealed. 

200,000 

299 

200 

1,200,000 

1,147 

715 

300,000 

405 

272 

1,300,000 

1,217 

756 

400,000 

503 

336 

1,400,000 

1,287 

796 

500,000 

595 

393 

1,500,000 

1,356 

835 

600,000 

682 

445 

1,600.000 

1,423 

873 

700,000 

765 

494 

1,700,000 

1,489 

910 

800,000 

846 

541 

1,800,000 

1,554 

946 

900,000 

924 

586 

1,900,000 

1,618 

981 

1,000,000 

1,000 

630 

2,000,000 

1,681 

1,015 

1,100,000 

1,075 

673 

Estimation  of  Resistance.— The  resistance  ot  any  conductor  is  directly  pro- 
portional to  its  length,  and  inversely  proportional  to  its  area' of  cross-sec- 
tion, or  R = K j,  where  K is  a constant.  If  L is  expressed  in  feet  and 

A is  expressed  in  circular  mils,  then  the  constant  K must  be  the  resistance 
of  a foot  of  the  wire  in  question  of  1 circular  mil  cross-section.  The  resist- 
ance of  1 mil-foot  of  copper  wire  at  75°  F.  is  about  10.8  ohms.  Hence, 

for  copper  wire,  we  have  R = 1^4 but  A = <P  when  d is  the  diameter 


^ but  A 

, . r)  10.8  L 

in  mils;  hence,  we  also  have  R = — • 

This  formula  is  easily  remembered,  and  is  very  convenient  for  estimating 
the  resistance  of  any  length  of  wire  of  given  diameter  when  a wire  table  is 
not  at  hand,  or  when  the  diameter  of  the  given  wire  does  not  correspond  to 
flnvthinsr  given  in  the  table.  . ^ . . _. 

EXAMPLE.-Find  the  resistance  of  1 mile  of  copper  wire  .20  m.  m diameter. 
1 mile  = 5 280  ft.  .20  in.  = 200  mils.  Area  of  cross-section  = (200)2  =* 
l mue  _ 10 .8  X L 10.8  X 5,280  _ i „0 

40,000  circular  mils.  Hence,  R — — 1,42  oiims* 


<P 


40,000 


210 


electricity. 


CALCULATION  OF  WIRES  FOR  ELECTRIC  TRANSMISSION. 

Direct-Current  Circuits.— No  matter  how  large  a wire  may  be,  some  energy 
must  always  be  expended  in  forcing  a current  through  it,  because  no  con- 
ductor can  be  entirely  devoid  of  resistance.  It  is  true  that  the  loss  may  be 
made  as  small  as  we  please  by  using  a very  large  conductor  but  m practice, 
this  would  not  pay,  because  the  interest  on  the  cost  of  the  copper  would 
more  than  counterbalance  the  gain  in  the  efficiency  of  transmission.  In 
starting  out,  then,  to  estimate  the  size  of  wire  to  transmit  a given 
of  power  over  a given  distance,  one  of  the  first  things  to  be  decided  is  the 
amount  of  power  that  may  be  allowed  for  loss  m the  line,  because  it  is  evi- 
dSit  that  the  greater  the  power  lost,  the  higher  may  be  the  line  resistance 
and  hence  the  smaller  the  wire.  The  pressure  required  to  force  a current 
C through  a wire  of  resistance  R is  C X R-  This  pressure  is  generally  spoken 
of  as  the  drop , for  the  reason  that  the  pressure  necessary  to  set  up  thecurrent 
through  the  line  is  lost,  and,  consequently,  the  pressure  falls  off  or  drops 
from  tke  dynamo  to  the  receiving  end  of  the  line.  In  all  cases,  the  pressure 
at  the  end  of  the  line,  or  point  where  the  power  is  delivered,  is  equal  to  the 
nressure  at  the  dynamo  less  the  drop  in  the  line,  and  conversely,  the  pres- 
sure that  must  be  maintained  by  the  dynamo  m order  to  obtain  a given 
nressure  at  the  end  will  be  equal  to  the  pressure  at  the  receiving  end  plus 
the  drop  in  the  line.  To  illustrate  the  above,  take  the  case  shown  m Fig.  3, 
where  a dynamo  D supplies  current  to  a motor  if  situated  1 mile  distant. 
Tn  order  that  the  motor  may  operate  properly,  the  pressure  at  its  terminals 
must be kept 'constant  at,  say',  50&  volts  It  “entt^ 
between  a and  b (the  dvnamo  terminals)  must  be  more  than  500  volts,  bj  the 
drop  o?  pressure  necessary  to  force  the  current  through  the  line  If  the 
motor  is  taking  very  little  current,  i.  e.,  if  it  is  running  on  a very  light  load, 
the  current  will  be  small,  and  hence  the  drop  in  the  line  will  be  small.  In 
order  then  that  the  pressure  at  the  motor  may  remain  constant,  or  nearly 

!^jtrS^ee:ly\n 

present,  we  are  concerned  only  with  the  caleuhttionof  The  toe 

with  regard  to  the  maximum 
current  it  has  to  carry.  We 
will  suppose,  for  the  sake  of 
illustration,  that  the  motor 
takes  50  amperes  at  full  load 
and  that  the  line  wire  is  of 
such  size  that  it  has  a resist- 
ance of  .2  ohm  per  mile.  The 
current  has  to  pass  through  2 
miles  of  wire  (because  it  has 
to  flow  out  through  1 mile  and 
back  through  1 mile),  and 
hence  encounters  a resistance 
of  .4  ohm.  The  drop  in  the 
line  will  then  be  .4  X 50  = 20  volts,  and  in  order  to  obtain  a pressure  of 
500*volts  at  the  motor,  the  pressure  at  the  dynamo  would  have  to  be  520 
volts  The  loss  of  power  in  the  line  would  be  current  X drop  — 50  X 20  — 
1 000  watts  or  about  U horsepower.  The  drop  in  an  electrical  transmission 
line  iJ analogous  to  the  loss  in  pressure  due  to  the  friction  encountered 

size  of  wire  were  used  such  that  its 
resistance  would  be  .1  ohm  per  mile,  it  is  evident  that  the  loss  in  the  line 
would  be  halved,  but  the  weight  of  copper  required  doubled,  because  the 
wire  would  have  to  be  double  the  cross-section.  The  question  as  to  whether 
it  would  pay  better  to  invest  more  money  m the  line  or  to  put  up  with  the 
larger  loss  is  something  that  must  be  determined  m each  case  by  the  relative 

C0SIn0manyecaase^  the^oss  allowed  in  the  line  is  about 10*  of  the  power to  be 
delivered,  though  sometimes  the  loss  may  be  allowed  to  run  as  high  as  15$ 
or  25^  This  applies  only  to  transmission  lines.  For  local  electric-hght  or 
power-distributing  systems,  the  amount  of  drop  allowed  is  usually  about  2$ 
for  the  former  and  5$  for  the  latter. 

f The  problem  of  calculating  line  wires  usually  presents  itself  in  the 
following  form:  Given,  a certain  amount  of  power  to  transmit  over  a known 


CALCULATION  OF  WIRE. 


211 


distance  with  a certain  allowable  loss,  to  determine  the  cross-section  of  the 
wire  required. 

Let  P = power  to  be  delivered,  expressed  in  watts;  P will  be  equal 
to  horsepower  delivered  at  end  of  line  multiplied  by  746; 

</o  — allowable  percentage  of  loss  in  line,  i.  e.,  percentage  of 
power  delivered  that  may  be  lost  in  transmission; 

E = voltage  at  end  of  line  where  power  is  delivered; 

C = current  at  full  load; 

L — length  of  wire  through  which  current  flows. 

The  cross-section  of  the  copper  conductor  will  then  be  given  by  the 
following  formula: 

. 10.8  X LX  <7X100 

A = e x :< ' (1) 

A will  be  expressed  in  circular  mils,  and  the  corresponding  size  of  wire 
may  be  found  by  consulting  the  wire  table.  It  should  be  noticed,  particu- 
larly, that  in  this  formula,  L is  the  average  length  of  conductor  through 
which  the  current  C flows.  The  application  of  distance  of  transmission  in 
the  formula  will  be  understood  Irom  what  follows. 

Example.— A mine  pump,  driven  by  an  electric  motor,  is  situated  2 miles 
from  the  power  station.  The  electrical  input  of  the  motor  at  full  load  is 
50  H.  P.,  and  the  voltage  at  its  terminals  is  to  be  500.  • Estimate  the  size  of 
line  wire  necessary  to  supply  the  motor,  the  allowable  loss  in  the  line  being 
15^6  of  the  power  delivered. 

The  actual  length  of  line  through  which  the  current  will  flow  will  be 
4 miles,  because  the  current  has  to  flow  out  to  the  motor  and  back  again. 
W e have 


watts  50  X 746 
~ E ~ 500 


Applying  formula  (1),  we  have 


74.6  amperes. 


10.8  X 2 X 2 X 5,280  X 74.6  X 100 
500  X 15 


226,880  circular  mils,  nearly. 


By  consulting  the  wire  table  it  is  found  that  this  calls  for  a wire  a little 
larger  than  No.  0000,  which  has  a cross-section  of  211,600  circular  mils; 
No.  0000  wire  would  probably  be  used  in  this  case,  as  it  is  near  enough  to  the 
calculated  size  for  all  practical  purposes.  In  case  the  calculated  size  comes 
out  larger  than  any  size  given  in  the  table,  a number  of  wires  may  be  used 
in  multiple  to  make  up  the  required  cross-section,  or,  what  is  better,  a 
stranded  cable  may  be  used.  These  heavy  stranded  cables  may  now  be 
obtained  in  different  sizes,  up  to  2,000,000  circular  mils  cross-section. 

It  is  evident  that,  in  the  above  examples,  if  it  were  allowable  to  waste 
twice  as  much  power  in  the  line,  or  what  is  equivalent  to  having  a line  drop 
of  150  volts  instead  of  75  volts,  the  cross-section  of  wire  required  would  have 
been  one-half  of  that  found  above.  Such  a large  amount  of  loss  would, 
however,  be  objectionable  unless  power  was  very  cheap.  A large  drop  in 
the  line  is  in  any  case  objectionable,  because  the  voltage  at  the  receiving 
end  of  the  circuit  will  fall  off  greatly  unless  the  voltage  at  the  generating 
station  is  raised,  as  the  load  comes  on,  in  order  to  compensate  for  the  line 
drop.  Most  of  the  uses  to  which  electricity  is  put,  in  mines  or  other  places, 
requires  that  the  pressure  at  the  point  where  the  power  is  utilized  shall  be 
kept  approximately  constant.  For  example,  in  the  case  of  incandescent 
lights,  the  lamps  will  fall  off  greatly  in  brightness  if  the  pressure  decreases 
even  by  a comparatively  slight  amount.  Also,  if  motors  are  being  operated, 
the  speed  will  vary  considerably  if  the  pressure  is  not  kept  constant,  and  it 
may  be  stated,  in  general,  that  a large  line  loss  tends  to  poor  regulation  at 
the  end  of  the  circuit  where  power  is  delivered. 

From  the  above  considerations,  it  will  be  seen  that,  in  the  majority  of 
cases,  the  size' of  wire  to  be  used  under  given  conditions  is  determined  by 
the  allowable  amount  of  drop.  In  some  cases,  however,  especially  if  the 
current  is  to  be  used  near  at  hand,  the  size  of  wire  so  determined  might  not 
be  large  enough  to  carry  the  current  without  overheating.  Of  course,  in 
such  cases,  the  safe  carrying  capacity  of  the  wire  determines  the  size  to  be 
used,  and  the  drop  will  be  correspondingly  less.  > 

The  amount  of  current  that  a given  wire  can  carry  without  overheating 
depends  very  largely  on  the  location  of  the  wire.  For  example,  a wire 
strung  in  the  open  air  will  carry  a greater  current,  with  a given  temperature 
rise,  than  the  same  wire  would  if  boxed  up  in  a molding  or  conduit.  The 


212 


ELECTRICITY. 


table  on  page  209  giyes  the  approximate  sate  carrying  capacity  of  wires 

when  strung  in  the  air.  , , 

In  order  to  keep  down  the  size  of  wire  required  to  transmit  a given 
amount  of  power  over  a given  distance,  with  a certain  allowable  loss,  the 
current  must  be  kept  as  small  as  possible.  Now,  for  a given  amount  of 
power  the  current  can  only  be  made  small  by  increasing  the  pressure, 
because  the  number  of  watts,  or  power  delivered,  is  equal  to  the  product  of 
the  current  and  the  pressure.  As  a matter  of  fact,  if  the  pressure  m any 
given  case  be  doubled,  the  amount  of  copper  required  will  be  only  one- 
fourth  as  great;  in  other  words,  for  a given  amount  of  power  transmitted, 
the  weight  of  copper  required  decreases  as  the  square  of  the  voltage.  It  is 
at  once  seen  then,  that  if  anv  considerable  amount  of  power  is  to  be  trans- 
mitted over  long  distances,  a high  line  pressure  must  be  used  or  else  the  cost 
of  copper  becomes  prohibitory:  The  use  of  high  pressures  m power  trans- 
mission will  be  taken  up  in  connection  with  alternating  currents. 

Insulated  Wires.— For  most  overhead  line  work  using  modern  voltages, 
weather-proof  insulated  wire  is  used.  This  wire  is  covered  with  two  or  three 
braids  of  cotton,  and  treated  with  insulating  compound.  For  inside  work 
and  in  places  where  a better  quality  of  insulation  is  required,  rubber-covered 
wires  are  used.  The  following  table  gives  the  approximate  weight  of 
weather-proof  line  wire.  The  cost  of  the  wire  per  pound  vanes  considerably 
owing  to  the  variations  in  the  price  of  copper;  about  18  cents  per  pound 
may  be  taken  as  an  approximate  figure  in  making  calculations. 

Weather-Proof  Line  Wire  (Roebling’s). 


Number. 

B.&S. 

Gauge. 

Double  Braid. 

Triple  Braid. 

Outside 
Diameter. 
32ds  Inch. 

Weight. 

Pounds. 

Outside  ; 
Diameter. 
32ds  Inch. 

Weight. 

Pounds. 

Per 

1,000  Ft.  ; 

Per 

Mile. 

Per  i 
1.000  Ft. 

Per 

Mile. 

0000 

20 

716 

3,781 

24 

775 

4,092 

000 

18 

575 

3,036 

22 

630 

3,326 

00 

17 

465 

2,455 

18 

490 

2.58/ 

0 

16 

375 

1.9S0 

17 

400 

2,112 

1 

15 

285 

1,505 

16 

306 

1,616 

2 

14 

245 

1.294 

15 

268 

1,415 

3 

13 

190 

1.003 

14 

210 

1,109 

4 

11 

152 

803 

12 

164 

866 

5 

10 

120 

634 

11 

145 

766 

6 

9 

98 

518 

10 

112 

591 

g 

8 

66 

349 

9 

78 

412 

10 

7 

45 

238 

8 

55 

290 

12 

6 

30 

158 

7 

35 

1 185 

14 

5 

20 

106 

6 

26 

137 

16 

4 

14 

74 

5 

20 

106 

18 

3 

10 

53 

4 

16 

85 

For  high-tension  lines,  it  is  customary  to  use  bare  wires  ana  msuiaie 
them  thoroughlv  on  special  porcelain  insulators.  The  ordinary  weather- 
proof wire  insulation  is  of  little  or  no  use  as  a protection  when  these  high 
pressures  are  used,  and  it  only  makes  the  line  more  dangerous  because  of 
the  appearance  of  false  security  that  it  gives.  In  many  cases,  ^ is  also 
better  to  use  bare  feeders  for  mine-haulage  plants,  because  the  ordinary 
insulation  soon  becomes  defective  in  a mine,  and  a wire  in  thisconditionis 
really  more  dangerous  than  a bare  wire,  because  the  latter  is  known  to  be 
dangerous  and  will  be  left  alone.  

CURRENT  ESTIMATES. 

Before  calculating  the  size  of  wire  required  for  any  given  case,  it  is 
necessary  to  know  the  current,  and  the  method  of  getting  at  this  will  depend 
on  what  the  current  is  to  be  used  for. 


INCANDESCENT  LAMPS. 


213 


Incandescent  Lamps.— These  are  usually  operated  ou  110-volt  circuits,  Fig. A, 
or  on  the  three-wire  system,  as  shown  in  Fig.  5.  In  the  three- Wire  system, 
two  110-volt  dynamos  are  connected  in  series  so  that  the  voltage  across  the 
outside  wires  is  220.  The  neutral 
wire  a a connects  to  the  point  b 
where  the  machines  are  connected 
together.  The  wire  a a merely 
serves  to  carry  the  difference  in 
the  currents  on  the  two  sides  of 
the  system,  in  case  more  lamps 
should  he  burning  on  one  side 
than  on  the  other.  The  outside 
wires  for  such  a system  are  calcu- 
lated as  if  the  lights  were  operated  . . ..  . ,.  . 

two  in  series  across  220  volts.  The  middle  wire  is  usually  made  equal  m size 
to  the  outer  wires.  An  ordinary  16  c.  p.  incandescent  lamp  requires  about 


55  watts  for  its  operation;  a 32  c.  p.  lamp 


requires  about  110  watts. 
Hence,  in  the  case  of 
ordinary  parallel  dis- 
tribution, as  shown 
in  Fig.  4,  the  dy- 
namo will  deliver 
about  i ampere  for 
each  16  c.  p.  lamp 
operated,  and  1 am- 
pere for  each  32  c.  p. 
lamp.  In  the  case  of 
the  three-wire  sys- 
tem, each  pair  of  16 
c.  p.  lamps  will  take 
\ ampere,  and  the 

total  number  of  amperes  in  the  outside  wires  will  be  one-fourth  the  num- 
ber of  lamps  operated.  . , ...  . , „ _ 

Example.— A certain  part  of  a mine  is  to  be  illuminated  by  fifty  16  c.  p. 
lamps  and  ten  32  c.  p.  lamps.  This  portion  of  the  mine  is  1,000  ft.  from  the 
dynamo  room,  and  the  allowable  drop  in  pressure  is  5 °J.  The  lamps  are  to 
be  run  on  a 110-volt  system.  Find  the  size  of  wire  required. 

Fifty  16  c.  p.  lamps  require - 25  amperes 

Ten  32  c.  p.  lamps  require 10  amperes 

Total  current 35  amperes 

We  have,  then, 

circular  mils  = 10'8X  * 35  *—  = 137-454  circular  mils’ 

or  about  a No.  00  B.  & S.  wire.  , . , , ., 

Example. — Take  the  same  case  as  in  the  last  example,  but  suppose  the 
lights  to  be  operated  on  the  three-wire  system.  There  will  then  be  twenty - 
five  16  c.  p.  lamps  and  five  32  c.  p.  lamps  on  each  side  of  the  circuit,  and 
the  total  current  in  the  outside  wires  will  be  17.5  amperes.  The  voltage 
between  the  outside  wires  will  be  220,  and  we  will  have 

10.8  X 1,000  X 2 X 17.5  X 100  _ 34  353  circular  mils, 

220  X 5 

or  about  a No.  5 B.  & S.  wire.  

If  We  make  the  central  wire  also  of  this  size,  it  is  seen  that  this  system 
would  require  three-eighths  the  amount  of  copper  called  for  by  the  Plald 
110-volt  system.  There  is  the  disadvantage  that  two  dynamos  are  needed. 

Note.— The  length  to  be  used  in  the  wiring  formula  is  the  average  dis- 
tance traversed  by  the  current  in  the  conductor.  For  example,  it,  a$  in 
Fig.  6 (a),  the  lamps  were  all  grouped  or  bunched  at  the  end  of  the  line,  tne 
length  used  in  the  formula  would  be  twice  that  from  G to  A,  because 
the  whole  current  has  to  flow  out  to  A through  one  main  and  back  through  the 
other.  In  other  words,  the  whole  current  here  passes  through  the  whole 
length  of  the  line.  In  case  the  load  is  uniformly  distributed  all  along  the 
line,  as  shown  in  Fig.  6 (5),  it  is  evident  that  the  current  decreases  step 'by 
step  from  the  dynamo  to  the  end.  In  such  a case,  the  length  or  distance  to 
be  used  in  the  formula  is  one-half  that  used  in  the  former  case,  or  simply 
the  distance  from  the  dynamo  to  the  end,  instead  of  twice  this  distance. 


circular  mils 


214 


ELECTRICITY. 


Arc  LamDS  — Arc  lamps  are  frequently  run  on  constant-potential  circuits, 
and  usually  consume  from  400  to  500  watts.  There  are  so  many  types  of 
these  lamps  that  it  is  difficult  to  give  any  current  estimates  that  will  be  gen- 
erally applicable.  Enclosed  arc  lamps  usually  take  from  3 to  5 amperes 
when  run  on  110-volt  circuits. 

Motors  —Practically  all  the  motors  used  in  mining  work  are  run  on  the 
constant-potential  system,  either  at  250  or  500  volts.  The  efficiency  of  ordi- 
narv  motors  will  vary  from  70 $ to  9 096  or  higher,  depending  on  the  size.  The 
efficiency  is  greater  with  the  larger  machines,  and,  for  the  ordinary  run  o( 
motors,  it  will  probably  lie  between 1 80$  and  90/,.  By  efficiency  is  here  meant 
the  ratio  of  the  useful  output  at  the  pulley  or  pinion  of  the  motor  to  the 
total  input.  The  accompanying  table  gives  the  efficiency  of  motors  of 

oidinary  size.  approximate  Motor  Efficiency. 

f to  11  H.  P.,  inclusive  = 75 $ efficiency 
3 to  5 H.  P.,  inclusive  = 80$  efficiency 
71  to  10  H.  P.,  inclusive  = 85$  efficiency 
15  H.  P.  and  upwards  = 90$  efficiency 
If  the  required  output  in  horsepower  is  known,  the  input  will  be 
w _ H.  P.  X 746 


efficiency 


W 


and  the  current  required  at  full  load  will  be  C = where  E is  the  voltage 
between  the  mains  at  the  motor. 

Conductors  for  Electric-Haulage  Plants.-In  electric-haulage  plants  the  rails 
take  the  place  of  one  of  the  conductors,  so  that,  m calculating  the * size  of 
feeders  required,  only  the  overhead  conductors  are  taken  into  account.  It 
is  a difficult  matter  to  assign  any  definite  value  to  the  resisto 
circuit,  as  it  depends  very  largely  on  the  quality  of  the  rail  bonding  at  the 


ioints.  If  this  bonding  is  well  done,  the  resistance  of  the  return  circuit 
should  be  very  low,  because  the  cross-section  of  the  rails  is  comparatively 
large.  For  calculating  the  supply  feeders,  we  may  use  the  approximate 

fOTmUla’  • . . ..  14XXXCX100 

circular  mils  = £x^drop  • 

In  this  case,  L is  the  average  length  of  feeder  over  which  the  power  is  to 
be  transmitted.  It  will  be  noticed  that  the  constant  10.8  appearing  m the 
previous  formulas  has  here  been  increased  to  14.  This  has  been  done  to  allow, 
approximately,  for  the  track  resistance,  but  this  cons tant  might  vary  con- 
siderablv,  depending  on  the  quality  of  the  rail  bonding.  If  1 ;^^ad  is  ali 
bunched  at  the  end  of  the  feeder,  X is  the  actual  length  of  the  feeder  in  fee 
If  the  load  is  uniformly  distributed  all  along  the  line,  as  it  would  be  it  a 
number  of  locomotives  were  continually  moving  along  the  line,  the  dis- 
tance L in  the  above  formula  would  be  taken  as  one-half  that  used  in l the 
case  where  the  load  was  bunched  at  the  end.  In  other  words the  whole 
current  C would  only  flow  through  an  average  of  one-half  the  length  of  tne 
line. 


DYNAMOS  AND  MOTORS. 


215 


Example.- In  Fig.  7,  a b represents  a section  of  track  4,°°0  ft.  long. 
thp  dvnamo  c to  the  beginning  of  the  section,  the  distance  is  1,200  ft.  The 
Jmllev  wheis  No  00  B & S.,  and  is  fed  from  the  feeder  at  regular  mterva Is. 
Two  mining  locomotives  are  operated,  each  of  which  takes  an  average  cur 
W 75 ZZr  The  total  allowable  drop  to  the  end  of  the  line  is  to  be 

xrf  0f  +^0  terminal  voltage,  which  is  500  volts.  Calculate  the  size  of  feeder 
required,  assuming  that  the  constant  14,  in  the  formula,  takes  account  of  the 

reSSince  the  locomotives^are  moving  from  place  to  place ’iJie4c™tefj0f 
tribution  for  the  load  may  be  taken  at  tne  center  of  the  4,000  ft.  1 e 


distance  L will  then  be  1,200  + 2,000  = 3,200  ft 
150  amperes;  hence,  we  have  ^ ^ x 150  x 100 

circular  mils 


The  total  current  will  be 


= 268,800. 


500X5  . 

This  would  require  either  a stranded  cable  or  the  use  of  two  No.  00  wires 
in  uarahSfrom^to  o From  a to  b we  have  the  No  .00  trolley  wire  m 
narallel  with  the 'feeder;  hence,  the  section  of  feeder  a b may  be  a J^g  e 
No  00  wire  In  many  cases,  the  drop  is  allowed  to  run  as  high  10/n, 
because  the  loads  are  usually  heavier,  and  the  distances  longer,  than  m the 
example  given  above.  . 

DYNAMOS  AND  MOTORS. 

A dynamo  is  a machine  for  converting  mechanical  energy  into  electrical 
energv  bv  moving  conductors  relatively  to  a magnetic  field.  riT.rr.r 

Any  electric  motor  is  a machine  for  converting  electrical  energy  into 
mechanical  energy  by  the  relative  motion  between  conductors  carrying  a 

current  and  a ma^netic^eld.  b of  conductors  are  made  to  move 

across  a magnetic  held  by  means  of  a steam  engine  or  other  prime  mover, 
and  the  result  is  that  an  E.  M.  F.  is  set  up  in  the  conductors,  and  this  E.  M.  I . 
will  set  up  a current  if  the  circuit  is  closed.  • A,  ,,  , 

In  the  case  of  a motor,  a number  of  conductors  are  arranged  so  that  they 
are  free  to  move  across  a magnetic  field,  and  a current  is  sent  through  these 
“nd"s  from  some  source  of  electric  current  The  current  flowing 
through  these  conductors  reacts  on  the  magnetic  field  and  causes  tne 
conductors  to  move,  thus  converting  the  electrical  energy  delivered  to  the 

m°Asr fa^as^e^^ica^coni^uction  goes,  dynamos  and  motors  are  almost 
identical,  and  the  operation  of  the  motor  is  exactly  the  reverse  to  that  of  the 

dyDvSamos  and  motors  may  be  divided  into  two  general  classes: 

mos  and  motors  for  direct  current ; (5)  dynamos  and  motors  for  alternating 

current.  . 

DIRECT-CURRENT  DYNAMOS. 

Prinrinle  of  Action. -Direct-current  dynamos  are  those  that  furnish  a 
current  that  always  flows  in  the  same  direction.  This  kind  of  dynamo  is 
largely  used  for  incandescent  lighting,  and  also  for  the  operation  of  street 

raUA  dynamo  generates  an  E.  M.  F.  by  the  motion  of  conductors  across  a 
magnetic  field;  hence,  at  the  outset,  it  is  seen  that  there  must  be  at  least  two 
essential  parts  to  a dynamo;  namely,  a magnet  of  some  kind  to  set  up  a 
magnetic  field,  and  a ‘series  of  conductors  arranged  so  that  they  may  be 
moved  or  revolved  in  the  magnetic  field.  The  first  part  is  known  as  the 


216 


DYNAMOS  AND  MOTORS. 


field  magnet,  or  very  often,  simply  as  the  field.  The  second  part  is  known  as 
the  armature.  The  field  is  supplied  by  means  of  a powerful  electromagnet 
which  is  magnetized  by  the  current  in  the  field  coils.  Fig.  8 shows  a typical 
six-pole  magnet  of  this  kind;  B , B are  the  magnetizing  coils,  which,  when  a 
current  is  sent  through  them,  form  powerful  magnetic  poles  at  N,  S.  The 
framework  A of  such  a field  magnet  is  usually  made  of  cast  iron  or  cast  steel. 

These  field  magnets  may 
have  any  number  of  poles, 
but  machines  of  ordinary 
size  are  usually  provided 
with  from  two  to  eight  poles. 

The  armature  usually  con- 
sists of  a number  of  turns  of 
insulated  copper  wire, 
arranged  around  the  periph- 
ery of  a ring  or  drum  built 
up  of  soft  iron  sheets.  Fig.  9 
shows  the  construction  of  a 
typical  armature  of  the  ring 
type.  The  winding  is 
divided  into  a number  of 
sections,  and  the  terminals 
connected  to  the  commutator. 

This  commutator  consists 
of  a number  of  copper  bars, 
insulated  from  each  other  by 
means  of  mica,  the  bundle  of 
bars  being  clamped  firmly 
into  place  and  turned  up  to 
form  a true  cylindrical  sur- 
face. The  sections  in  the 
commutator  correspond  with 
those  in  the  armature,  and 
the  use  and  operation  of  the 
commutator  will  be  described  later.  The  winding  on  the  ring  is  endless, 
i.  e.,  it  consists  of  a number  of  coils  or  sections  c,  the  end  of  one  section 


Fig.  8. 


COMPLETE  ARMATURE.  conductor 


Fig.  9. 


being  joined  to  the  beginning  of  the  next,  thus  forming  an  endless  coil,  as 
shown  in  Fig.  10.  The  construction  of  such  a ring  armature  would  be  as 
shown  in  Fig.  9. 


DIRECT-CURRENT  DYNAMOS. 


217 


Qnrmnsp  the  rin<*  shown  in  Fig.  10  with  its  endless  winding  to  be  rotated 

enter^he  FK^ 

hand  face  of  the  ring  are  moving  upwards,  they  will  have  an  E.  M.  F.  ge 

erated to them  in  one  direction,  while  the  E.  M.  F.  in  the  conductors  on  the 
left  lade  will  have  an  E.  M.  F.  in  the  opposite  direction,  because  all  the 
conductors  on  this  side  are 
moving  downwards,  or  in 
the  opposite  direction,  to 
those  on  the  other  side. 

These  two  opposing  E.  M. 

F.’s  will  meet  at  a,  as 
shown  by  the  arrowheads, 
and  will  neutralize  each 
other  so  that  no  current 
will  flow  through  the 
windings  of  the  armature. 

Suppose,  however,  that 
taps  are  connected  a£  the 
points  a and  a',  as  shown 
by  the  dotted  lines,  and 
these  taps  connected  to 
two  rings  r,  r',  mounted  so 
as  to  revolve  with  the 
armature.  By  allowing 
brushes  b,  bf  to  press  on 
these  rings,  we  can  make 


Fig.  10. 


connection  with  an  outside  circuit  d,  which  may  consist  of  a number  of 
lamns  or  any  other  device  through  which  we  wish  to  send  a current.  By 
nuUiL  in  the  taps  at  a and  a',  we  have  allowed  the  two  opposing  E.  M.  F.’s 
to  set  up  a current  through  the  common  connections  to  the  S 

thence  trough  the  outside  circuit.  Current  now  flows  in  each  halt  of  the 
armature  winding,  unites  at  a,  flows  out  by  means  of  ring  r and  brush  b , 
thence  through  the  outside  circuit  d to  brush  b and  ring  r,  from  whence  it 
nasses  to  a ' and  thus  completes  the  circuit.  When  the  ring  1?^es  a 
revolution  from  the  position  shown  in  the  figure,  it  is  seen  that  the  current 
in  the  ouside  circuit  will  flow  in  the  opposite  direction.  In  fact,  an  arrange- 
ment  of  this  kind  would  deliver  a current  t^wouldte 

it  would  be  what  is  known  as 
an  alternating  current. 

Instead  of  simply  bringing 
out  two  terminals  to  rings, 
suppose  the  winding  to  be 
tapped  at  a fairly  large  number 
of  points,  and  connections 
brought  down  to  a number  of 
insulated  strips,  as  shown  in 
Fig.  11.  If  the  armature  be 
now  revolved,  it  is  seen  that 
the  brushes  will  come  in  contact 
with  successive  bars  and  keep 
the  outside  circuit  in  such  re- 
lation to  the  armature  winding 
that  the  current  will  always 
flow  through  it  in  the  same 
direction . Moreover,  if  the  num- 
ber of  divisions  in  the  armature 
be  large,  the  current  will  fluc- 
tuate veiv  little,  being  nearly  as  steady  as  that  obtained  from  a battery. 
The  arrangement  made  up  of  insulated  bars  is  called  the  commutator, 
because  it  commutes  or  changes  the  relation  of  the  outside  circuit  to  the 
armature  winding  so  that  the  current  in  the  outside  circuit  always  flows 
in^the  same  direction.  All  practical  machines  used  for  the  generation 
of  direct  current  must  be  provided  with  such  a commutator.  When  alter- 
nating currents  are  used  it  is  only  necessary  to  use  plain  collector  rings,  as 


y 

-vAAAAAf* 

Re. 

Fig.  11. 


218 


DYNAMOS  AND  MOTORS. 


shown  in  Fig.  10.  The  foregoing  brief  description  will  give  a general  idea 
as  to  the  construction  of  an  ordinary  direct-current  dynamo  or  motor. 
Drum- wound  armatures  are  more  frequently  used  than  the  ring  type  shown, 
but  the  action  is  the  same  in  either  case. 

Factors  Determining  E.  M.  F.  Generated— A dynamo  should  be  looked  upon 
as  a machine  for  maintaining  an  electrical  pressure  rather  than  as  a machine 
for  generating  a current.  A pump  does  not  manufacture  water — it  merely 
maintains  a head  or  pressure  that  causes  water  to  flow  wherever  an  outlet  is 
provided  for  it  to  flow  through.  In  the  same  way,  a dynamo  maintains  a 
pressure,  and  this  pressure  will  set  up  a current  whenever  the  circuit  is 
closed,  so  that  the  current  can  flow.  The  important  thing  to  consider, 
therefore,  is  the  E.  M.  F.  that  the  dynamo  is  capable  of  generating. 

The  E.  M.  F.  generated  by  an  armature  depends  on  the  total  number  of 
magnetic  lines  cut  through  per  second  by  the  armature  conductors.  This 
means  that,  in  the  first  place,  the  faster  the  armature  runs,  the  higher  will  be 
the  E.  M.  F.;  in  the  second  place,  the  greater  number  of  conductors  or  turns 
there  are  on  the  armature,  the  higher  will  be  the  E.  M.  F.;  and  in  the  third 
place,  the  stronger  the  magnetic  field,  the  higher  will  be  the  E.  M.  F.  The 
E.  M.  F.  in  terms  of  these  quantities  may  be  written 

= nCN 

100,000,000’ 

where  n = speed  in  revolutions  per  second; 

C = number  of  conductors  oh  face  of  the  armature; 

N = number  of  magnetic  lines  flowing  from  one  pole. 

The  constant  100,000,000  is  necessary  to  reduce  the  result  to  volts.  This 
equation  enables  us  to  make  calculations  relating  to  any  two-pole  dynamo, 
and  with  slight  modification  it  is  applicable  to  machines  with  field  magnets 


having  a number  of  poles.  It  will  not  be  necessary  to  consider  this  formula 
further  here,  as  the  main  thing  to  fix  in  mind  is  that  the  E.  M.  F.  is  propor- 
tional to  the  three  quantities:  speed,  number  of  conductors,  and  strength  of 
field. 

Field  Excitation  of  Dynamos.— In  the  earliest  form  of  dynamo,  the  magnetic 
field  in  which  the  armature  rotated  was  set  up  by  means  of  permanent 
magnets.  Permanent  magnets  are,  however,  very  weak  compared  with 
electromagnets,  which  are  excited  by  means  of  current  flowing  around 
coils  of  wire  wound  on  a soft-iron  core,  as  shown  in  Fig.  13.  As  soon  as  the 
current  ceases  flowing  around  the  coils  of  an  electromagnet,  the  magnetism 
almost  wholly  disappears,  but  a small  amount,  known  as  the  residual  magnet- 
ism remains.*  It  is  to  this  residual  magnetism  that  the  dynamo  owes  its 
ability  to  start  up  of  its  own  accord  and  excite  its  own  field  magnets. 
When  the  armature  is  first  started  to  revolve,  a very  feeble  E.  M.  F.  is  gener- 
ated in  it,  but  the  armature  is  connected  to  the  field  coils  in  such  a way 
•that  this  small  E.  M.  F.  is  able  to  force  a small  current  through  the  field 
coils,  and  thus  set  up  a larger  amount  of  magnetism  in  the  field.  This  in 
turn  increases  the  E.  M.  F.  in  the  armature,  and  the  building-up  process  goes 
on  rapidly  until  the  dynamo  generates  its  full  pressure.  There  are  three 
different  methods  in  use  for  supplying  the  field  coils  with  current,  and  con- 
tinuous-current. dynamos  are  divided  into  three  classes,  according  to  the 
method  used  for  exciting  their  fields.  These  three  classes  are:  (a)  Series- 
wound  dynamos;  (6)  shunt-wound  dynamos;  (c)  compound- wound  dynamos. 


SHUNT- WOUND  DYNAMOS. 


219 


fa'*  Series-Wound  Dynamos.— In  this  class  of  machine,  the  field  coils  are 
connected  in Series  with  the  armature,  and  all  the  current  that  passes 
through  the  armature  also  passes  through  the  field  and  the  outside  circuit. 
This  arrangement  is  shown  in  Fig.  12,  where  JS 
and  6’  represent  the  poles  of  the  magnet,  B 
and  — B the  brushes,  and  Re  the  outside  cir- 
cuit, which  may  consist  of  lamps,  motors,  or 
any  other  device  in  which  it  is  desired  to 
utilize  the  current.  It  will  be  noticed  that  with 
an  arrangement  of  this  kind,  the  E.  M.  F.  will 
increase  as  the  current  increases,  because  the 
field  will  become  stronger  and  the  speed  is  sup- 
posed to  remain  constant.  This  will  be  true  up 
to  the  point  where  the  field  carries  all  the  mag- 
netism it  is  capable  of,  or,  in  other  words,  until 
it  becomes  saturated.  After  this  point  is 
reached,  the  E.  M.  F.  will  increase  very  little 
with  increase  of  current.  In  most  ot  the 
work  connected  with  lighting  or  power  trans- 
mission, it  is  desirable  to  have  the  voltage  „pri-PQ  method  of 

remain  nearly  constant.  For  this  reason  therefore,  the  senes  method  ot 

“^erator^whic^it^s  been6  applied  at  all  ?e“®™Uy  i£  Regulator  of 

motors.  , 

(b)  Shunt-Wound  Dynamos.— This  style  of  machine  has  n0\ 
largely  of  late  years,  although  it  was  formerly  very  co^on  Its  use  t 
present  confined  more  particularly  to  machines  of  smal  hv  nass  to  the 
method  of  excitation,  the  field  is  connected  as  a sh  unt ; or .by  pass  to  me 
ormatnrp*  i p the  field  winding  is  connected  in  parallel  with  tne  armature. 

?e“^^  current  flows  th rou|h  £ 

Halt  shows \he  connections  for  this  kind  of  field  excitation  An  adpt 

SS& 

the  dynamo  is  well  designed,  the  pressure  at  more  or^kS 

mately  constant.  The  pressure  will,  however,  always  fall  off  more  or  less, 

on  account  of  the  drop  in  the  armature,  due  to  fh£  field 

the  tendency  that  the  current  m the  armature  has  of  weakening  tne  e . 
The  shunt  winding  is  used  quite  largely  for  motors. 

/>\  Pom nound -Wound  Dvnamos.— 1 The  compound-wound  dynamo  is  the  one 
most  largely  used  for  direct-current  power  and  light  distribution,  and  it  is  so 
SSsette  winding  used  forfeiting  ^ » a««ntagtonofft| 

«pri p<?  and  shunt  windings  previously  described.  me  senes  yuuing 

serves  the  purpose  of  keeping  up  the  field  ^^even^makes  itfris^with 
increased  and  thus  keeps  the  pressure  constant,  or  even  makes  it  rise  wiin 

increased  load,  if  so  deSred, . When  the  series  winding  is  so  admsted  that 
the  pressure  rises  as  the  load  is  increased  the  machine  is  said  to  be  overcow 
wounded  Fig.  14  shows  the  connections  for  such  a machine.  It  will  oe  see 
?hat  the  shunt  winding  is  connected  as  before,  a field  resistance  or  rheosta  , 
Xhown  in  the  figurl,  being  inserted  for  the  ™f 
age.  One  brush  connects  directly  to  one  terminal  0.tthe  machine  + wnue 
the  other  brush  connects  to  one  end  of  the  series  wmding  on  tfie  field  rl  he 
other  end  of  the  series  winding  forms  the  other  terimna . - ^t? 
nnt«idp  pircnit  R e is  connected.  It  is  thus  seen  that  the  shunt  con  supplies 
a certain  amount  of  initial  magnetization  that  is  ^ ^that 

ism  supplied  by  the  series  coils.  Of  course,  care,  must  be  taken  to^ see  that 
the  current  in  the  series  coils  circulates  around  the  field  in  the  same  mrec 
tion  as  that  in  the  shunt  coils,  otherwise  the  effect  would  be  to  make  tne 
E.  M.  F.  fall  off  with  increasing  toad  instead of  keeping it up.  This  lstim.tyie 
of  dynamo  used  almost  exclusively  for  electric  haulage  plants,  as  well  as 
plants  for  direct-current  illuminating  purposes. 


220 


DYNAMOS  AND  MOTORS. 


DIRECT-CURRENT  MOTORS. 

Direct-current  motors  are  in  general  almost  identical,  so  far  as  construc- 
tion goes,  with  direct-current  dynamos.  Motors  are  often  required  to  oper- 
ate under  very  trying  conditions,  as  for  example,  in  mine  haulage  or  pump- 
ing plants  or  on  the  ordinary  street  car.  For  this  reason,  their  mechanical 
construction  often  differs  somewhat  from  that  of  the  dynamo,  the  design 
being  modified  in  such  a way  as  to  enclose  the  working  parts  as  completely 
as  possible,  and  thus  protect  them  from  dirt  and  injury.  The  two  kinds  of 
motors  most  commonly  used  are  the  series  and  shunt  varieties.  Compound- 
wound  motors  are  only  used  for  a few  special  kinds  of  work.  Practically  all 
of  the  motors  in  use*  are  operated  from  constant-pressure  mains;  i.  e.,  the 
pressure  at  the  terminals  of  the-  motor  is  practically  constant,  no  matter 
what  load  it  may  be  carrying.  We  will  here  consider  constant-potential 
motors  only. 

Principles  of  Operation.— If  the  fields  of  an  ordinary  constant-potential 
dynamo  are  excited  and  a current  supplied  to  the  armature  from  some  out- 
side source,  such  as  another  dynamo  D , Fig.  15,  so  that  the  current  enters 

at  +B,  and  passing  through 
the  winding  in  the  direc- 
tion indicated  by  the 
arrowheads, leaves  at  brush 
— B,  it  will  be  found  that 
all  of  the  conductors  under 
the  S pole  face,  b,  c,  d,  e , /, 
and  g , will  tend  to  move 
downwards , and  all  those 
under  the  N pole  face,  j,  k , 
Z,  m,  ?2,  and  o,  will  tend  to 
move  upwards,  as  indicated 
by  the  small  arrows. 

These  forces  combine  to 
produce  a tendency  of  the 
armature  to  rotate  about 
its  axis  as  indicated  by  the 
large  arrows,  which  ten- 
dency is  called  the  torque 
of  the  motor. 

The  amount  of  this 
torque— which  is  usually 
expressed  in  pound-feet; 
that  is,  a certain  number  of  pounds  acting  at  a radius  of  a certain  number 
(usually  1)  of  feet— depends  on  (1)  the  strength  of  the  field,  (2)  the  number 
of  conductors,  (3)  their  mean  distance  from  the  axis  of  the  armature,  and 
(4)  the  amperes  in  each  conductor.  In  any  given  machine,  the  second  and 
third  conditions  are  constant,  so  that  tho  torque  depends  on  the  strength  of 
the  field  and  the  current.  . , A _ A_ 

If  the  armature  is  stationary,  the  E.  M.  F.  required  to  send  the  current 
through  the  winding  is  only  that  necessary  to  overcome  the  drop,  Avhich  is 
due  to  the  resistance  of  the  winding.  If  the  torque  exerted  by  this  current 
is  greater  than  the  opposition  to  motion,  so  that  it  causes  the  armature  to 
revolve,  the  motion  of  the  conductors  through  the  field  generates  in  them 
an  E.  M.  F.  that  is  opposed  to  the  E.  M.  F.  that  is  sending  the  current  through  the 

armature.  . 

This  opposing  E.  M.  F.,  or  counter  E.  M.  F.  as  it  is  called,  then  diminishes 
the  effect  of  the  applied  E.  M.  F.,  so  that  the  current  is  reduced,  reducing 
the  torque.  Should  the  torque  still  be  greater  than  the  opposition  to 
motion,  the  speed  of  the  armature  will  continue  to  increase,  increasing  the 
counter  E.  M.  F.,  and  thereby  further  reducing  the  current  and  the  cor- 
responding torque,  until  the  torque  just  balances  the  opposition  to  the  motion , 
when  the  speed  will  remain  constant.  ' _ , 

At  all  times,  the  drop  of  potential  through  the  armature  is  equal  to  the 
difference  between  the  counter  and  the  applied  E.  M.  F.'s , and  as  the  product  of 
this  drop  and  the  current  represents  energy  wasted,  it  is  desirable  to  make  it 
as  low  as  possible.  In  good  motors  of  about  10  H.  P.  output,  the  drop  m 
the  armature  is  seldom  more  than  about  5$  of  the  applied  E.  M.  F.,  and  is 
less  in  larger  machines.  , . . ..  , 

This  being  the  case,  it  is  evident  that  if  the  armature  is  at  rest,  so  that  it 


DIRECT-CURRENT  MOTORS. 


221 


has  no  counter  E.  M.  F.,  and  is  connected  directly  to  the  mains,  a very  large 
current  will  flow  through  it,  which  would  be  liable  to  damage  the  armature. 
On  this  account  an  external  resistance,  called  a starting  resistance , is  con- 
nected in  series  with  the  armature  when  it  is  to  be  started.  This  resistance 
isma^Sreat  enough  to  prevent  more  than  about  the  normal  current  from 
flowing  through  the  armature  when  it  is  at  rest;  as  the  armature  speeds  up 
and  develops  some  counter  E.  M.  F.,  this  resistance  is  gradually  cut  out 
until  the  armature  is  connected  directly  to  the  mams,  and  is  running  at 

n°  The  energy  represented  by  the  product  of  drop  in  the  armature  and  the 
current  is  wlsted;  that  represented  by  the  product  of  the  current  and  the 
rest  of  the  E.  M.  F.,  that  is,  the  counter  E.  M.  F.,  is  the  energy  required  to 

ke<Aside  fTom  Secom^aratively  small  amount  of  current  required  to  furnish 
the  toraue  necessary  for  overcoming  the  frictional  losses  m the  motor  itself, 
which  are  SS^SSfy  constont,  the  Amount  of  current  taken  from  the  mams 
is  directly  proportional  to,  and  varies  automatically  with,  the  amount  of  the 
external  load-  for,  if  this  external  load  is  increased  the  current  which  has 
been  flowing’ in  the  armature  cannot  furnish  sufficient  torque  for  this 
increased  loaxl,  so  that  the  machine  slows  down.  This  decreases  the  counter 
E.  M.  F.,  which  immediately  allows  more  current  to  flow  though plnaf^ad 
ture  increasing  the  torque  to  the  proper  amount.  If  the  external  load 

is  decreased,  tie  current  flowing  furnishes  an  excess  oftorque.  wjK'fl 
causes  the  speed  to  increase,  increasing  the  counter  E.  M.  *.,  and  ae 
creasing  the  current  until  it  again  furnishes  only  the  required  amount 

°f  Sincere  counter  E.  M.  F.  is  very  nearly  equal  to  the  aPP^,  it  is  only 
necessarv  for  it  to  vary  a small  amount  to  vary  the  current  within  wide 
limits  For  example,  if  the  resistance  of  a certain  armature  is  1 ohm,  and  it 
is  supplied  with  current  at  a constant  potentialof  250  volts  then,  when  a 
current  of  10  amperes  is  flowing  through  it,  the  drop  is  10  XI  — 10  \oits 
and  the  counter  E M F.  is  250  — 10  = 240  volts.  Now,  if  the  current  is 
reduced  to  ? ampere,  the  drop  is  1 X 1 = 1 volt,  and  the  counter  E.  M.  F.  is 

9 

250  _ ! = 249  volts;  that  is,  the  counter  E.  M.  F.  only  varies  ^5,  or  3.75$, 


while  the  current  varies  or  90$. 

As  stated  before,  the  field  magnets  of  constant-potential  motors  are 
nsiiallv  either  shunt-wound  or  series-wound.  . , . 

If  shunt-wound,  and  supplied  from  a constant-potential  circuit,  the  mag- 
netizing force  of  the  field  coils  is  constant,  giving  a pracacally  constant 
field.  This  being  the  case,  the  counter  E.  M.  F.  is  directly  proportional  to 
the  speed,  so  that  variations  of  the  load  make  only  slight  variation  m 
the  speed.  A shunt-wound  motor  is  then  (practically)  a constant-speed 

m°With  series-wound  motors,  the  strength  of  the  field  varies  with  the  cur- 
rent; if  the  load  on  such  a motor  is  reduced,  the  excess  of  torque makes  1 the 
armature  speed  up,  but  as  the  resulting  decrease  of  the  cu^t  fn 

the  field  strength,  the  armature  must  speed  up  to  a much  greater  extent,  m 
order  to  increase  the  counter  E.  M.  F.  to  the  right  degree,  than  would  be 
necessary  if  the  field  were  constant.  If  the  load  is  increased,  the  increase 
in  the  current  so  increases  the  field  strength  that  the  speed  must  decrease 
considerably,  in  order  to  decrease  the  counter  E.  M.  F.  by  the  right  amount. 
The  speed  of  a series-wound  motor,  then,  varies  largely  with  variations  in 

thAnaadvantage  of  the  series  motor  is  that  if  a torque  greater  than  the 
normal  is  required,  it  can  he  obtained  with  less  current  than  with  a shunt 
motor,  since  the  increased  current  increases  the  field  strength,  and  tne 

torque  is  proportional  to  both  these  factors.  . „ , . „_x_, 

It  would  not  be  practicable  to  make  the  field  strength  of  a shunt  motor 
as  great  as  is  possible  to  get  with  a series  motor,  since  it  would .require  a 
very  large  magnetizing  force,  and  with  the  shunt  winding,  this  extra 
magnetizing  force  would  have  to  be  expended  all  the  time,  whether  the 
strong  field  was  required  or  not,  which  would  be  very  wakeful,  ^ the 
series  motor,  however,  this  extra  magnetizing  force  is  only  expended  while 
it  is  needed. 


222 


DYNAMOS  AND  MOTORS. 


A disadvantage  of  the  series  winding  is  that  if  all  the  load  is  taken  off, 
the  current  required  to  drive  the  motor  is  very  small,  making  a weak  held, 
which  requires  such  a high  speed  to  generate  the  proper  counter  E.  M.  F. 
that  the  armature  is  liable  to  be  damaged.  In  other  words,  the  motor  will 
race  or  run  away,  if  the  load  is  all  removed.  This  cannot  occur  with  the 
shunt  motor  as  long  as  the  field  circuit  remains  unbroken. 

On  account  of  the  above  features,  shunt  motors  are  used  to  drive 
machinery  that  requires  a nearly  constant  speed  with  varying  loads,  or 
which  would  be  damaged  if  the  speed  should  become  excessive,  such  as 
ordinary  machinery  in  shops  and  factories,  pumps,  etc.  Series  motors  are 
used  on  street  cars,  to  operate  hoists,  etc.,  where,  on  account  of  the  gearing 
used,  the  load  cannot  be  entirely  thrown  off,  and  the  torque  required  at 
starting  and  getting  quickly  up  to  speed  is  much  greater  than  the  normal 

^Speed  Regulation  of  Motors.— The  torque  of  a motor  depends  on  the  current; 
that  is,  for  a given  current,  the  torque  will  be  the  same  whatever  may  be 
the  speed,  provided  the  field  strength  remains  the  same.  . The  speed  at 
which  the  armature  runs  is  a matter  of  E.  M.  F.  only;  that  is,  with  a given 
current  the  speed  will  be  proportional  to  the  applied  E M.  F.,  or,  more 
strictlv,  the  counter  E.  M.  F.,  other  conditions  remaining  the  same. 

It  has  been  shown  that  the  torque  will  automatically  regulate  itself  for 
changes  in  the  load.  The  speed,  however,  may  be  varied  by  varying  the 
applied  E.  M.  F.  or  the  strength  of  the  field.  A change  m speed  may  or 
may  not  result  in  a change  in  the  torque  required,  depending  on  the 
character  of  the  work  done  by  the  motor. 

The  simplest  way  to  vary  the  applied  E.  M.  F.  is  to  insert  a resistance,  in 
series  with  the  armature,  similar  to  the  starting  resistance.  By  varying 
this  resistance,  the  applied  E.  M.  F.  at  the  terminals  of  the  motor  is  also 
varied,  although  the  E.  M.  F.  of  the  mams  remains  constant.  It  is  evident 


Trolley 


Rail 


f — UUUU  " 

^ 250  Volts > 

1- 250  Volts H 

ow  y oils 

Fig.  16. 

that  the  energy  represented  by  the  product  of  the  current  and  the  drop 
through  the  resistance  is  converted  into  heat,  and  is  thereby  wasted, 
therefore,  for  great  variations  in  speed,  this  method  is  not  economical, 

though  often  very  convenient.  . , . at  t?  mo 

The  applied  E.  II.  F.  may  also  be  varied  by  varying  the  E M.  F.  of  the 
generator  supplving  the  current,  but  this  can  only  be  done  iv  here  a single 
generator  is  supplying  a single  motor,  or  several  motors, 
all  oe  varied  at  the  same  time;  so  that  this  method  is  only  used  in  special 

CRS6S 

If ’the  strength  of  the  field  is  changed,  the  speed  necessary  to  give  a cer- 
tain counter  E.  M.  F.  will  also  be  changed,  which  gives  a convenient 
method  of  varying  the  speed.  If  the  strength  of  the  field  is  lessened,  the 
speed  will  increase*  and  if  the  field  is  strengthened,  the  speed  will  decrease 
With  shunt  motors,  the  field  may  be  weakened  by  inserting  a suitable 
resistance  in  the  field  circuit,  as  in  shunt  dynamos;  with  senes  motor* 3 the 
same  result  mav  be  obtained  by  cutting  out  some  of  the  turns* of  the  field 
coils  or  by  placing  a suitable  resistance  m parallel  with  the  field  coils. 

This  method  of  regulation  Is  also  of  limited  range,  since  it  is  not  econom- 
ical  to  maintain  the  strength  of  the  field  much  above  or  betow  a certain 
density.  The  resistance  method  described  above  being  rather  more 
it  is  generally  used.  For  special  cases,  such  as  street:railroad  work,  various 
special  combinations  of  the  above  methods  of  regulation  are  used. 

One  of  the  most  common  of  these  is  known  as  the  series-parallel  method, 
and  is  the  method  of  regulation  generally  used  at  present  for  operating 
street  cars.  This  method  is  equivalent  to  the  method  of  cutting  down  the 
speed  by  reducing  the  E.  M.  F.  applied  to  the  motor,  and  is  only  applicab  e 
where  at  least  two  motors  are  used.  It  is  also  used,  to  some  extent,  m 
haulage  plants.  When  a low  speed  is  desired,  or  when- the  cm  to  be 
started  up  the  motors  are  thrown  m series,  as  shown  in  Fig.  16,  thus  making 
?he  voltaV  across  each  motor  equal  to  one-half 

lines,  and  cutting  down  the  speed  accordingly.  When  a high  speed  is 


CONNECTIONS  FOR  MOTORS. 


223 


Trolley 


-SOOVoltSr 

Fig.  17. 


Ground 


desired  the  motors  are  thrown  in  multiple,  as  shown  in  Fig.  17,  and  each 
motor  runs6 a?1 full1  speed  because  it  gets  the  full  ine  pressure.  ^ practice, 
ctartino-  resistances  are  used  in  connection  with  the  above  to  maKe  me 
startini  smooth  but  the  two  running  positions  are  as  shown,  the  motors 
beiim  connected  in  series  in  the  one  case,  and  in  parallel  in  the  other. 

C®nnXnStr  CrntinUouS.Curr?nt  Motors.-Fig.  18  shows  the  manner  n 
which  a shunt  motor  is  connected  to  the  terminals  + and  — ot  the  circuit. 
It  will  be  seen  that  the  current 

through  the  shunt  field  does  not  /TWTT'' — — 

pass  through  the  resistance  R KAAAJ 

which  is  connected  in  the  arma- 
ture circuit.  This  is  necessary, 
since  to  keep  the  field  strength 
constant,  the  full  difference  of 
potential  must  be  maintained  be- 
tween the  terminals  of  the  field 

weak  field  that  an  excessive  current  would  be  required  to  turnisn  ine 

,ie  Whtn’  connected  afshown!  hZcver,  the  field  is  brought  up  to  its  full 
strength  before  any  curreiU  passes  through  the  armature;  so  this  difficulty 

d°fin?e  fnfseries  motor  the  same  current 

field  coils,  the  starting  resistance  may  be  placed l in  any  part  trf  “e^ciM 
^fhe'tffe  terminlds1?  the  motor nC6  ^ 

" fToC  reverse^  the 

either  Urn  direction  of  the  field  or  the  direct™  of  the 
armature.  It  is  usual  to  reverse  the  direction  of  the  current ; in  tne  a 
ture  a switch  being  used  to  make  the  necessary  changes  in  the  conne CtlrS!l~ 
l on  chows  the  connections  of  one  form  of  reversing  switch  Two 

“nTLpplied  with  "a1  h^nd^e^^^d tthee two^ar^  ^Sn^togethe? by®a 

“ft  c are^Sanged’on't^e'base* of  SK&?  eS& 


bars  B and  Bl  may  rest  either  on  a and  b,  as  shown  by  the  full 

c as  shown  by  the  dotted  lines.  The  line  is  connected  to  the  terminals 
T and  Tn,  and  they motor  armature  between  a and  b,  or  vice  versa,  a an 

be ^“elwttehfsm^the  position  shown  by  the  full  lin^  r is  connected 


224 


DYNAMOS  AND  MOTORS. 


between  c and  a.  The  direction  of  the  current  through  the  motor 
armature,  or  whatever  circuit  is  connected  between  a and  b , is  thus  reversed. 

In  order  to  reverse  only  the  current  in  the  armature,  the  reversing  switch 
must  be  placed  in  the  armature  circuit  only.  Fig.  21  represents  the  connec- 
tion for  a reversing-shunt  motor  (a)  and  a reversing- 
series  motor  (6);  + and  — are  the  line  terminals;  R, 
the  starting  resistance;  B and  B\,  the  brushes  of  the 
motor,  and  F \ the  field  coil  of  the  motor.  Some  man- 
ufacturers combine  the  starting  resistance  and  revers- 
ing switch  in  one  piece  of  apparatus. 

In  connecting  up  motors,  some  form  of  main  switch 
is  used  to  entirely  disconnect  the  motor  from  the  line 
when  it  is  not  in  use. 

To  prevent  an  excessive  current  from  flowing 
through  the  motor  circuit  from  any  cause,  short  strips 
of  an  easily  melted  metal,  known  as  fuses,  mounted  on 
suitable  terminals,  known  as  fuse  boxes,  are  placed  in 
the  circuit.  These  fuses  are  made  of  such  a sectional 
area  that  a current  greater  than  the  normal  heats 
them  to  such  an  extent  that  they  melt,  thereby  breaking  the  circuit  and 
preventing  damage  to  the  motor  from  an  excessive  current.  The  length 
of  fuse  should  be  proportioned  to  the  voltage  of  the  circuit,  a high  voltage 
requiring  longer  fuses  than  a low  voltage,  in  order  to  prevent  an  arc  being 
maintained  across  the  terminals  when  the  fuse  melts. 

If  desired,  measuring  instruments  (ammeter  and  voltmeter)  may  be 
connected  in  the  motor  circuit,  so  that  the  condition  of  the  load  on  the 
motor  may  be  observed  while  it  is  in  operation.  All  these  appliances, 
regulating'  resistance,  reversing  switch,  fuses,  instruments,  etc.,  are  placed 


inside  the  main  switch;  that  is,  the  current  must  pass  through  the  main 
switch  before  coming  to  any  of  these  appliances,  so  that  opening  the  main 
switch  entirely  disconnects  them  from  the  circuit,  when  they  may  be 
handled  without  fear  of  shocks. 


ALTERNATING-CURRENT  DYNAMOS. 

An  alternating-current  dynamo  is  one  that  generates  a current 
that  periodically  reverses  its  direction  of  flow.  It  was  shown  in 
connection  with  Fig.  10  that  an  armature  provided  simply  with  collector 
rings  produced  an  alternating  current  in  the  outside  circuit.  This 
current  may  be  represented  by  a curve  such  as  that  shown  in  Fig.  22. 
The  complete  set  of  values  that  the 
current  or  E.  M.  F.  passes  through 
repeatedly  is  known  as  a cycle.  For 
example,  the  values  passed  through 
during  the  interval  of  time  represented 
by  the  distance  a c would  constitute  a 
cycle.  The  set  of  values  passed 
through  during  the  interval  a b is 
known  as  an  alternation.  An  alternation  is,  therefore,  half  a cycle.  The 
number  of  cycles  passed  through  per  second  is  known  as  the  frequency  of  the 
current,  or  E.  M.  F. 

Alternating-current  dynamos  are  now  largely  used  both  for  lighting  and 
power  transmission,  especially  when  the  transmission  is  over  long  distances. 
The  reason  that  the  alternating  current  is  specially  suitable  for  long-distance 


Fig.  22. 


ALTERNATORS. 


225 


work  is  that  it  may  be  readily  transformed  from  one  pressure  to  another. 
We  have  already  seen  that  in  order  to  keep  down  the  amount  of  copper  in 
the  line,  a high  line  pressure  must  be  used.  Pressures  much  over  500  or  600 
volts  cannot  be  readily  generated  with  direct-current  machines,  owing  to  the 
troubles  that  are  likely  to  arise  due  to  sparking  at  the  commutator.  On  the 
other  hand,  an  alternator  requires  no  commutator  or  even  collecting  rings, 
if  the  armature  is  made  stationary  and  the  field  revolving,  as  is  frequently 
done.  Alternators  are  now  built  that  generate  as  high  as  8,000  or  10,000  volts 
directly.  If  a still  higher  pressure  is  required  on  the  line,  it  can  be  easily 
obtained  by  the  use  of  transformers,  to  be  explained  later.  It  is  thus  seen 
that  where  power  is  to  be  carried  over  long  distances,  the  alternating  current 
is  indispensable.  _ . . , , 

Alternating-current  dynamos,  like  direct-current  machines,  consist  ot 
two  main  parts,  i.  e.,  the  field  and  armature.  Either  of  these  parts  may 
be  the  revolving  member, 
and  in  many  modern  ma- 
chines the  armature,  or  the 
part  in  which  the  current 
is  induced,  is  the  revolving 
member.  Fig.  23  shows  a 
typical  alternator  of  the 
belt-driven  type,  having  a 
revolving  armature.  It  is 
not  unlike  a direct-current 
machine  as  regards  its  gen- 
eral appearance.  The 
number  of  poles  is  usually 
large,  in  order  to  secure 
the  required  frequency 
without  running  the  ma- 
chine at  a high  rate  of 
speed.  The  frequencies 
met  with  in  practice  vary 
all  the  way  from  25  to  150. 

The  higher  frequencies 
are,  however,  passing  out 
of  use,  and  at  present  a 
frequency  of  60  is  very  , 

common.  This  frequency  is  well  adapted  both  for  power  and  lighting  pur- 
poses. When  machines  are  used  almost  entirely  for  lighting  work,  frequen- 
cies of  125  or  higher  may  be  used.  The  frequency  of  any  machine  may  be 
readily  determined  when  the  number  of  poles  and  the  speed  is  known,  as 
follows:  ' 

number  of  poles  v , rev.  per  min. 

Frequency  = t> X ^ • 

For  example,  if  an  eight-pole  alternator  were  run  at  a speed  of  900  R.  P.  M., 
the  frequency  would  be 

8 _ 900 
2 


/ = — x ^77  = 60  cycles  per  second. 


60 


Alternators  may  be  divided  into  the  two  following  classes:  (a)  Single*  • 
phase  alternators;  ( b ) Multiphase  alternators.  , , 

(a)  Single-Phase  Alternators.— These  machines  are  so  called  because  they 

generate  a single  alternating  current  (as  represented  by  the  curve  shown  in 
Fig.  22).  The  armature  is  provided , with  a single  winding  and  the  two 
terminals  are  brought  out  to  collector  rings,  as  previously  described.  Single- 
phase machines  have  been  largely  used  in  the  past  for  lighting  work,  but 
they  are  gradually  being  replaced  by  multiphase  machines,  because  the 
single-phase  machines  are  not  well  suited  for  the  operation  of  alternating- 
current  motors.  . „ , , .. 

( b ) Multiphase  Alternators.— These  machines  are  so  called  because  they 
deliver  two  or  more  alternating  currents  that  differ  in  phase;  i.  e.,  when  one 
current  is,  say,  at  its  maximum  value,  the  other  currents  are  at  some  other 
value.  This  is  accomplished  by  providing  the  armature  with  two  or  more 
distinct  windings  which  are  displaced  relatively  to  each  other  on  the 
armature.  One  set  of  windings,  therefore,  comes  under  the  poles  at  a later 
instant  than  the  winding  ahead  of  it,  and  the  current  in  its  winding  comes 


226 


DYNAMOS  AND  MOTORS. 


to  its  maximum  value  at  a later  instant  than  the  current  in  the  first  wind- 
ins.  In  practice,  the  two  types  of  multiphase  alternator  most  commonly 
used  are  (1)  two-phase  alternators,  (2)  three-phase  alternators. 

Two-phase  alternators  are  machines  that  deliver  two  alternating  currents 
that  differ  in  phase  by  one-quarter  of  a complete  cycle;  i.  e.,  when  the 
current  in  one  circuit  is  at  its  maximum  value,  the  current  m the  other 
circuit  is  passing  through  its  zero  value.  By  tapping  four  equidistant  points 
of  a regular  ring  armature,  as  shown  in  Fig.  24,  and  connecting  these  points 
to  four  collector  rings,  a simple  two-pole  two-phase  alternator  is  obtained. 
One  circuit  connects  to  rings  1 and  T , the  other  circuit  connects  to  rings 
2 and  ft  It  is  easily  seen  from  the  figure  that  when  the  part  of  the  winding 
connected  to  one  pair  of  rings  is  in  its  position  of  maximum  action,  the 
E M F in  the  other  coils  is  zero,  thus  giving  two  currents  m the  two 
different  circuits  that  differ  in  phase  by  one-quarter  of  a cycle  or  one-half 

Three-phase  alternators  are  machines  that  deliver  three  currents  that  differ 
in  phase  by  one-third  of  a complete  cycle;  i.  e.,  when  one  current  is  flowing 
in  one  direction  in  one  circuit,  the  currents  in  the  other  two  circuits  are  one- 
half  as  great,  and  are  flowing  in  the  opposite  direction.  By  tapping  three 
equidistant  points  of  a ring  winding,  as  shown  in  Fig.  25,  a simple  three- 
phase  two-pole  alternator  is  obtained.  Three  mams  lead  from  the  collecting 
rinsrs 

In  order  to  have  three  distinct  circuits,  it  would  ordinarily  be  necessary 
to  have  six  collecting  rings  and  six  circuits;  but  this  is  not  necessary  in  a 
three-phase  machine  if  the  load  is  balanced  in  the  three  different  circuits, 
because  one  wire  can  be  made  to  act  alternately  for  the  return  of  the  other 

tU<Uses  of  Multiphase  Alternators— Multiphase  alternators  are  coming  largely 
into  use,  because,  by  using  them,  alternating-current  motors  can  be  readily 
operated.  By  using  multiphase  machines,  motors  can  be  operated  that  will 


Fig.  24. 


Fig.  25. 


start  from  rest  under  load,  whereas  with  single-phase  machines  the  motor 
has  to  be  brought  up  to  speed  from  some  outside  source  of  power  before  it  can 
be  made  to  run.  For  this  reason,  such  machines  are  used  for  the  operation 
of  modern  power-transmission  plants.  As  far  as  the  general  appearance  of 
three-phase  machines  goes,  they  are  similar  to  ordinary  single-phase  alter- 
nators^ the  only  difference  being  in  the  armature  winding  and  the  larger 
number  of  collector  rings.  The  multiphase  alternator  is  also-adapted  tor 
the  operation  of  lights,  so  that  by  using  these  machines,  both  lights  and 
motors  may  be  operated  from  the  same  plant.  They  are  well  adapted  for 
power-transmission  purposes  in  mines,  especially  for  the  operation  of  pump- 
ing and  hoisting  machinery,  because  the  motors  operated  by  them  are  very 
simple  in  construction  and  therefore  not  liable  to  get  out  of  order. 


ALTERNATING-CURRENT  MOTORS. 

Alternating-current  motors  may  be  divided  into  two  general  classes: 

(a)  Synchronous  motors;  (5)  Induction  motors.  .. 

'(a)  Synchronous  motors  are  almost  identical,  so  far  as  construction  goes, 
with  the  corresponding  alternator.  For  example,  a two-phase  synchronous 
motor  would  be  constructed  in  the  same  way  as  a two-phase  alternator. 


alternating-current  motors. 


227 


They  are  called  synchronous  motors  because  they  always  run  in  synchro- 
nism, or  in  step,  with  the  alternator  driving  them.  This  means  that  the 
motor  runs  at  the  same  frequency  as  the  alternator,  and  if  the  motor  had 
the  same  number  of  poles  as  the 
alternator,  it  would  run  at  the  same 
speed,  no  matter  what  load  it  might 
be  carrying.  This  type  of  motor  has 
many  good  points,  and  is  especially 
well  suited  to  cases  where  the 
amounts  of  power  to  be  transmitted 
are  comparatively  large  and  where 
the  motor  does  not  have  to  be 
started  and  stopped  frequently. 

Multiphase  synchronous  motors  will 
start  up  from  rest  and  will  run  up  to 
synchronous  speed  without  aid  from 
any  outside  source.  They  will  not, 
however,  start  with  a strong  starting 
torque  or  effort,  and  will  not,  there- 
fore, start  up  under  load,  and  can- 
not be  used  in  places  where  a strong 
starting  effort  is  required.  For  this 
reason  synchronous  motors  are  not 
suitable  for  intermittent  work. 

(6)  Induction  motors  are  so  called 
because  the  current  is  induced  in  the 


Fig.  26. 


because  the  current  is  induced  in  me  , „hrsW55 

armature  instead  of  being  led  into  it  from  some  outside  eS  mle hin^i 

a typical  induction  motor.  There  are  two  essential  parts ^n .these ! machines, 
viz  the  field  into  which  multiphase  currents  are  led  from  the  line,  and  me 
armature  in  which  currents  are  induced  by  the  magnetism  set  up  by  the 
field .SherWe^SS  may  be  the  stationaryorrevolvmg  member  but 
in  most  cases  the  field,  or  part  that  is  connected  to  the  hue,  is  stationary. 
Fig.  27  shows  the  construction  of.  the  stationary  member  or  field.  This  con 
sists  of  a number  of  iron  laminations,  built  up  to  n?titu«nff 

with  slots  around  the  inner  periphery.  Theform- woundcoils  constitu  ting 
the  field  winding  are  placed  in  these  slots  and  connected  the  mains.  This 

winding  is  arranged  in  the  same  way  as  the  ar^ature  nse  absent 

phase  alternator.  When  the  alternating  currents _differing  in .phase are 
through  the  winding,  magnetic  poles  are 

the  constant  changing  of  the 
currents  causes  these  poles  to 
shift  around  the  ring,  thus  set- 
ting up  what  is  known  as  a 
revolving  magnetic  field.  This 
armature,  Fig.  28,  consists  of  a 
laminated  iron  core  provided 
with  a number  of  slots,  in  each 
of  which  is  placed  a heavy 
copper  bar  b.  The  ends  of 
these  bars  are  all  connected 
together  by  two  heavy  short- 
circuiting  rings  r,  r running 
around  each  end  of  the  arma- 
ture. The  bars  and  end  rings 
thus  form  a number  of  closed 
circuits.  When  such  an  arma- 
ture is  placed  in  the  revolv- 
ing field,  the  magnetism  will 
cut  across  the  armature  con- 
ductors, inducing  E.  M.  F.’s 
in  them,  and  since  the  conduc- 
tors are  joined  up  into  closed 
circuits,  currents  will  flow  in 
mmr  them.  These  currents  will 
react  on  the  field,  and  the  armature  will  be  forced  to  revolve.  Such  an 
armature  will  not  run  exactly  in  synchronism,  because  if  it  did,  it  would 
revolve  just  as  fast  as  the  magnetic  field,  and  there  would  be  no  cutting  ot 


i 


228 


DYNAMOS  AND  MOTORS . 


tines  of  force.  The  speed  drops  slightly  from  no  load  to  full  load,  but  if  the 
motor  is  well  designed,  this  falling  off  in  speed  is  slight. 

Induction  motors  possess  many  advantages  for  mine  work.  One  of  the 
chief  of  these  is  the  absence  of  the  commutator  or  any  kind  of  sliding  con- 
1 tacts  whatever.  Such  motors  can 


vide  the  armature  with  a winding  simils 
the  terminals  to  collecting  rings,  so  that 
armature  circuit. 


therefore  operate  with  absolutely 
no  sparking— a desirable  feature 
for  mine  work.  The  motors  are 
also  very  simple  in  construction, 
and  are  therefore  not  liable  to 
get  out  of  order.  They  have  an 
additional  advantage  over  the  syn- 
chronous motor  in  that  they  start 
up  with  a strong  starting  effort, 
and,  in  fact,  behave  in  most  re- 
spects like  any  good  shunt-wound 
direct-current  motor.  They  are 
used  quite  successfully  for  all 
kinds  of  stationary  work,  such  as 
pumping,  hoisting,  etc.,  but  so  far 
have  not  been  used  to  any  great 
extent  for  haulage  purposes. 
When  these  motors  are  used  for 
purposes  where  a variable  speed  is 
required,  it  is  customary  to  pro- 
r to  that  of  the  field  and  bring  out 
resistance  may  be  inserted  in  the 


TRANSFORMERS. 

Reference  has  already  been  made  to  the  use  of  transformers  for  changing 
an  alternating  current  from  a higher  to  a lower  pressure,  or  vice  versa,  with 
a corresponding  change  in  current.  Transformers  used  for  raising  the  volt- 
age are  known  as  step-up  transformers;  those  used  for  lowering  the  pressure 
are  known  as  step-down  transformers. 

The  transformer  consists  of  a laminated  iron  core  upon  which  two  coils 
of  wire  are  wound.  These  coils  are  entirely  distinct,  having  no  connection 
with  each  other.  One  of  these  coils,  called  the  primary , is  connected  to  the 
mains;  the  other  coil,  called  the  secondary , is  connected  to  the  circuit  to 
which  current  is  delivered.  Fig.  29  shows  the  arrangement  of  coils  and  core 
for  a common  type  of  transformer.  The  secondary 
coil  is  wound  in  two  parts  S,  S',  and  the  primary  coii, 
also  in  two  parts  P,  P', 
is  placed  over  the  sec- 
ondary. C is  the  core, 
built  up  of  thin  iron 
plates.  Fig.  30  shows  a 
weather-proof  cast-iron 
case  for  this  transformer. 

When  a current  is  sent 
through  the  primary  it 
sets  up  a magnetism  in 
the  core  which  rapidly 
alternates  with  the 
changes  in  the  current. 

This  changing  magnet- 
ism sets  up  an  alterna- 
ting E.  M.  F.  in  the  sec- 
ondary, and  this  second- 
ary E.  M.  F.  depends 
upon  the  number  of  turns  in  the  secondary  coil.  If  the  secondary  turns  are 
greater  than  the  primary,  the  secondary  E.  M.  F.  will  be  higher  than  that 
of  the  primary.  The  relation  between  the  primary  E.  M.  F.  and  secondary 
E.  M.  F.  is  given  by  the  following: 

Secondary  E.  M.  F.  = primary  E.  M.  F.  X ^ecQn(^ary  ^urns. 

primary  turns 


Fig.  29. 


BATTERIES. 


22, 


, ^ ,,  primary  E.  M.  F. 

or,  secondary  E.  M.  F.  = - — . — - — - . 

’ . primary  turns 

secondary  turns 

. . primary  turns  . . , , 

The  ratio  — — z is  known  as  the 

secondary  turns 

ratio  of  transformation  of  the  transformer. 
For  example,  if  a transformer  had  1,200  pri- 
mary turns  and  60 


Phase  1. 

Phase 

2. 

lOOO  V. 
P 

JLSSJJLSL 

* 1000  P* 
P' 

3— 

3 

f 000 0006 
F-J  OOP- 


n 


secondary  turns,  its 
ratio  of  transforma- 
tion would  be  20  to  1,  Fig.  32. 

and  the  secondary 

voltage  would  be  one-twentieth  that  of  the  primary. 
Transformers  are  made  for  a number  of  different 
ratios  of  transformation,  the  more  common  ones 
being  10  to  1 or  20  to  1.  Of  course,  a transformer 
never  gives  out  quite  as  much  power  from  the  sec- 
ondary as  it  takes  in  from  the  primary  mains, 
because  there  is  always  some  loss  in  the  iron  core 
and  in  the  wire  making  up  the  coils.  The  efficiency 


1000  V- 
p 


I 


-1000  V 
p' 

mwiim 


Fig.  33. 


|— *100  V — 


loo  r- 

Fig.  31. 


C5 

lOO  V — * 


of  transformers  is,  however,  high,  reaching  as  high  as  97$  or  98$  in  the 
larger  sizes.  Transformers  are  always  connected  in  parallel  across  the 
mains,  and  if  they  are  well  designed,  will  furnish  a very  nearly  constant 
secondary  pressure  at  all  loads,  when  furnished  with  a constant  primary 
pressure.  Fig.  31  shows  transformers  connected  on  a single-phase  circuit, 
Fig.  32  shows  the  connection  for  a two-phase  circuit,  and  Fig.  33  shows 
one  method  of  connection  for  a three-phase  circuit. 


ELECTRIC  SIGNALING. 


BATTERIES. 

Batteries  are  used  for  various  purposes  in  connection  with  mining  work, 
principally  for  the  operation  of  bells  and  signals. 

The  LeclancM  cell  is  one  that  is  widely  used  for 
bell  and  telephone  work.  It  is  made  in  two  or 
three  different  forms, 
one  of  the  most  com- 
mon of  these  being  as 
shown  in  Fig.  34  (a). 

The  zinc  element  of 
this  battery  is  in  the 
form  of  a rod  Z,  and 
weighs  about  3 oz.  The 
other  electrode  is  a car- 
bon plate  placed  in  a 
porous  cup  and  sur- 
rounded with  black 
oxide  of  manganese, 
mixed  with  crushed 
coke  or  carbon.  The 
electrolyte  used  in 
the  battery  is  a satura- 
ted solution  of  sal  Fig.  34, 


(a) 


0 


ELECTRIC  SIGNALING. 


ammoniac.  The  E.  M.  F.  of  this  cell  is  about  1.48  volts  when  the  cell  is  in 
good  condition.  In  another  form  of  the  cell,  known  as  the  Gonda  type,  the 
black  oxide  of  manganese  is  pressed  into  the  form  of  bricks  and  clamped 
against  each  side  of  the  carbon  plate  by  means  of  rubber  bands.  This  cell 
will  do  good  work  if  it  is  only  used  intermittently,  i.  e.,  on  circuits  where 
the  insulation  is  good  and  where  there  is  no  leakage  causing  the  cell  to  give 


out  ^nrrpnt,  mntinuouslv.  If  current  is  taken  from  it  for  any  length  of 


The  simple  bell  circuit  is  shown  in  Fig.  35,  where  p is  the  push  button,  b 
the  bell,  and  c,  c the  cells  of  the  battery  connected  up  in  series  When  two 
or  more  bells  are  to  be  rung  from  one  push  button,  they  may  be  joined  up 


in  parallel  across  the  battery  wires,  as  in  Fig.  37  at  a and  6,  or  they  may  be 
arranged  in  series,  as  in  Fig.  36.  The  battery  B is  indicated  in  each  diagram 
by  short  parallel  lines,  this  being  the  conventional  method.  In  the  parallel 
arrangement  of  the  bells,  they  are  independent  of  each  other,  and  the 
failure  of  one  to  ring  would  not  affect  the  others;  but  in  the  series  grouping, 
all  but  one  bell  must  be  changed  to  a single-stroke  action,  so  that  each 
impulse  of  current  will  produce  only  one  movement  of  the  hammer.  The 
current  is  then  interrupted  by  the  vibrator  in  the  remaining  bell,  the  result 


Fig.  36. 


BELL  WIRING. 


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232 


ELECTRIC  SIGNALING. 


si 


Fig.  40. 


being  that  each  bell  will  ring  with  full  power.  The  only  change  necessary 
to  produce  this  effect  is  to  cut  out  the  circuit-breaker  on  all  but  one  bell  by 

connecting 
the  ends  of 
the  magnet 
wires  directly 
to  the  bell 
terminals. 

When  it  is 
desired  to 
ring  a bell 
from  one  of 
two  places  some  distance  apart,  the 
wires  may  be  run  as  shown  in  Fig. 
38.  The  pushes  p,  p'  are  located  at 
the  required  points,  and  the  battery 
and  bell  are  put  in  series  with  each 
other  across  the  wires  joining  the 
pushes. 

A single  wire  may  be  used  to  ring 
signal  bells  at  each  end  of  a line,  the 
connections  being  given  in  Fig.  39. 
Two  batteries  are  required,  B and 
B',  and  a key  and  bell  at  each  sta- 
tion. The  keys  k,  k'  are  of  the 
double-contact  type,  making  connections 
normally  between  bell  b or  b'  and  line 
wire  L.  When  one  key,  as  A:,  is  depressed, 
a current  from  B flows  along  the  wire 
through  the  upper  contact  of  k'  to  bell  b' 
and  back  through  ground  plates  G',  G. 

When  a bell  is  intended  for  use  as  an 
alarm  apparatus,  a constant-ringing 
attachment  may  be  introduced,  which 
closes  the  bell  circuit  through  an  extra 
wire  as  soon  as  the  trip  at  door  or  window 
is  disturbed.  In  the  diagram,  Fig.  40,  the 
main  circuit,  when  the  push  p is  depressed, 
is  through  the  automatic  drop  d by  way  of 
the  terminals  a,  b to  the  bell  and  battery. 
This  current  releases  a pivoted  arm  which, 
on  falling,  completes  the  circuit  between 
b and  c,  establishing  a new  path  for  the 
current  by  way  of  e , independent  of  the 
push  p. 

For  operating  electric  bells,  any  good 
type  of  open-circuit  battery  may  be  used. 
The  Leclanche  cell  is  largely  used  for  this 
purpose,  also  several  types  of  dry  cells. 

Annunciator  System.— The  wiring  dia- 
gram for  a simple  annunciator  system  is 
shown  in  Fig.  42.  The  pushes  1,  2,  3,  etc. 
are  located  in  various  places,  one  side  being  con- 
nected to  the  battery  wire  b,  and  the  other  to  the 

1 1 - • 7 ' IITlfll  + Vl  77  071111111. 


Fig.  41. 


leadin 

ciator 


Fig.  42. 


, wire  l in  communication  with  the  annun- 
irop  corresponding  to  that  place.  A bat- 
tery of  two  or  three  Leclanche  cells  is  placed 
at  B in  any  convenient  location.  The  size  of 
wire  used  throughout  may  be  No.  18  annuncia- 
tor wire.  „ . 4„  . 

A return-call  system  is  illustrated  in  Fig.  41,  in 
which  there  is  one  battery  wire  b,  one  return 
wire  r,  and  one  leading  wire  l , lo,  etc.  for  each 
place  The  upper  portion  of  the  annunciator 
board  is  provided  with  the  usual  drops,  and  below 
these  are  the  return-call  pushes.  These  are 
double-contact  buttons,  held  normally  against 
the  upper  contact  by  a spring.  When  in  this 


SELL  WISING. 


233 


position,  the  closing  of  the  circuit  by  the  push  button  in  any  room,  such  as 
No.  4,  rings  the  office  bell  and  releases  No.  4 drop,  the  path  of  the  current  in 


Fig.  43. 

this  case  being  from  push  4 to  ct-c-d-e-f-g-B-h-b 
back  to  the  push  button.  On  the  return  sig- 
nal being  made  by  pressing  the  button  at  the 
lower  part  of  the  annunciator  board,  the 
office-bell  circuit  is  broken  at  d,  and  a new 
circuit  formed  through  k as  follows:  From 
the  battery  B to  g-m-r-n-o-a-c-k-p  to  battery, 
the  room  bell  being  in  this  circuit.  A gen- 
eral fire-alarm  may  be  added  to  this  system, 
consisting  of  an  automatic  clockwork  appa- 
ratus for  closing  all  the  room-bell  circuits  at 
once,  or  as  many  at  a time  as  a battery  can 
ring.  When  this  system  is  installed,  the  bat- 
tery wire  should  be  either  No.  14  or  No.  16. 
Four  or  five  Leclanch6  cells  are  usually  re- 
quired in  this  case. 

It  will  be  seen  that  the  connections  are 
so  arranged  that  the  room  bell  will  ring  when 
the  push  in  that  room  is  pressed.  If  this  be 
not  desired,  a double-contact  push  may  be 
substituted,  so  that  the  room-bell  circuit  is 
broken  at  the  same  time  that  the  circuit  is 
made  through  the  annunciator.  This  double 
push  should  be  so  connected  that  the  circuit 
is  normally  complete  through  the  bell,  the 
leading  wire  being  connected  to  the  tongue, 
and  the  battery  wire  being  connected  to  the 
second  contact  point,  which  is  normally  out 
of  circuit. 

Telephones  are  also  used  for  signaling  and 
communicating  purposes.  It  has  been  found 
that  a first-class  long-distance  bridging  tele- 
phone is  the  best  type  to  use.  Bridging  tele- 
phones are  so  called  because  they  are  bridged 
or  connected  in  parallel  across  the  line,  and 
are  not  connected  in  series.  If  one  telephone 
should  get  out  of  order,  the  others  are  not 
likely  to  be  disabled.  Fig.  43  shows  a com- 
plete bell  annunciator  and  telephone  outfit, 


MTft  LEVEL 


SBD.  LEVEL 


234 


ELECTRIC  SIGNALING . 


Hoi  it  mg  Engine  House. 


p 


Battery. 


Surface. 


as  installed  in  one  of  the  anthracite 
coal  mines  of  the  D.,  L.  & W.  R.  R.  Co. 
It  will  be  noticed  that  bridging  instru- 
ments are  used  and  that  each  bell  in 
the  shaft  is  provided  with  a return- 
call  button.  This  bell  wiring  should 
be  put  up  in  a substantial  manner, 
and  it  is  best,  if  possible,  to  run  all  the 
wires  down  the  shaft  in  the  shape  of  a 
lead-covered  cable. 

Another  shaft-signaling  apparatus 
is  shown  in  Fig.  44,  as  used  at  the 
West  Vulcan  mines,  Mich.  Fig.  45 


ilFS 


H 


9f-t‘ level 


to*-*  level 


//'- Level 


/£tE  level 


Fig.  44. 


shows  a form  of  waterproof  push  but- 
ton used  at  the  same  mine.  Fig.  46 
shows  the  arrangement  of  flash  signals 
as  used  in  Montana.  This  consists  of 
a switch  cut  into  this  main  circuit  at 


PROSPECTING. 


235 


L _ 

firS 


Fig.  47. 


each  level  of  the  mines.  By  pulling  out  the  handle  bar 
of  the  switch,  the  lights  on  this  circuit  can  all  be  flashed 
at  once,  and  by  a properly  arranged  code  9f  flash  sig- 
nals, the  system  can  be  used  for  communicating  between 
the  surface  to  any  part 
of  the  mine,  and  between 
different  portions  of  the 
mine. 

A system  of  signaling 
by  which  signals  can  be 
sent  to  the  engine  room 
from  any  point  along  the 
haulage  road  is  shown  in  , 

Fig.  47.  The  conductors  a and  6,  leading  from  the  battery 
run  parallel  to  each  other  along  the  roadside,  and  about 
6 in.  apart.  A short  iron  rod,  placed  across  the  wires  a,  o, 
signals  to  the  engineer,  or  by  simply  bringing  the  two  wires 
together  a signal  may  be  sent.  , . . 

When  the  engineer  hauls  from  different  roads,  the  signal- 
ing system  should  be  supplemented  with  indicators,  so  that 
when  the  bell  rings  the  indicator  would  show  from  which 
point  the  signal  came,  and  in  case  several  signals  were 
given  at  the  same  time,  the  engineer  should  not  heed  any 
until  the  indicator  shows  that  a complete  signal  came 
from  one  place.  , . . . 

A system  of  signaling  for  showing  whether  or  not  a 
section  of  track  is  occupied  by  another  motor  is  shown 


/ 27S 


Lamp  Circuit 


Fig.  48. 


Ma/ns 


/oo’ 


200 


f 300* 


400 


SOO' 


in  Fig.  48.  White  lights  indicate  a clear  track  and  dark- 
ness an  occupied  section.  A single-center  hinge,  double- 
handle  switch  at  each  signal  station  is  used  and  a touch  of  Fig.  46. 

the  handle  throws  the  switch  in  the  desired  direction.  The 

switches  are  placed  in  the  roof,  4£  ft.  above  rails  within  easy  reach  of  motor- 
man.  Fig.  48  shows  the  connections.  Each  switch  is  provided  with  a spring 
(not  shown  in  the  figure)  which,  drawing  across  the  center  hinge,  when  the 
handles  are  in  their  central  position,  insures  a perfect  contact  when  the 
switch  is  inclined  toward  either  the  trolley  or  rail-terminal  plug. 


PROSPECTING. 


The  prospector  should  have  a general  knowledge  of  the  mineral-bearing 
strata,  and  should  know  from  the  nature  of  the  ledges  exposed  whether  to 
expect  to  find  mineral  or  not.  He  should  also  possess  such  a kno  wledgeof  the 
use  of  tools  as  will  enable  him  to  construct  simple  structures,  and  a sufficient 
experience  in  blacksmithing  to  enable  him  to  sharpen  picks  and  drills,  or 
to  set  a horseshoe,  if  necessary.  . , . . , ... 

Outfit  Necessary.— The  character  of  the  prospecting  being  carried  on  will 
have  considerable  effect  on  the  outfit  necessary,  which  should  always  be  as 
simple  as  possible.  In  general,  when  operating  in  a settled  country,  the 
outfit  is  as  follows:  A compass  and  clinometer  for  determining  the  dip  and 
strike  of  the  various  measures  encountered;  a pick  and  shovel  for  excavating, 
and,  where  rock  is  liable  to  be  encountered,  a set  of  drills,  hammer,  spoon 
for  cleaning  the  holes,  tamping  stick,  powder  and  fuse,  or  dynamite  fuse 
and  cap;  a blowpipe  outfit;  a small  magnifying  glass;  an  aneroid  barometer 
for  determining  elevations,  and  a small  hand  pick;  the  latter  should  weigh 
about  If  lb.,  and  should  have  a pick  on  one  end  and  a square-faced  ham- 
mer on  the  other,  the  handle  being  from  12  to  14  in.  long. 

If  the  region  under  consideration  has  been  settled  for  some  time,  there 
will  probably  be  geological,  county,  railroad,  or  other  maps  available. 


236 


PBOSPECTISG. 


These  mav  not  be  accurate  as  to  detail,  but  will  be  of  great  assistance  in  the 
work  on  account  of  the  fact  that  they  give  the  course  of  the  railroads, 
streams,  etc. 

When  operating  in  a mountainous  region,  away  from  a settled  country, 
and  especially  when  searching  for  precious  metals,  the  following  materials, 
in  addition  to  that  already  mentioned,  may  be  required:  A donkey  or  pony 
packed  with  a couple  of  heavy  blankets,  an  A tent,  cooking  utensils,  etc.;,  a . 
supply  of  flour,  sugar,  bacon,  salt,  baking  powder,  and  coffee,  sufficient  for 
at  least  a month.  It  is  also  well  to  take  some  fruit,  but  all  fruit  containing 
stones  or  pits  should  be  avoided,  as  they  are  only  dead  weight,  and  every 
pound  counts.  For  the  same  reason,  canned  goods  should  be  avoided,  on 
account  of  the  laTge  amount  of  water  they  contain.  A healthy  man  will 
require  about  3 lb.  of  solid  food  per  day.  Many  prefer  to  vary  the  diet  by 
taking  rice,  corn  meal,  beans,  etc.,  in  place  of  a portion  of  the  flour. 

The  additional  tools  necessary  are  an  ax,  a pan  for  washing  gold  ore, 
making  concentrating  tests,  etc.,  and,  in  some  cases,  an  assay  furnace 
and  outfit  packed  upon  another  animal.  Where  game  is  abundant,  a shot- 
gun or  rifle  will  be  found  useful  for  supplying  fresh  meat.  In  regions 
abounding  in  swamps  it  becomes  necessary  to  operate  from  canoes,  or  to  - 
take  men  for  porters  or  packers,  who  carry  the  outfit  on  their  backs  or 
heads.  These  men  will  carry  from  60  to  125  lb. 

Plan  of  Operations.— When  the  presence  of  mineral  is  suspected  in  a tract 
of  land,  a thorough  examination  of  the  surface  and  a study  of  the  exposed 
rocks,  in  place,  may  result  in  its  immediate  discovery,  or  in  positive  proof 
of  its  absence;  or  it  mav  result  in  still  further  increasing  the  doubt  of,  or  the 
belief  that,  it  does  exist.  The  first  procedure  in  prospecting  a tract  of  land 
is  to  thoroughly  traverse  it.  and  note  carefully  any  stains  or  traces  of  smut, 
and  all  outcrops  of  every  description;  and.  whenever  possible,  take  the  dip 
and  the  course  of  the  outcrop  with  a pocket  compass.  Any  fossils  should 
also  be  carefully  noted,  to  assist  in  determining  the  geological  age  of  the 
region.  These  outcrops  are  frequently  more  readily  found  along  roads  or 
streams  than  anv  other  place  on  the  tract.  In  traveling  along  the  streams, 
the  prospector  should  pav  particular  attention  to  its  bed  and  banks,  to  see 
whether  there  are  any  small  particles  of  mineral  in  the  bed  of  the  stream, 
or  any  stains  or  smut  exposed  along  the  washed  banks.  If  small  pieces  of 
mineral  are  found  in  the  stream,  a search  up  it  and  its  tributaries  will  show 
where  the  outcrop  from  which  the  find  came  is  located.  When  the  ravines 
and  vallevs  are  so  filled  with  wash  that  no  exposures  are  visible,  and  nothing 
is  gained*  bv  a careful  examination  of  them,  the  prospector  must  rely  on 
topographical  features  to  guide  him.  . _ 

Any  gold  present  in  the  vein  material  usually  remains  in  the  float  as  free 
or  metallic  gold,  but  other  valuable  metals  are  often  leached  out.  The  fact 
that  the  float  itself  may  be  barren  does  not  indicate  that  it  may  not  have 
come  from  a very  rich  deposit,  and  hence  it  will  often  pay  to  follow  barren 
float  since  the  outcrop  of  the  vein  itself  is  often  either  entirely  barren,  low 
grade,  or  of  a different  nature  from  the  deeper  deposits.  In  cases  where 
there  are  no  outcrops  or  any  other  surface  indications,  it  would  become 
necessary  to  sink  shafts  or  test  pits,  or  to  proceed  by  drilling. 

The  absence  of  any  indication  of  mineral  in  the  soil  may  not  prove  that 
there  is  not  an  outcrop  near  at  hand,  for  the  soil  is  frequently  brought  from 
a distance,  and  bears  no  relation  to  the  material  underlying  it.  In  like 
manner,  glacial  soil  often  contains  debris  transported  from  deposits  many 
miles  away;  but  such  occurrences  can  usually  be  distinguished  by  the  gen- 
eral character  of  the  associated  wash  material. 

Frequently,  the  weathered  outcrop  of  a deposit  has  been  overturned  or 
dragged  back  upon  itself,  so  as  to  indicate  the  presence  of  a very  thick 
deposit  For  this  reason,  anv  openings  made  to  determine  the  character  of 
the  material  should  be  continued  until  the.  coal  or  other  mineral  is  of  a firm 
character,  and  both  floor  and  roof  are  well  exposed.  Sometimes,  in  the  case 
of  steeplv  pitching  coal  beds,  the  surface  may  be  overturned  for  a consider- 
able depth,  so  that  it  is  difficult  to  tell  which  is  the  roof  and  which  is  the 
floor  Usually,  if  Stigmariee  are  found  in  the  rocks  of  one  wall,  it  is  supposed 
that  this  wall ’is  the  floor  of  the  seam,  while  if  Sigillariae.  fern  leaves,  etc.  are 
found  in  the  wall  rock,  it  is  probably  the  roof  of  the  deposit.  These  indi- 
cations are  not  positive  proof,  for  both  of  these  fossils  may  occur  in  either 
the  top  or  bottom  wall  of  a coal  deposit,  though  they  are  usually  found  in 
the  positions  noted.  Coal.  clav.  gypsum,  salt.  etc.  usually  occur  m unaltered 
deposits,  i.  e.,  in  rocks  that  have  not  undergone  metamorphism. 


PROSPECTING. 


237 


The  accompanying  table  gives  the  names  of  the  various  geological  periods, 
both  as  they  occur  in  America  and  their  foreign  equivalents,  together  with 
the  name  of  the  principal  form  of  life  during  each  period.  The  various 
terms  employed  in  geology  are  defined  in  the  glossary. 


238 


PROSPECTING. 


Mptals  and  metallic  ores  usually  occur  in  rocks  that  have  undergone 

MSSSBIE 

mmmm 

siT=^g^@gi 

SHIS 

&S5MS  «FtKndih^K^ 

toward  the  top  of  the  hf^l^¥eTT{ice  or  indication  of  the  outcrop  of  a 
to  sink  a shallow  shaft  above  the  terrace.  importance  have  as  yet 

1>eSrB^^’&,a5KSai<^^i»«  gs^s&'asr'pSEa: 

a[>y  “ePd^rik  odfThe  coal hat up to  been  found 

although  the  bulk  ot  the  nest  coai ^xma,  up  metamorphic  regions  con- 

s j|  t£S> » jp-s-i&'K 

gassa  A’g.vvpyp.^^sa.ntq 
SMSS3SS&' "^cssrsisiSti*  w.  -»-»  ■» 

frequently  associated  with  beds  or iron  01^  lly  foUnd  in  mountainous 


ORE  DEPOSITS . 


239 


economic  products  as  coal,  petroleum,  building  stone,  clays,  etc.,  but  not  often 
of  the  precious  metals.  The  reason  for  this  appears  to  be  that  the  latter  are 
commonly  found  to  be  associated  with  evidences  of  more  or  less  heat.  In 
the  Rocky  Mountains  they  are  rarely  found  except  where  volcanic  eruptions 
have  at  some  time  been  active,  or  where  the  strata  have  been  changed  or 
metamorphosed  and  crystallized  by  heat. 

As  metallic  ore  bodies  occupy  fissures  and  other  openings  in  the  earth’s 
crust,  we  must  go  to  regions  where  the  greatest  disturbances  and  uplifts 
have  occurred,  accompanied  by  the  greatest  rending  and  contortions  of  the 
rocks,  and  eruptions  of  volcanic  matter. 

As  a broad  assertion,  we  may  say  that  the  greater  part  of  any  mountain 
region  is  a prospecting  field,  with  the  exception  of  those  areas  we  have 
restricted  as  unpromising.  But  over  this  wide  area  of  more  or  less  metamor- 
phosed and  crystalline  rocks,  there  are  regions  and  localities  where  the 
precious  metals  have  already  been  found,  and  others  where  on  geological 
grounds  they  are  most  likely  yet  to  be  found,  and  those  are  generally  where 
eruptive  forces  have  been  especially  active,  where  once  molten  eruptive 
rocks  are  most  abundant,  and  the  disturbance  and  crystallizing  of  the  strata 
most  pronounced.  _ 

Position  of  Veins  and  Ore  Deposits.— Ores,  as  a rule,  are  to  be  looked  for  at 
the  junction  of  any  two  dissimilar  rocks,  rather  than  in  the  mass  of  those 
rocks.  However,  there  are  many  exceptions  to  this,  where  the  mass  of  a 
decomposed  dike  or  sheet  of  porphyry  has  been  impregnated  by  free  gold  or 
gold-bearing  pyrites,  and  the  whole  rock  is  practically  a gold  vein.  In  this 
mass,  the  richest  gold  is  often  found  in  a network  of  little  quartz  veins  run- 
ning through  the  porphyry  mass.  Some  of  our  richest  gold  mines  are  found 
in  “ rotten,”  decomposed,  oxidized  dikes  and  sheets  of  porphyry;  but  this  is 

rarely  the  case  with  lead-silver  ores, 
which  frequent  rather  the  lines  of  con- 
tact in  limestones  or  in  fissure  veins  in 
granite.  The  Cambrian  quartzites  a few 
years  ago  were  rather  avoided  by  the 
prospectors,  their  extreme  hardness  pre- 
senting great  difficulties  in  mining,  and 
from  the  fact  that  they  were  generally 
supposed  to  be  barren.  The  late  disco v- 
b eries  of  very  rich  gold  deposits  in  them, 
and  of  similar  deposits  in  quartzites  of 
a later  age,  have  drawn  more  attention 
to  them.  The  gold  has  been  found  in 
a free  state  associated  with  oxide  of  iron 
in  cavernous  deposits,  and  in  close  prox- 
imity to  eruptive  rocks.  In  the  granitic 
rocks,  both  gold  and  silver  occur  in  fissure  veins  associated  with  pyrites, 
galena,  etc.  These  fissures,  occupied  by  mineralized  quartz  veins,  may  occur 
in  the  granite  or  gneiss  alone,  or  be  at  the  contact  of  these  rocks  with  a 
porphyry  dike. 

Veins  in  overflows  of  volcanic  lava  generally  fill  a fissure  having  a more 
or  less  steep  inclination,  penetrating  the  lava  sheets,  caused  probably  by 
shrinkage  of  the  molten  lava  on  cooling.  These  fissures,  in  some  cases,  are 
likely  to  be  limited  in  depth  to  the  thickness  of  the  lava  sheet.  Where,  in  a 
few  rare  cases,  the  fissure  has  been  traced  down  to  the  underlying  granite  or 
some  other  rock,  it  has  come  abruptly  to  an  end. 

Underground  Prospecting. — Frequently  a seam  or  deposit  becomes  faulted 
or  pinched  out  underground,  and  it  is  necessary  to  continue  the  search  by 
means  of  underground  prospecting.  Underground  prospecting  is,  to  a large 
extent,  similar  to  surface  prospecting,  the  underground  exposures  being 
simply  additional  faces  for  the  guidance  of  the  engineer.  In  the  case  of 
coal  beds  or  similar  seams,  if  a fault  or  dislocation  is  encountered,  the  man- 
ner of  carrying  on  the  search  will  depend  on  the  character  of  the  fault. 
Where  sand  faults  or  washouts  are  encountered,  the  drift  or  entry  should 
be  driven  forwards  at  the  angle  of  the  seam  until  the  continuation  of  the 
formation  is  encountered,  when  a little  examination  of  the  rocks  will  indi- 
cate whether  they  are  the  underlying  or  overlying  measures.  In  the  case 
of  dislocations  or  throws,  the  continuation  of  the  vein  may  be  looked  for  by 
Schmidt’s  law  of  faults,  which  is  as  follows:  Always  follow  the  direction  of  the 
greatest  angle.  It  has  been  discovered  by  observation  that,  in  the  majority 
of  cases,  the  hanging-wall  portion  of  the  fault  has  moved  down,  and  on  this 


240 


PROSPECTING . 


account  such  faults  are  commonly  called  normal  Jaults.  For  instance,  ii  the 
bed  a b,  Fig.  1,  were  being  worked  from  a toward  the  fault,  upon  encoun- 
tering the  fault,  work  would  be  continued  down  on  the  farther  side  of  the 
fault  toward  d,  until  the  continuation  of  the  bed  toward  b was  encountered. 
In  like  manner,  had  the  work  been  proceeding  from  6,  the  exploration 
would  have  been  carried  up  in  the  direction  of  the  greatest  angle,  and  the 
continuation  toward  a thus  discovered.  A reverse  fault  is  one  in  which 
the  movement  has  been  in  the  opposite  direction  to  a normal  fault.  Espe- 
cially in  the  case  of  precious  metal  mines,  where  the  material  occurs  as 
perpendicular  or  steeply  pitching  veins,  faults  are  liable  to  displace  the 
deposit,  both  horizontally  and  vertically,  in  which  case  it  may  be  difficult 
to  determine  the  direction  of  the  continuation  of  the  ore  body;  but  fre- 
quently pieces  of  ore  are  dragged  into  the  fault,  and  these  serve  as  a guide 
to  the  miner,  and  indicate  the  proper  direction  for  exploration.  Where  a 
bed  or  seam  is  faulted,  its  continuation  can  frequently  be  found  by  breaking 
through  into  the  measures  beyond,  when  an  examination  of  the  formation 
will  indicate  whether  the  rocks  are  those  that  usually  occur  above  or  below 


the  desired  seam.  „ , , , ..  . 

Prospecting  for  Placer  Deposits.— Placers  are  fragmental  deposits  from  water 
in  which  the  heavier  minerals  have  been  concentrated  in  certain  portions, 
usually  next  the  underlying,  or  bed,  rock.  The  materials  that  are  recovered 
from  placer  deposits  are  metallic  gold,  tinstone,  monazite,  sand,  or  precious 
stones.  Placer  deposits  are  modern  or  ancient.  Modern  placers  are 
deposits  of  washed  material,  or  debris,  in  the  beds  or  along  the  banks  of 
streams  that  are  either  now  in  existence  or  existed  in  comparatively  recent 
times.  Placer  deposits  may  also  occur  in  deposits  along  the  seashore. 
Ancient  placers  are  fragmental  accumulations,  similar  to  the  modern 
placers,  which  have  been  buried  under  accumulations  of  strata  or  flows  of 
lava,  and  they  may  or  may  not  have  become  consolidated  into  rock. 

At  times,  placers  are  very  compact,  owing  to  the  presence  of  large  quanti- 
ties of  oxide  of  iron  or  calcium  carbonate,  or  similar  cementing  material. 
Often,  in  the  case  of  modern  placers,  the  streams,  or  other  sources  of  water 
that  deposited  the  material,  have  changed  their  course  so  that  the  placer 
deposit  is  now  high  up  in  the  benches  bordering  the  streams,  or,  possibly 
even  on  the  top  of  the  present  hills.  Such  deposits  are  commonly  called 
bench  deposits , while  those  along  the  sides  of  the  streams  below  the  high- 
water  mark  are  called  bar  deposits , diggings , or  placers.  ..... 

Frequently,  a large  portion  of  the  gold  or  other  valuable  material  is 
found  in  pockets  or  irregularities  in  the  bed  rock,  but  the  pot  holes  under 
waterfalls  are  frequentlv  barren  of  gold,  on  account  of  the  fact  that  the 
current  there  was  sufficiently  swift  to  wash  everything  out,  either  heavy  or 
light.  When  the  soil  is  saturated  with  water,  the  mass  may  partake  of  the 
nature  of  a semifluid  through  which  the  heavy  particles  of  gold  settle  until 
they  accumulate  on  the  bed  rock.  . ^ . . 

When  prospecting  for  placers,  the  miner  examines  the  country  for  any 
indications  of  present  or  ancient  watercourses  in  which  the  deposits  ot 
placer  material  have  been  formed.  He  pans  the  dirt  from  any  deposits  dis- 
covered, to  see  if  it  contains  colors  (small  particles  of  metallic  gold).  It 
colors  are  found,  more  extensive  operations  are  in  order,  and  hence  he 
sinks  to  bed  rock  and  examines  the  material  thoroughly,  to  see  if  it  contains 
a paying  quantity  of  the  valuable  mineral.  . e ^ ..  . . 

The  form  of  placer  deposit  in  dry  or  and  regions  differs  from  that  in 
regions  where  the  rivers  have  a continuous  flow,  on  account  of  the  tact  that 
the  deposits  are  largely  the  result  of  sudden  rushes  of  water  partaking  of  the 
nature  of  cloudbursts*,  hence  the  rich  portions  in  the  placer  material  are 
very  irregular,  and  are  rarelv  situated  on  bed  rock,  but  are  usually  found  on 
any  strata  that  formed  the  bottom  of  the  ravine  during  the  sudden  rush  of 
water.  During  the  rainy  season  in  arid  regions,  the  surface  soil  is  some- 
times softened  for  a few  inches,  so  that  it  becomes  practically  a mud,  and 
particles  of  gold  that  it  may  contain  tend  to  settle  to  the  bottom  of  the  sott 
portion,  thus  rendering  the  surface  barren.  This  barren  surface  may  be 
subsequently  washed  away  by  the  rain,'  or  blown  away  as  dust  during  the 
dry  season.  The  repeating  of  this  process  year  after  year  results  in.  the 
removal  of  considerable  of  the  original  surface  and  the  formation  of  a rich 
stratum  iust  below  the  grass  roots.  Prospectors  in  and  regions,  who  have 
been  used  to  operating  in  an  ordinarily  well-watered  country,  are  frequently 
deceived  by  finding  this  rich  ground  so  high  up  in  the  deposit,  not  knowing 
that  it  is  no  indication  as  to  the  value  of  the  material  at  a greater  depth. 


OEMS  AND  PRECIOUS  STONES. 


241 


In  many  cases,  in  the  arid  regions  the  portion  of  the  deposit  upon  bed  rock 
is  entirely  barren.  In  like  manner,  frozen  ground  may  play  an  important 
part  in  the  formation  and  distribution  of  the  values  in  placer  deposits. 

Gems  and  precious  stones  are  prospected  for  in  a manner  similar  to  that 
employed  in  searching  for  placer  material,  and  are  usually  found  in  alluvial 
deposits,  from  which  they  are  obtained  by  washing.  In  a few  cases  gems 
are  found  in  the  rocks  themselves;  as,  for  instance,  diamonds  in  the  hard 
matrix  that  occurs  as  pipes  or  chimneys  in  metamorphic  rocks,  and  which, 
upon  exposure  to  the  atmosphere,  becomes  decomposed,  so  that  the  stones 
are  easily  removed.  Some  of  the  corundum  minerals  are  found  in  lime- 
stone and  metamorphic  or  crystalline  rocks.  Turquoise  usually  occurs  in 
veins,  the  outcrop  of  which  is  stained  with  carbonate  of  copper.  In  most 
cases,  it  does  not  pay  to  extract  gems  from  rock  formations  when  the  rock  is 
extremely  hard,  owing  to  the  fact  that  the  gems  are  liable  to  become  broken 
in  separating  them  from  the  rock  matrix. 

For  gem  prospecting,  the  following  outfit  has  been  recommended:  A 
shovel  and  pick;  two  sieves,  one  of  2 or  3 meshes  to  the  linear  inch,  and  the 
other  of  20  or  more  meshes  to  the  inch  (the  coarse  sieve  should  be  arranged 
to  fasten  on  top  of  the  finer  one  for  use  together);  a tub  in  which  the  sieves 
can  be  submerged  in  water;  an  oilcloth  on  which  to  sort  the  gravel;  several 
stones  and  crude  gems  as  a scale  of  hardness;  a small  pocket  magnifying 
glass,  and  a dichroscope.  In  some  cases,  a portion  of  the  outfit  is  dispensed 
with.  The  use  of  the  outfit  may  be  explained  as  follows:  The  tub  is  partially 
filled  with  water,  the  two  sieves  fastened  together,  and  a shovelful  of 
material  placed  in  the  upper  one,  when  they  are  submerged  in  water,  the 
large  stones  cleaned  and  examined,  and  all  of  the  fine  material  worked 
through  the  upper  sieve,  which  is  then  removed,  the  material  on  it  examined 
and  disposed  of.  The  material  in  the  fine  sieve  is  then  washed  until 
free  from  clay,  when  a little  jigging  motion  in  the  water  will  carry  the 
lighter  material  to  the  top.  The  sieve  is  then  quickly  inverted  and  the 
material  dumped  out  on  the  oilcloth,  thus  bringing  the  heavier  stones  to 
the  top.  The  various  pieces  should  now  be  examined  with  the  magnifying 
glass,  scale  of  hardness,  etc.,  and  the  identity  of  any  doubtful  colored  gems 
settled,  by  means  of  the  dichroscope.  Few  precious  stones  are  of  sufficient 
specific  gravity  to  be  concentrated  in  distinct  beds,  like  gold  or  tinstone,  but 
they  are  usually  fairly  well  concentrated  and  freed  from  much  of  the  lighter 
worthless  material. 

Value  of  Free  Gold  per  Ton  of  Ore.— The  accompanying  table  was  prepared 
by  Mellville  Atwood,  F.  G.  S.,  and  its  use  may  be  explained  as  follows' 
If  a 4-lb.  sample  of  quartz  be  crushed,  the  gold  separated  by  panning  and 


Value  of  Free  Gold  per  Ton  of  Ore. 
( Risdon  Iron  Works.) 


Weight, 
Washed  Gold. 
4-Lb.  Sample. 
Grains. 

Fineness, 

780. 

Value  per  Oz., 
$16.12. 

Fineness, 

830. 

Value  per  Oz., 
$17.15. 

Fineness, 

875. 

Value  per  Oz., 
$18.08. 

Fineness, 

920. 

Value  perOz., 
$19.01. 

5.0 

$83.97 

$89.36 

$94.20 

$99.05 

4.0 

67.18 

71.49 

75.36 

79.24 

3.0 

50.38 

53.61 

56.52 

59.43 

2.0 

33.59 

35.74 

37.68 

39.62 

1.0 

16.79 

17.87 

18.84 

19.81 

.9 

15.11 

16.08 

16.95 

17.82 

.8 

13.43 

14.29 

15.07 

15.84 

.7 

11.75 

12.51 

13.19 

13.86 

.6 

10.07 

10.73 

11.30 

11.88 

.5 

8.40 

8.93 

9.42 

9.90 

.4 

6.71 

7.14 

7.53 

7.92 

.3 

5.03 

5.36 

5.65 

5.94 

.2 

3.36 

3.57 

3.76 

3.96 

.1 

1.68 

1.78 

1.88 

1.98 

amalgamation,  the  quicksilver  volatilized  by  blowpiping  or  otherwise,  and 
the  resulting  button  weighed,  the  value  of  the  ore  per  ton  of  2,000  lb.  will 


242 


PROSPECTING. 


be  found  opposite  the  weight  of  the  button.  The  values  are  given  for  fine- 
ness of  gold  varying  from  780  to  920.  . 

To  determine  the  value  of  gravel,  a 6-lb.  sample  will  give  the  same 
results  as  that  obtained  from  a 4-lb.  sample  of  quartz,  on  account  of  the 
fact  that  18  cu.  ft.  of  gravel  measured  in  a bank  weigh  1 ton,  or  2,000  lb.; 
hence,  a cubic  vard  of  gravel  measured  in  a bank  weighs  3,000  lb.,  and 
for  this  reason  a sample  one  and  one-half  times  as  large  as  that  required 
for  quartz  must,  be  taken.  In  case  the  gravel  is  of  low  grade,  a sample  ten 
times  as  large,  or  60  lb.,  mav  be  taken,  in  which  case  the  value  opposite 
the  weight  of  the  button  will  have  to  be  divided  by  10. 

As  an  example,  in  the  use  of  the  table  we  may  suppose  that  a button 
from  4 lb.  of  ore  or  6 lb.  of  gravel  weighs  3.8  gr.,  and  that  the  fineness  of 
the  gold  is  830.  Opposite  3 in  the  table  we  will  find  $53.61  as  the  value  of 
the  button  in  dollars  containing  3 gr.  of  gold,  and  opposite  .8  we  will  find 
$14.29.  The  sum  of  these  is  $67.90,  the  value  of  the  ore  per  ton,  or  the  gravel 
per  cubic  yard. 


EXPLORATION  BY  DRILLING  OR  BORE  HOLES. 

Earth  Augers.— When  testing  soil  or  searching  for  placer  gold,  sand,  soft 
iron,  or  manganese  ores,  and  similar  materials  that  usually  occur  compara- 
tively near  the  surface,  hand  augers  may  be  employed  to  great  advantage. 
A good  form  of  hand  auger  consists  of  a piece  of  fiat  steel  or  iron,  with  a 
steel  tip,  twisted  into  a spiral  about  1 ft.  long,  and  having  four  turns.  The 
point  is  split  and  the  tips  sharpened  and  turned  in  opposite  directions  and 
dressed  to  a standard  width,  usually  2 in.  The  auger  is  attached  to  a short 
piece  of  1"  pipe,  and  is  operated  by  joints  of  1"  pipe,  which  are  coupled 
together  witlr  common  pipe  couplings.  The  auger  is  turned  by  means  of  a 
double-ended  handle  having  an  eye  in  the  center  through  which  the  rod 

D&SS6S 

The  handle  is  secured  by  means  of  a setscrew.  In  addition  to  the  auger, 
it  is  well  to  have  a straight-edged  chopping  bit  for  use  in  comparatively  hard 
seams.  This  may  be  made  from  a piece  of  If"  octagon  steel,  with  a 2 cut- 
ting edge.  The  upper  end  of  the  steel  is  welded  on  to  a piece  of  pipe  similar 
to  that  carrying  the  auger.  When  the  chopping  bit  is  employed,  it  is 
necessary  to  have  a heavy  sinking  bar,  which  may  be  made  from  a piece  ot 
solid  U"  iron  bar,  fitted  with  ordinary  1"  pipe  threads  ()n  the  ends.  Pros- 
pecting can  be  carried  on  to  a depth  of  from  50  to  60  ft.  with  this  outfit.  The 
number  of  men  necessary  to  operate  the  rods  varies  from  2 to  4,  depending 
on  the  depth  of  the  hole  being  drilled.  When  more  than  30  ft.  of  rods  are  in 
use,  it  is  usually  necessary  to  have  a scaffold  on  which  some  of  the  men  can 
stand  to  assist  in  withdrawing  the  rods.  When  withdrawing  the  rods, 
to  remove  the  dirt,  they  are  not  uncoupled  unless  over  40  ft.  of  rods  are  in 
use  at  one  time,  and  sometimes  as  many  as  50  or  60  ft.  are  drawn  without 

Un Percussion  or  churn  drills  are  frequently  employed  in  drilling  for  oil, 
water,  or  gas,  and  were  formerly  much  used  in  searching  for  coal  and  ores, 
but,  owing  to  the  fact  that  they  all  reduce  the  material  passed  through  to 
small  pieces  or  mud,  and  so  do  not  produce  a fair  sample,  and  to  the  fact 
that  they  can  only  drill  perpendicular  holes,  they  are  at  present  little  used 
in  prospecting  for ‘either  ore  or  coal.  . , , 

The  cost  and  rate  of  drilling  by  means  of  a percussive  or  churn  drill 

varies  greatly,  being  affected  much  more  by 
the  character  of  the  strata  penetrated  than  is 
the  case  with  the  diamond  drill.  In  the  case 
of  highly  inclined  beds  of  varying  hardness, 
the  holes  frequently  run  out  of  line  and  be- 
come so  crooked  that  the  tools  wedge,  and 
drilling  has  to  be  suspended.  For  drilling 
through  moderately  hard  formations,  usually 
encountered  in  searching  for  gas  or  water, 
such  as  sandstones,  limestones,  slates,  etc.,  the 
accompanying  costs,  from  the  American  Well 
Works,  Aurora,  111.,  may  be  taken  per  foot 
for  wells  from  500  to  3,000  ft.  deep  for  the 
central  or  eastern  portion  of  the  United 
This  cost  includes  the  placing  of  the  casing,  but 


Cost  of  Well-Drilling. 


Size  of  Well. 
Inches. 

Cost  per  Foot. 

6 

$1.50 

8 

2.25 

10 

3.00 

12 

5.00 

15 

8.00 

States  at  present  (1900). 
not  the  casing  itself. 


drilling  or  bore  HOLES. 


243 


When  drilling  wells  for  oil  or  gas  to  a depth  of  approximately  1^0®  ft^, 
usinff  the  ordinary  American  rig  with  a cable,  the  cost  is  sometimes  reduced 
per  foot  i5r  6"  or  Sewells.  Tto  “ 

usually  njpch 

ifjA  mav  be  drilled  in  a single  day,  and  at  other  times,  when  very  hard 

to  make  more  than  from  1 to  2 ft.  per 

^ The  diamond  drill  is  the  only  form  that  has  been  universally  successful  in 
drilling  in  any  direction  through  hard,  soft,  or  variable  material.  Even 
rhp  of  the  diamond  drill,  many  difficulties  present  themselves,  and 

KISS  Mate  is  smt  JSBftfswa  a 

practice,  Dy  u.  m ^ « > . *?  ’ t econ0mv  to  employ  a machine  of  large 

When  a large  machine  is  operating  small  rods  on  light  work,  the  ariner 

in  which  the  feed  is  independent  of  the  material  being  cut,  as  m the  case 

thTheflrIte K’^advantageous  when  drilling  through  variable. measures 
in  sea?ch  of  fofrly firm  material,  which  does  not  occur  m very  thm  beds  or 
seams  On  account  of  the  fact  that  this  class  of  feed  insure©  the  maximum 

amount  of  advance  of  which  the  bit  is  capable in  1 rounl  upland 
danger  is  that  the  core  from  any  thin  soft  seam  may  be  grouna  up  ana 
washed  away  without  any  indication  of  its  presence  having  been  given. 

The  second  class  or  positive  gear-feed,  if  properly  operated,  requires 
somewhat  greater  skill  but  if  used  in  connection  with  a thrust  register,  it 
ffi^s^ehaffi^in^rmation  as  to  the  material  being  cAit,  andisespeciaHy 

useful  when  prospecting  for  soft  deposits  of  vey^1^J®T^t^|,1rfze  of  the 
Size  of  Tools  —The  size  of  tools  and  rods,  and  consequently  the  size  oi  ine 
core  extracted  depends  on  the  depth  of  the  hole  and  the  character  of  the 
materialTeing  prospected.  When  operating  in  firm  measures  such  as 
“nthracite  coal,  hardrock,  etc.,  it  is  best  to  employ  a rattw; small  bU  even 
when  drilling  ud  to  700  ft.,  or  more,  m depth.  For  such  work,  a core  oi 
U in.  to  1*  in.  is  usually  extracted.  The  rate  of  driUing  with  a small  outfit 
is  verv  much  greater  than  with  a large  one,  owing  to i the  fact _ that  there 
is  a small  cutting  surface  exposed,  and  the  rate  of  rotation  of  the  rods  can  be 
much  treater  When  prospecting  for  soft  materials,  such  as  bitummo 
coal  valuable  soft  ores,  or  for  disseminated  ores,  such  as  lead^copper,  gold, 

silver  etc  it  is  best  to  employ  a larger  outfit  and  extract  a core  2 or  3 in.  in 
diameter,  and  sometimes  even  larger,  even  though  a comparatively  small 

maD rift  of1Sd ia m ond° d°r H?h d es^o/the  divergence  from 

becomes  a serious  matter.  This  trouble  may b®  wito 

tools  about  the  bit  as  nearly  up  to  gauge  as  possible. . Core oarnfia wim 
spiral  water  grooves  about  them,  answer  this  purpose  very  well  if  they  are 
renewed  before  excessive  wear  has  taken  place.  of  tw0 

Surveying  of  diamond  drill-holes  may  be  carried  onfb,y  oei^trict  Where 
methods,  depending  on  the  magnetic  conditions  of  tte  E F 

there  is  no  magnetic  disturbance,  the  system  developed  by  Mr.  -b.  . 

MacGeorge  of  Australia,  may  be  employed.  This  consists  m introducing 
into  the  hole,  at  various  points,  small  tubes  containing ^lted  gelat  , 
which  are  suspended  magnetic  needles  and  small  P^mmets.  After  t 
gelatine  has  hardened  the  tubes  are  removed,  and J the  angle s ^^between  me 

center  line  of  the  tube,  the  plummet,  and  the  need^  noted L’/  This  methol 
the  data  from  which  the  course  of  the  hole  can  be  plotted,  lhismetnoa 
gives  both  the  vertical  and  the  horizontal  dn.t. 


244 


PROSPECTING. 


Where  there  is  magnetic  disturbances  the  needle  cannot  be  used,  but  a 
system  brought  out  by  Mr.  G.  Nolten,  of  Germany,  has  been  quite  exten- 
sively employed.  In  this  case,  tubes  partly  filled  with  hydrofluoric  acid  are 
introduced  into  the  hole,  at  various  points,  and  the  acid  allowed  to  etch  a 
ring  on  the  inside  of  the  tube.  After  the  acid  has  spent  itself  the  tubes  are 
withdrawn,  and  by  bringing  the  liquid  into  such  a position  that  it  corre- 
sponds with  the  ring  etched  on  the  inside  of  the  tube,  the  angle  of  the  hole 
at  the  point  examined  can  be  determined.  This  method  gives  a record  of 
the  vertical  drift  of  the  hole  only. 

The  value  of  the  record  furnished  by  the  diamond  drill  depends  largely  on 
the  character  of  the  material  sought.  The  core  extracted  is  always  of  very 
small  volume  when  compared  with  the  large  mass  of  the  formation  pros- 
pected, and  hence  will  give  a fair  average  sample  only  in  the  case  of  very 
uniform  deposits.  The  value  of  the  diamond  drill  for  prospecting  may  be 
stated  as  follows:  More  dependence  can  be  placed  on  the  record  furnished  by 
the  diamond  drill  when  prospecting  for  materials  that  occur  in  large  bodies  of 
uniform  composition  than  when  prospecting  for  materials  that  occur  in  small 
bunches  or  irregular  seams.  To  the  first  class  belong  coal,  iron  ore,  low-grade 
finely  disseminated  gold  and  silver  ores,  many  deposits  of  copper,  lead,  zinc, 
etc.,  as  well  as  salt,  gypsum,  building  stone,  etc.  To  the  latter  class  belong 
small  but  rich  bunches  of  gold,  silver  mineral,  or  rich  streaks  of  gold  telluride. 

The  arrangement  of  holes  has  considerable  effect  upon  the  results  fur- 
nished. If  the  material  sought  lies  in  beds  or  seams  (as  coal),  the  dip  of 
which  is  fairly  well  knowTn,  it  is  best  to  drill  a series  of  holes  at  right 
angles  to  the  formation.  If  the  material  sought  occurs  in  irregular  bunches, 
pockets,  or  lenses,  it  will  be  necessary  to  drill  holes  at  two  or  more  angles,  so 
as  to  divide  the  ground  into  a series  of  rectangles,  thus  rendering  it  prac- 
tically impossible  for  any  vein  or  seam  of  commercial  importance  to  exist 
without  being  discovered.  Where  the  surface  of  the  ground  is  covered  with 
drift  and  wash  material,  it  may  be  best  to  sink  a shaft  or  drill  pit  to  bed 
rock,  and  locate  the  machine  on  bed  rock.  After  this,  several  series  of  fan 
holes  may  be  drilled  at  various  angles  from  the  bottom  of  the  pit.  Owing 
to  the  upward  drift  of  diamond-drill  holes,  the  results  furnished  from  a set 
of  fan  holes  drilled  from  a single  position  would  make  a flat  bed  appear  as 
an  inverted  bowl,  or  the  top  of  a hill.  On  this  account,  it  is  best  to  drill 
sets  of  fan  holes  from  two  or  more  locations,  so  that  they  will  correct  one 
another.  If  fan  holes  from  different  positions  intersect  the  same  bed,  a care- 
ful examination  of  them  will  usually  furnish  a check  on  the  vertical  drift 
of  the  holes. 

The  cost  and  speed  of  drilling  depend  greatly  on  the  formation  being 
penetrated.  As  a rule,  it  is  more  expensive  to  sink  the  stand  pipe  than  to  do 
the  subsequent  drilling.  Stand  pipes  may  cost  $5  or  more  per  foot  to  sink, 
while  the  cost  of  drilling  in  firm  rock  varies  from  $0.50  to  $2  per  foot;  in  the 
case  of  difficult  drilling,  the  cost  may  run  over  $4  per  foot.  Where  a large 
amount  of  drilling  has  to  be  done,  a fair  average  estimate  for  shallow  holes 
up  to  700  ft.  deep  would  be  $2  per  foot,  under  such  conditions  as  exist  in 
most  mineral  districts  of  the  United  States.  The  cost  of  labor,  fuel,  etc., 
enter  into  the  problem,  and  frequently  affect  it  to  a considerable  extent. 

The  rate  of  drilling  varies  considerably,  but  in  firm  rock  an  average  of 
1 ft.  per  hour,  including  all  delays  for  changing  rods,  etc.,  would  be  a fair 
average  up  to  700  ft.  Greater  speed  than  this  could  be  made  in  soft  shales  or 
sandstones,  and  somewThat  less  in  hard  rock.  The  hardness  of  the  rock 
affects  the  rate  of  drilling  much  less  than  does  its  character.  A conglomer- 
ate rock  containing  loose  pebbles  that  come  out  during  the  drilling,  or  a 
crystalline  rock  containing  angular  pieces  that  come  out  during  drilling, 
will  cause  far  greater  trouble  than  the  hardest  material  ever  encountered  in 
diamond  drilling.  The  following  tables  will  give  some  idea  as  to  the  cost 
of  diamond  drilling  under  various  conditions. 

The  cost  of  drilling  2,084  ft.  of  hole  in  prospecting  the  ground  through 
which  the  Croton  aqueduct  tunnel  was  to  pass  is  given  as  follows: 

814  ft.  of  soft  rock  (decomposed  gneiss),  in  w hich  an  average  of  23.1  ft.  per 
dav  w7as  drilled,  at  a cost  of  $1.15  per  ft. 

347  ft.  of  hard  rock  (gneiss),  in  which  an  average  of  11.1  ft.  per  day  was 
drilled,  at  a cost  of  $3.97  per  ft. 

923  ft.  of  clay,  gravel,  and  boulders,  in  which  from  6£  to  9 ft.  per  day  were 
drilled,  at  a cost  of  $4.07  per  ft. 

The  average  progress  per  day  in  drilling  the  entire  2,084  ft.  was  10.2  ft 
per  day. 


245 


1 


DRILLING  OR  BORE  HOLES.  ^*5 

In  the  Minnesota  Iron  Co.’s  mines,  at  Soudan,  Minn.,  the  diamond  drill  is 
used  for  drilling  holes  from  10  to  40  it.  in  depth  in  the  back  of  the  stopes, 
practically  all  the  work  being  done  in  iron  ore.  The  average  cost  per  foot 
of  drilling  13,512  ft.  of  hole  was  $0.7703,  which  was  divided  as  follows. 

Carbons 

Supplies,  oil,  etc JJJc 

Fuel 

ifc::::::::::::::::::::;  o:^ 

Total  $0.7703 

The  following  tables  give  the  cost  of  boring  at  two  Ishpeming,  Mich., 
mines: 

TABLE  I. 


f 400|  days  setter  at  $3.00 $1,200.75  1 

T , J 372  days  runner  at  2.25 837.00 

Labor  -j  23oa  days  runner  at  2.00 460.50 

[ 4i  days  laborer  at  1.75 7.85  j 

Carbon  68f  carats  at  $15.144 .• 

Bits,  lifters,  shells,  barrels,  and  repairs 

Oil,  candles,  waste,  and  supplies 

Estimated  cost  compressed  air  

Total 

Cost. 

L $2,506.10 

. 1,035.47 
..  433.81 

128.09 
374.60 

Cost 
per  Ft. 

$0,669 

0.276 

0.115 

0.035 

0.100 

..  $4,478.07 

$1,195 

28 

193  ft. 

Ullllt/U  111  lltJlIlall 

646  ft. 

986  ft. 

urnieu  in  ihiacu  uic  

Drilled  in  dioritic  schist 

Total  drilling  

1,921  ft. 
3,746  ft. 

Number  of  10-hour  shifts  drill  was  running,  including 

moving  and  setting  up  - V?o  «• 

Amount  drilling  per  10-hour  shift II* 


TABLE  II. 

Underground  drilling W5  £* 

Surface  drilling  5* 

Stand  pipe  sunk — 4/U 

Total  distance  run 7,959  ft. 

Actual  drilling  time  underground 672  shifts 

Actual  drilling  time  on  surface  "*2  shins 

Time  of  foreman,  setter,  moving,  and  stand-piping 1,314  sums 

Total  time  worked shifts 


Average  progress  per  man  per  shift  

Average  progress  per  drill  per  shift  actually  run- 
ning   - 

Weight  of  carbon  consumed - 

Distance  drilled  per  carat  of  carbon  consumed 


3.70  ft. 

8.95  ft. 
111.00  carats 
67.38  ft. 


Cost  of  carbon 

Cost  of  supplies  and  oils.. 

Cost  of  fuel  

Cost  of  shop  material,  etc, 

Pay  roll 

Total  cost 


Amount. 

$1,887.00 

134.13 

360.73 

663.36 

4,000.03 

$7,045.25 


Per  Ft. 
$0,237 
0.017 
0.045 
0.083 
0.502 


$0,884 


246 


PROSPECTING. 


Records  of  Cost  per  Foot  in  Diamond  Drilling. 


A 

B 

C 

D 

E 

F 

G 

11 

/ 

J 

K 

L 

M 

N 

O 

Labor 

.707 

1.040 

2.483 

1.150 

.581 

1.615 

1.030 

1.720 

1.189 

1.284 

.721 

1.200 

.939 

.812 

.984 

Fuel 

.094 

.270 

.256 

.019 

.000 

.216 

.090 

.214 

.157 

.339 

.419 

.329 

.126 

.182 

.251 

Camp  account 
Repairs  .... 

.373 

.559 

.789 

.538 

.295 

.621 

.384 

.549 

.516 

.495 

.519 

.595 

.644 

.722 

.636 

.139 

.110 

.294 

.171 

.135 

.144 

.103 

. .185 

.154 

.165 

.040 

.087 

.138 

.126 

.116 

Supplies  . . . 

.034 

.065 

.039 

.074 

.023 

.032 

.011 

; .039 

.048 

.097 

.020 

.092 

.076 

.097 

.088 

Carbon  .... 

.263 

.658 

.859 

.860 

.843 

1.587 

.934 

; .684 

.684 

.733 

.227 

.209 

.553 

.239 

.330 

Supt 

.239 

.322 

.628 

.040 

.063 

.192 

.140 

.305 

.259 

.172 

.347 

.220 

.106 

.196 

.199 

Total . . . 

1.849 

3.024 

5.348 

2.852 

1.940 

4.407 

2.692 

1 

1 

3.696 

3.007 

3.285 

1 

2.293 

2.732 

2.582 

2.374 

2.604 

A 5 holes,  1,066  ft.  I 

Sandstone  and  marble. 

B 1 hole,  1,293  ft. 

Black  slate  and  jasper.  J 

C 3 holes,  478  ft. 

Jasper,  very  hard.  K 

D 5 holes,  780  ft. 

Jasper,  hard.  L 

E 1 hole,  216  ft. 

Iron  slates.  M 

F 1 hole,  174  ft. 

Jasper  and  slate.  N 

G 2 holes,  267  ft. 

Jasper  and  slate.  0 

H 3 holes,  410  ft. 

Jasper. 


Average  cost  of  total  work  of 
drilling  21  hoies.  Total  of 
4,684  ft. 

2 holes,  634  ft. 

Iron  slates. 

2 holes,  360  ft. 

Schist  and  jasper. 

6 holes,  1,350  ft. 

Iron  slates. 

2 holes,  611  ft. 

Schist,  jasper,  and  quartzite. 

6 holes,  2,091  ft. 

Quartzite. 

Average  cost  of  drilling  18  holes, 
5,046  ft. 


The  following  figures,  taken  from  a letter  written  by  T.  F.  Richardson, 
Departmental  Engineer  of  Dam  and  Aqueduct  Department,  Metropolitan 
Water  Board  of  Boston,  and  published  by  the  U.  S.  Geological  Survey,  are  of 
interest,  as  they  show  the  rate  and  cost  of  diamond  drilling  under  certain 
conditions.  The  costs  do  not  take  into  account  depreciation  of  machinery 
nor  losses  of  time  in  moving  machines,  etc.  The  machines  employed  in 
this  work  were  a Badger  drill,  manufactured  by  the  M.  C.  Bullock  Manu- 
facturing Co.,  of  Chicago,  111.,  and  an  S-510  drill,  manufactured  by  the 
Sullivan  Machinery  Co.,  Claremont,  N.  H. 

The  total  amount  drilled  was  2,814  ft.,  the  deepest  hole  being  286  ft.  deep, 
and  the  average  depths  of  holes  about  60  ft.  The  amount  accomplished  per 
day  was  from  0 to  32  ft.,  the  average  amount  being  probably  about  10  or  12 
ft.  per  day.  The  cost  of  drilling  varied  very  largely,  both  with  the  hard- 
ness of  the  rock  and  the  condition  of  the  rock  as  to  being  seamy. 


The  following  was  the  cost  of  drilling  321.2  ft.  of  rather  hard,  tough 
diorite  rock: 


Labor $341.25 

Diamonds 74.30 

Coal 17.50 


Total  $433.05 

Cost  per  foot 1.34 


(86.6  ft.  of  this  was  drilled  with  a If"  bit,  and  237.6  ft.  was  drilled  with  a 
U"  bit.) 


Drilling  150.7  ft.  of  very  hard  syenite  rock: 


Labor  $158.00 

Diamonds 298.69 

Coal 10.50 


Total - $467.19 

Cost  per  foot ' 3.10 


(Size  of  drill,  1$  in.) 


1 


drilling  or  bore  holes. 


247 


The  following  was  the  cost  of  drilling  286.1  ft.  of  soft  schist  rockt^ 

Labor..  87/75 

Diamonds 11.50 

Coa!n';zv *m25 

Cost  per  foot 

(Size  of  drill,  If  in.) 

The  following  figures  will  be  of  considerable  interest,  owing ; to  the  fact 
that  the  work  is  practically  all  of  the  nature  of  sinking  stand  pip.es  the 

Cost  of  operation  per  month  of  bed-rock  exploration: 

TThtpiti  Tl  HpXOU.UU 

6 laborers,  at  $1 ! 50  per  day,  28  days 234.00 

lcook 1—  $429.00 

240  rations,  at  60  cents.  - - 144,00 

Total  repairs,  pipe  and  lumber  for  one 

party  for  10  months ■•••••• 5UU*UU 

Total  commissary  charges  for  team,  teed, 

dOU.UO 

Total  simdry  incident^ 

Total  supervision hm.w 

Totals  10  months $2,070.00  2^000 

Sundry  expenses  per  month 

Total  cost  per  month 803.00 

10  months,  at  $803 jymuu 

Total  number  of  feet  sunk ^254.20 

Total  cost 2 4g 

Cost  per  hole,  7,227  -s-  52 154  42 

The  drills  were  purchased  second-hand  from  the  Nicaragua  Canal  Co^, 
and  the  other  apparatus  was  new.  If  the  ongmai  cost  of  all  this  machinery 
were  distributed  over  the  work,  the  results  would  be  as  follows. 

Machinery 

Total  cost $9,632  86 

Or  average  cost  per  foot 

Both  machines  are  still  in  good  repair,  after  having  been  used  in  Nicara- 
gua and  in  various  localities  in  Arizona  and  California.  . .. 

g xhe  total  depths  penetrated  in  all  materials  at  the  various  dam  sites  are 
as  follows : 


The  Buttes  ... 
Queen  Creek. 

Riverside 

Dikes 

San  Carlos ... 

Total  


Covering. 


1,621.2 

357.8 

729.8 
80.0 

143.2 


2,932.0 


Rock. 

Total. 

196.0 

1,817.2 

55.6 

413.4 

40.2 

770.0 

0.0 

80.0 

30.4 

173.6 

322.2 

3,254.2 

248 


PROSPECTING . 


Fig.  2. 


Magnetic  Prospecting.— Bodies  of  magnetic  iron  ore  are  frequently  discov- 
ered or  located  on  account  of  their  magnetic  properties.  Two  forms  of 
compasses  are  employed  in  this  work:  the  dipping  needle,  or  miners’ 
compass,  and  the  ordinary  compass.  The  ordinary  compass  is  used  to  find 
the  center  of  magnetic  attraction  in  the  horizontal  plane,  and  after  this  has 
been  found  the  ground  may  be  run  over  with  the 
dipping  needle,  to  locate  the  center  of  attraction 
by  this  means.  The  ordinary  compass  does  not 
give  good  results  when  operating  over  a mag- 
netic deposit,  but  is  only  useful  in  determining 
its  outside  edge,  and  thus  locating  its  general 
position.  The  dipping  needle  differs  from  the 
ordinary  compass  in  that  the  needle  is  hung  in  a 
vertical  plane  in  place  of  horizontally,  so  that 
the  needle  is  free  to  assume  any  position  varying 
from  the  horizontal,  depending  on  the  downward  component  of  magnetic 
attraction  at  that  point.  The  vertical  magnetic  component  at  the  point 
should  be  compensated  for  by  balancing  the  dipping  needle  so  that  it  will 
ordinarily  stand  horizontally  when  not  affected  by  local  disturbances. 

The  actual  work  of  prospecting  may  be  carried  on  as  follows:  If  there 
were  an  outcrop  of  a vein  of  magnetic  material,  as  shown  in  Fig.  2,  covered 
with  a capping  of  wash  material,  the  preliminary  prospecting  would  be 
carried  on  as  shown  in  Fig.  3,  the  dipping  needle  being  carried  backwards 
and  forwards  zigzag  across  the  deposit,  noting  the  point  of  maximum  dip  in 
each  case  and  establishing  a stake  there  as  indi- 
cated by  the  crosses.  After  these  stakes  had  all 
been  established,  an  average  straight  line  would 
be  struck  through  them  that  would  follow  the 
course  of  the  deposit  as  nearly  as  possible.  Stakes 
would  be  placed  at  the  ends  of  this  line,  as  at  X and 
Y,  and  the  line  X Y divided  off  into  100'  dis- 
tances by  means  of  stakes  marked  A , B,  etc.  Lines 
at  right  angles  to  the  original  line  would  then  be 
turned  off  at  these  100'  points,  and  stakes  placed 
every  10  ft.  upon  the  branch  lines.  These  points 
on  the  branch  lines  would  be  lettered  with  small 
letters,  corresponding  to  the  large  letter  on  the  line 
X Y,  as  shown  in  Fig.  4,  which  represents  the  obser- 
vations taken  at  the  first  station.  The  dip  would 
be  noted  at  each  one  of  the  10'  stations,  and 
recorded  in  the  note  book.  A convenient  method 
of  keeping  the  notes  is  to  have  a vertical  line  down 
the  center  of  the  page  for  the  line  X Y,  and  other 
vertical  lines  to  the  right  and  left  of  it  for  the  indi- 
vidual stations  10  ft.  apart,  each  side  of  the  main 

line,  the  horizontal  lines  across  the  page  being  lettered  A,  B , etc.,  the  sta- 
tions to  the  right  and  left  being  marked  with  primes  and  subscripts  of  the 
small  letters  corresponding  to  the  line.  After  the  observations  have  been 
taken,  lines  may  be  drawn  through  points  of  equal  dip  and  equal  deflection 

(isogonic  lines).  By  this 
means  the  general  form  of 
the  bed  is  determined. 

The  maximum  dip,  in  the 
case  of  an  inclined  deposit 
like  that  shown  in  Fig.  2, 
would  occur  at  c,  over  the 
hanging  wall  of  the  outcrop, 
the  dip  at  b being  consider- 
ably less,  and  the  dip  at  a 
being  less  than  that  at  b. 
After  the  center  of  magnetic 
attraction  has  been  discov- 
ered, prospecting  may  be  continued  by  means  of  the  diamond  drill,  or  by 
sinking  shafts  or  test  pits.  Sometimes,  where  deposits  of  magnetic  iron  ore 
have  been  eroded,  the  sands  near  the  surface  may  contain  such  a considerable 
amount  of  magnetic  disturbance  as  to  indicate  the  presence  of  a body  of  iron 
ore.  while  in  reality  there  may  be  such  a small  quantity  disseminated 
through  the  sand  that  it  could  not  be  made  to  pay  for  its  removal. 


Fig.  3. 


GEOLOGICAL  MAPS  AND  CROSS-SECTIONS. 


249 


Any  body  of  magnetic  iron  ore  is  affected  by  polarity,  and  one  end  of  it 
will  attract  one  end  of  the  dipping  needle,  while  the  other  end  will  attract 
the  opposite  end.  Where  the  body  is  badly  broken  up,  this  dip  oi  the 
needle  may  be  reversed  several  times  in  a comparatively  short  distance. 

Prospecting  for  Petroleum,  Natural  Ga3,  and  Bitumen.— Among  the  surface 
indications  of  petroleum  and  bitumen  may  be  mentioned  white  leached 
shales  or  sandstones,  shales  burned  to  redness,  fumaroles,  mineral  springs, 
and  deposits  from  mineral  springs.  Also  natural  gas,  springs  of  petroleum 
oil  and  naphtha,  porous  rocks  saturated  with  bitumen,  cracks  in  shale,  and 
other  rock  partly  filled  with  bitumen.  Petroleum  is  never  found  in  any 
Quantity  in  metamorphic  rocks,  but  always  in  sedimentary  deposits. 
Bitumen  can  be  told  from  coal,  vegetable  matter,  iron,  manganese,  and 
other  minerals,  which  it  sometimes  closely  resembles,  by  its  odor  and  taste, 
also  by  the  fact  that  it  melts  in  the  flame  of  a match  or  candle,  giving  a 
bituminous  odor.  (Iron  and  manganese  do  not  fuse,  and  coal  and  vegetable 
matter  burn  without  fusion.)  Bitumen  is  also  soluble  m bisulphide  of 
carbon,  chloroform,  and  turpentine,  usually  giving  a dark,  black  or  brown 
solution.  Frequently,  springs  or  ponds  have  an  iridescent  coating  ot  oil 
upon  the  surface.  Sometimes  iron  compounds  give  practically  the  same 
appearance,  but  the  iron  coating  can  always  be  distinguished  from  the  oil  py 
agitating  the  surface  of  the  water,  when  the  iron  coating  will  break  up  like 
a crust  of  solid  material,  while  the  oil  will  behave  as  a fluid,  and  tend  to 
remain  over  the  entire  surface  even  when  it  is  agitated.  , 

Frequently,  bubbles  of  gas  are  seen  ascending  from  the  bottoms  ot  pools 
or  creeks.  These  may  be  composed  of  carbureted  hydrogen  or  natural  gas, 
which  is  a good  indication  of  the  presence  of  petroleum  or  bitumen;  they 
may  be  composed  of  sulphurated  hydrogen  or  carbom c-acid  gas.  Garb  - 
reted  hydrogen  can  be  distinguished  by  the  fact  that  it  burns  with  a yellow 
luminous  flame,  whereas  sulphureted  hydrogen  burns  with  a bluish  flame, 
and  carbon  dioxide  will  not  support  combustion,  but,  on  the  contrary,  is  a 
product  of  combustion.  ,.  ~ 

When  carbureted  hydrogen  gas  is  discovered  ascending  from  water,  the 
bottom  of  which  is  not  covered  with  decaying  vegetation,  it  is  almost  a 
certain  sign  that  there  is  petroleum  or  bitumen  somewhere  in  the  underlying 
or  adiacent  formations.  „ _ , . ...  , 

If  natural  gas  or  bitumen  is  found  upon  the  surface  of  shale,  it  is  probable 
that  the  material  ascended  vertically  through  cracks  m these  rocks  from 
porous  strata  below;  while  if  it  is  found  in  connection  with  sandstones  it  is 
probable  that  the  material  was  derived  from  the  porous  sandstone  itsell. 
This  is  especially  liable  to  be  true  if  the  sandstone  has  a steep  pitch. 

As  a rule,  deposits  of  bitumen  or  petroleum  occur  m porous  formations 
overlaid  by  impervious  strata,  such  as  shales,  slates,  etc.  Anticlines  are 
more  liable  to  contain  such  deposits,  though  they  are  not  absolutely  neces- 
sary to  retain  them,  as  at  times  portions  of  the  underlying  porous  strata 
have  been  rendered  impervious  by  deposits  of  calcium  salts,  silica,  etc.,  ana 
hence  the  petroleum  or  bitumen  will  be  confined  to  the  porous  portmns. 
Natural  gas  also  occurs  under  similar  conditions,  but  usually  in  anticlines 

Construction  of  Geological  Maps  and  Cross-Sections.— After  the  surface  exam- 
ination of  a property  is  complete,  the  data  should  be  entered  on  the  best 
map  procurable,  or  a map  constructed.  The  scale  depends  on  the  size  of 
the  property,  the  complexity  of  the  geological  formation,  the  value  of  the 
property,  and  the  material  to  be  mined  from  it.  The  amount  of  work  that 
it  will  pay  to  put  on  the  survey  will  depend  largely  on  the  value  ot  the 
property,  more  detail  being  justified  in  the  case  of  high-grade  properties. 
If  a property  1,200  ft.  X 3,000  ft.  (the  size  of  four  U.  S.  mining  claims)  were  to  be 
surveyed  and  mapped  with  a scale  of  1 in.  equal  to  100  ft.,  the  map  would 
be  12  in.  X 30  in.  A vein  of  strata  10  ft.  wide  on  this  map  would  appear  as  T«  ot 
an  inch  wide,  which  is  about  the  smallest  division  that  could  be  shown 
with  its  characteristic  symbol;  for  greater  detail,  a larger  scale,  or  larger 
scaled  sheets  of  the  most  important  portions  of  the  deposit,  will  be 
necessary.  If  the  geologist  constructs  the  topographical  contour  map,  he 
can  take  notes  on  the  geology  at  the  same  time.  When  the  l^undanes  of 
the  property  are  being  surveyed,  certain  points  should  be  established,  botn 
vertically  and  horizontally,  as  stations  in  future  topographical  work.  If  the 
map  is  on  government  surveyed  land,  the  government  lines  may  be  used 
for  horizontal  locations,  but  it  will  be  necessary  to  determine  the  elevation 
of  the  different  points.  If  the  property  is  much  broken,  it  is  well  to  run  a 


250 


PROSPECTING . 


few  lines  of  levels  across  it,  to  establish  points  from  which  to  continue  the 
work.  This  work  is  usually  done  with  a Y level  and  chain,  the  other  details 
being  subsequently  filled  in  with  a transit  and  stadia,  the  levels  of  the  other 

points  being  taken 
either  by  using  the 
transit  as  a level,  by 
vertical  angles,  by  bar- 
ometric observations, 
or  by  means  of  a hand 
level.  Where  lines  of 
levels  are  run  across 
the  property  in  various 
directions,  it  is  best  to 
run  them  in  such  a 
direction  that  they  will 
cross  the  strike  of  the 
strata  as  nearly  at  right 
angles  as  possible,  so 
that  the  profile  thus  de- 
termined may  be  used 
in  constructing  a cross- 
section.  Sometimes, 
for  preliminary  work, 
simply  a sketch  map  is 
all  that  may  be  neces- 
sary. All  of  the  outcrops  and  exposures,  together  with  their  proper  dip, 
should  be  entered  on  the  map. 

To  Obtain  Dip  and  Strike  From  Bore-Hole  Records.— Before  the  results 
obtained  from  bore  holes  are  available  for  use  in  map  construction,  the  dip 
and  strike  of  the  various  strata  must  be  ascertained.  The  process,  in  the 
case  of  stratified  rock,  is  as  follows:  If  three  holes  were  drilled,  as  at  A,  B, 
and  <7,  Fig.  6,  each  intersecting  a given  bed,  the  strike  and  angle  of  dip  of  the 
bed  may  be  obtained  by  reducing  the  results  from  the  three  holes  to  a plane 
passing  through  the  highest  point  of  intersection,  which  is  at  A.  The  hole  B 
intersected  the  bed  at  the  distance  Be , and  C at  the  distance  Cd  below  the 
point  A.  By  continuing  the  line  CB  indefinitely,  and  erecting  two  lines  Be 
and  Cd  perpendicular  to  it,  each  representing  the  distance  from  the  hori- 
zontal plane  through  A to  the  intersection  of  the  strata,  two  points  in  the 
line  de  are  obtained,  which  line  intersects  CB  produced  at/;  / is  one  point 
in  the  line  of  strike  through  A.  In  order  to  find  the  angle  of  dip,  the 
perpendicular  Cg  is  dropped  from  the  deepest  hole  C unon  the  line  of 


Fig.  7. 

strike  Af.  The  distance  Ch,  equal  to  Cd , is  laid  off  at  right  angles  to  Cg , 
when  the  angle  Cg  li  gives  the  maximum  dip.  The  results  obtained  from 
bore  holes  may  thus  be  reduced  to  such  form  that  the  dips  can  be  projected 
on  the  surface  to  obtain  the  line  of  outcrop  for  each  stratum.  Bore  holes  also 
furnish  data  for  constructing  underground  curves  in  cross-sections  of 
stratified  rocks,  and  in  locating  the  probable  outline  of  ore  bodies  in  other 
formations. 


SAMPLING  AND  ESTIMATING  AVAILABLE  MINERAL. 


251 


-r-r  • r»«  thp  man  all  exoosures,  whether  surface  or  those 

lines  ran,  op,  gr  are '^ontours.  M the  g|s  s^L  b eds  or  deposits  would  be 
seam  the  crost  ^cfion  must  he  taken  along  the  u“«  P€^dioulw  to  the 

surface >of  the  cross-section .u i noi  a i th  p s.section>  on  this  cross-section, 
accordingT^their  SpM'S  co'nsiderZe  danger  of  exaggerating  their 
tl* i fn e m a r!s''” t hVIu wwsed  course  of  the  beds  should  he  sketched  in, 

the  property  ^ei^0  “el should  be  tied  to  monuments  or  natural 

iSSSsSfe  r Si  ss 
gg^gSTfiSfiSSSSHaSSS 

material  as  it  will  be  extracted  the  coal,  shSuld  be 

a«ta  Sr3e°  When 

may^lira  te'^ay^^nd^n^wag^obtm^^later^or  th^different^^ples 

BffigMBBBi 

which  may  be  described  as  follows.  , throwing  each  shovel- 

ful^  to'r'fpe^oY^co'nr  Vl^h^he  Sne'mly  le  reduced  by 


252 


PROSPECTING. 


scraping  it  down  with  a shovel,  passing  slowly  around  it.  If  the  amount 
of  material  is  small,  a flat  plate  may  be  introduced  into  the  cone,  and  the 
pile  flattened  by  revolving  the  plate.  The  pile  is  then  divided  into  quarters 
by  drawing  lines  across  it.  After  this,  two  alternate  quarters  are  scraped 
out  and  shoveled  away,  and  the  other  two  quarters  are  left  as  the  sample. 
The  process  may  be  repeated  until  the  block  has  been  sufficiently  reduced. 
In  shoveling  away  the  discarded  portions,  care  should  be  taken  to  see  that 
the  fine  dust  under  them  is  brushed  away  also,  as  they  often  contain  fine 
and  valuable  mineral  that  would  unduly  increase  the  value  of  the  resulting 
sample.  When  the  sample  consists  of  only  a few  pounds,  it  may  be  reduced 
by  means  of  a riffle.  Large  samples  consisting  of  several  tons  are  sometimes 
sent  to  sampling  works  to  be  reduced  by  automatic  sampling  machines.  If 
the  property  being  examined  is  a mine  in  active  operation,  samples  may 
be  taken  from  the  working  faces,  and  also  from  cars,  loading  chutes,  etc. 
Usually  the  samples  from  the  face  are  kept  separate  from  those  from  the  cars 
and  loading  chutes,  the  latter  being  intended  as  a check  on  the  former. 
In  the  case  of  ores  of  the  precious  metals,  large  samples  are  sometimes  taken 
and  used  for  mill  runs. 

Stock  piles,  or  dumps,  may  be  roughly  sampled  by  taking  pieces  from 
intervals  over  the  surface,  being  careful  to  obtain  a fair  avenge  of  coarse 
and  fine  material,  and  of  rock  and  ore.  These  samples  are  quartered  djwn 
and  assayed,  but  if  a close  valuation  is  d esired,  it  will  be  necessary  to  drive 
cuts  or  tunnels  through  the  mass,  and  to  take  a certain  amount,  as  every 
fifth  or  tenth  shovelful,  for  the  sample.  When  sampling  dumps  of  fine 
material  (as,  for  instance,  tailings)  it  is  possible  to  take  samples  from  the 
pile  by  means  of  a drill,  an  auger  1 in.  or  2 in.  in  diameter  usually  being 
employed  for  this  purpose. 

The  human  factor  always  plays  a large  part  in  the  value  of  a sample  as 
finally  selected,  and  hence  it  should  be  taken  by  a man  who  has  had  con- 
siderable experience  in  this  class  of  work.  For  this  reason,  it  is  best  to 
employ  a mining  engineer.  One  not  accustomed  to  sampling  very  rarely 
undervalues  a property,  owing  to  the  fact  that  it  seems  to  be  human  nature 
to  pick  up  a rich  piece  of  ore  or  coal,  rather  than  the  barren  gangue  material 
or  slate. 

When  only  surface  exposures  or  shallow  prospect  openings  are  available, 
it  is  impossible  to  determine  the  amount  of  ore  in  sight,  or  to  form  more 
than  a guess  as  to  the  size  of  the  deposit.  It  is  not  safe  to  count  any  ore  in 
sight  unless  it  is  exposed  on  at  least  three  faces.  Ore  that  is  exposed  on  one  or 
two  faces  can  be  counted  as  probable  ore,  while  slight  exposures  can  be 
counted  only  as  chances  indicated. 

The  amount  of  material  available  in  coal  deposits  can  be  estimated  much 
closer  than  in  the  case  of  ores.  If  a seam  is  penetrated  by  a number  of  bore 
holes,  or  by  workings  extended  over  a considerable  area,  it  is  fair  to  esti- 
mate that  the  material  will  run  practically  as  exposed  for  a considerable 
area;  but  especially  in  the  case  of  bituminous  coal,  it  is  a comparatively 
easy  matter  to  form  some  estimate  as  to  the  amount  of  material  available. 

When  dealing  with  ores,  it  is  impossible  to  form  reliable  estimates,  owing 
to  the  fact  that  horses  or  other  masses  of  rock  may  be  exposed  at  any  point, 
and  the  ore  bodies  themselves  are  usually  very  irregular,  hence  it  will  be 
necessary  to  do  careful  blocking  out  before  making  anv  estimates. 

When  estimating  the  amount  of  mineral  available,  only  that  portion 
which  can  actually  be  removed  in  stoping  should  be  counted,  and  if  the 
seam  is  so  narrow  that  it  is  necessary  to  break  material  from  the  walls,  or  if 
there  are  masses  of  country  rock  that  have  to  be  removed  with  the  ore,  the 
expense  of  removing  them  should  be  estimated  and  deducted  from  the  value 
of  the  ore. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LANDS. 

The  following  diagram  will  be  useful  as  a guide  in  making  out  a report 
on  a mining  property: 


1.  Situation 
and  Sur- 
roundings. 


{ 


1. 


2. 


Name,  i 
Distance 


1.  Location,  if  on  surveyed  land. 

2.  Nearest  town  or  village. 

3.  Mineral  district. 

. 4.  County,  state,  or  territory. 

and  direction  from  one  or  more  points. 


REPORTS  ON  MINERAL  LANDS. 


253 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LAN DS  {Continued). 

f 1.  Hills  or  mountains.  . , 

2.  Topogra-  I 2.  Character  of  surface,  vegetation,  and  timber. 
phy.  1 3.  Streams  and  water  supply. 

L 4.  Elevations. 


3.  Geology. 


1.  Struc- 
ture. 


1.  Rocks. 

2.  Axes. 

3.  Faults. 


4.  Dikes. 


{ 


5.  Horses. 

2.  Geological  period. 

3.  (a) Coal  f 1.  Number, 
beds.  \ 2.  Thickness, 


1.  Stratified. 

2.  Crystalline. 

3.  Igneous. 

Anticlines  or  synclines. 

1.  Number. 

2.  Strike. 

3.  Dip. 

4.  Throw. 

1.  Number. 

2.  Strike. 

3.  Dip. 

4.  Filling. 

5.  Throw. 

1.  Number  and  size. 

2.  Location. 

3.  Material. 


I 


or 


(5)  Ore 
bodies. 


1.  Veins. 


2.  Beds  or 
lenses. 


Reported.  r 1 Reported. 

Averaee3'  J 2'  Accordin« 

Aveiage.  -j  tQ  meas, 

Umformity.  y urement. 
Number.  ^ 

Character. 

Strike. 

Dip. 

w. ,,,  f 1-  Maximum. 
Width.  1 2 Average. 

Vein  filling. 

Ore  chutes. 

Walls. 

Throw  of  walls. 

Number. 

Walls. 

Strike. 

Dip. 

Length. 

Height. 

Maximum  width. 

Average  width. 


4.  (a)  Quality  of 
coal,  specimens, 
appearance 
in  mine,  in  cars, 
benches. 


or 


, (6)  Ore. 


' l.  Color,  external,  powder. 

2.  Luster.  _ , . 

3.  Clearness  from  clay  or  sand,  shale, 

4.  Sulphur. 

5.  Resin.  . , . 

6.  Firmness,  size  of  lumps,  air  slaking. 

7.  Cleavage  or  fiber. 

8.  Coking. 

9.  Color  of  ashes.  . 

10.  Use:  Gas,  steam,  domestic,  forge, 
metallurgy. 

11.  Analyses  or  assays. 

: 1.  Shipping. 

2.  Concentrating. 

3.  Metals  or  minerals. 

4.  Gangue. 

5.  Impurities. 

6.  Assays  or  analyses. 


254 


PROSPECTING. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LAN DS — ( Continued). 


4.  Mining. 


1.  History. 


2.  Mine. 


,’Y>- 


1.  Dates  of  opening,  abandoning,  reopening, 
number  of  mines  and  names. 

2.  Ownership. 

3.  Superintendence. 

1.  Shaft,  slope,  or  tunnel. 

f 1.  Total  depth. 

2.  Extent  of  I 2.  Depth  below  water  level, 
workings,  j 3.  Number  of  levels. 

t 4.  Extent  of  levels. 

3.  Water  pumps,  size,  and  kind,  water  cars, 
number  and  size,  natural  drainage. 

4.  Ventilation,  natural,  furnace,  fan  (for- 
cing or  drawing  out),  sufficient  or  insuf- 
ficient. 

5.  Lighting,  system  used. 

6.  Powder,  kind  and  grade  used. 

7.  Explosive  or  noxious  gases. 

8.  Coal-cutting  machines  and  power  drills. 

9.  (a)  Mode  of  working,  holding  under, 

shearing,  blasting,  or  wedging. 

1.  Underhand  stoping. 

2.  Overhead  stoping. 

' 5.  Rooming  with  or  with- 
out timber. 

6.  Square  sets. 

10.  Rooms,  or  stopes,  pillars,  dimensions,  and 
general  plan. 

11.  Timbering,  timber  trees. 

12.  Roof,  or  hanging  wall,  strong  or  weak, 
air  slakes  or  not. 

13.  Floor,  or  foot- wall,  hard  or  soft,  creeps 
or  not. 

14.  Roads,  rails,  and  cars. 

1.  Men. 


15.  System  of  under- 
ground  tram- 
ming. 


16.  System  of  hoisting 


2.  Mules. 

3.  Electricity. 

4.  Compressed  air. 

5.  Wire  rope. 

6.  Chain. 

7.  Locomotive. 
Cage. 

Skip. 

Cars. 


■{I 


5.  Maps  and 

Drawings. 


1.  Of  the  whole  region. 

2.  Of  the  underground  workings. 

1.  Cross. 

2.  Longitudinal. 

(1.  General. 

3.  Columnar.  < 2.  Coal  bed  or  other  de- 
( posit. 

4.  Buildings,  works,  or  machinery. 

f 1.  Scale. 

2.  North  line,  magnetic  variations. 

3.  Date. 

4.  Maker. 

5.  Can  buy,  take,  borrow,  or  have 
copied. 


3.  Sections. 


5.  Explanation. 


6.  Concentra- 
tion, 


1.  Hand  picking. 

2.  Cobbing  and  picking. 

3.  Magnetic. 

4.  Mechanical,  Siy. 


REPORTS  OX  MINERAL  LANDS. 


255 


7.  Coke 

Ovens. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LANDS  ( Continued ). 

1.  History,  ownership,  etc. 

2.  Number. 

3.  Character  of  ovens. 

4.  Dimensions. 

5.  Construction,  materials,  etc. 
f l.  Charge,  quantity,  etc. 

6.  Operations.  \ 2.  Working. 

L 3.  Discharging,  quenching. 

7.  Repairs.  ..  , 

8.  Quality  of  product.  (Assays,  if  any.) 

9.  Disposition  of  by  products. 

1.  In  heaps. 

2.  In  stalls. 

1.  Roasted.  3.  In  kilns. 

4.  By  mechanical  calcmers. 

5.  Number  &nd  dimensions  of  roasters. 

' 1.  Base  bullion. 

f 1.  In  shaft  fur 
nace  to 


8.  Metallur- 
gical Works 
and  Treat- 
ment of  Ore. 


2.  Smelted. 


9.  Disposition 
of  Product.  ' 


1.  Shipped. 


2.  Shipment. 


10.  Statistics. 


2.  In  reverber- 
atory furnace 
to 


3.  In  retorts  to 


1.  As  mined  to 


2.  As  concen- 
trates or  coke. 

3.  Metal  or 

matte  to 

1.  Distance. 

2.  Roads. 

3.  Railroads. 

4.  Navigation, 
f 1.  Capacity. 


2.  Matte. 

3.  Metal. 

4.  Number  and  dimen- 
sions of  furnaces. 

1.  Metal. 

2.  Matte. 

3.  Number  and  dimen- 
sions of  furnaces. 

1.  Metallic  zinc. 

2.  Mercury. 

3.  Number  and  size  of 
retorts. 

1.  Smelter. 

2.  Concentrator. 

3.  Sampling  works. 

4.  Jobber  at 

1.  Smelter  or  furnace. 

2.  Sampling  works. 

3.  Jobber  at 

1.  Refinery. 

, 2.  Smelter. 

^ 3.  Jobber  at 


1.  Production. 


2.  Labor. 


: f 1.  Daily,  weekly,  or  month- 

2.  Actual.  , ^in-to-nS- 


3.  Prices. 


i 2.  Yearly  in  tons.* 

[3.  Average. 

1.  Whole  number  of  workers. 

2.  Number  of  workers  in  each  class. 

3.  Number  of  horses  or  mules. 

1.  Timber. 

2.  Tools. 

3.  Fuel. 

4 

5 


Oil. 

Powder. 

Day,  different  classes. 
Contract  or  piece,  yard  or 
ton. 

Porrip  (rp 

8.  Local  saies  of  product. 

rl.  Machinery. 


6.  Labor, 


r. 

{* 


9.  Value  of  plant. 


2.  Buildings. 

3.  Roads, tracks, etc. 

4.  Rolling  stock. 

5.  Supplies. 


256 


PROSPECTING. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LAN  DS — ( Continued), 


11.  Surface 


Plant. 


1.  Power  plant. 


2.  Shops. 


3.  Powder 

houses. 

4.  Offices. 


f 1.  Boilers. 

2.  Waterwheels. 

3.  Air  compressors. 

4.  Steam  and  gas  engines. 

5.  Electric  plants. 

1.  Power  for. 

2.  No.  of  forges. 

3.  Steam  hammers. 

4.  Other  tools. 

” 1.  Power  for. 

2.  Saws. 

3.  Lathes. 

4.  Other  machines. 
t 5.  Benches  and  vises. 

1.  Power. 

2.  Lathes. 

3.  Planers. 

4.  Shapers. 

5.  Drill  presses. 

6.  Other  tools. 

7.  Benches  and  vises. 


1.  Smith’s 
shop. 


2.  Carpenter 
shop. 


3.  Machine 
shop. 


5.  Dry  or  change  houses. 

6.  Storehouses. 

7.  Boarding  and  dwelling  houses. 

8.  Stables. 

9.  Shaft  houses. 

10.  Tipples. 

11.  Pockets  or  ore  bins. 

12.  Company  store. 

13.  Timber  yard  and  plant  for  preparing  timber. 

1 Cifv  nr  com-  L Quality  of  water 
i.  lAiy  or  com-  n 

mercial  * 


14.  Water. 


service. 


2.  Company 
service. 


Sufficient  or  in- 
sufficient. 

3.  Pressure. 

'1.  Quality  of  water. 

2.  Sufficient  or  in- 
sufficient. 

3.  Gravity  system. 

f 1.  Direct. 

4.  Pump- 
ing sys- 
tem. 


Reser- 
voir or 
stand 
pipe. 


15.  Lighting. 


1.  Character. 

2.  Origin. 


16.  Hoisting  or  wind 
ing  plant. 


17.  Surface  trans- 
portation. 


1.  Gas. 

2.  Electric. 

1.  Commercial  plant. 

2.  Company  plant. 
Sufficient  or  insufficient. 

1.  Steam  engines. 

2.  Compressed-air  engines. 

3.  Oil  or  gasoline  engines. 

4.  Electric  motors. 

5.  Water  motors. 

1.  Gauge. 

2.  Total  length. 

3.  Size  of  cars. 

4.  No.  of  cars. 

5.  Power  used. 

6.  No.  of  motors. 
r 1.  Character  and 

surface  of. 

2.  Length. 

3.  No.  of  wagons 
and  teams. 

1.  Size  and  capac- 
ity of. 

2.  No.  of  wagons 
for. 


1.  Railroad. 


2.  Wagon 
roads. 


3.  Traction 
engines. 


OPENING  A MINE. 


257 


Diagram  for  reporting  on  mineral  LANDS—  {Continued). 
12.  Miscellaneous. 

1.  Yearly  income,  last  year,  or  for  any  year.  NetfS 

2.  Average  cost  per  lb.,  or  ton  of  material. 

[ 1.  Quality  of  ore  Or  product. 

1.  Deposits  ~ * * ^ 

of  value. 


13.  Conclu- 
sions. 


3.  Merits  of 
property. 


4.  Advice. 


2.  Amount  of  ore  or  f 1.  Gross, 
material  in  sight.  ( 2.  Net. 
v 3.  Value  of  material  in  sight. 
2.  Value  of  plant  and  works. 


1.  Mining. 

2.  Disposition 
of  product. 


^ 5.  Local  considerations. 


1.  Continue  present  system. 

2.  Change  system  to . 

1.  Ship  as  mined. 

2.  Concentrate,  or  coke  and 
ship. 

3.  Smelt  and  ship. 

1.  Troubles. 

2.  Labor. 

3.  Supplies. 

4.  Climate. 

5.  Shipment  facilities. 

6.  Markets. 


OPENING  A MINE. 


The  location  of  the  surface  plant  and  the  mine  opening  depend  on  the 
formation  of  the  deposit  primarily,  and  secondarily  on  the  facilities  for 
transporting  the  product  to  market.  It  is  impossible  for  <me  not  on  the 
ground  and  unfamiliar  with  natural  or  railroad  transportation  facilities  in 
the  neighborhood,  to  give  an  idea  as  regards  the  second  consideration.  In 
regard  to  the  first  consideration,  the  following  observations  will  be  found 

°f  When  the  seam  or  vein  outcrops  within  the  limits  of  the  property  and  is 
flat,  a water-level  drift  is  the  best  method  of  opening  it.  If  it  has  any  con- 
siderable inclination,  it  should  be  opened  by  a slope,  or  by  a tunnel  driven 
across  the  intervening  measures.  Where  the  deposit  has  an  inclination  of 
but  from  A*  of  1°  to  H°,  the  water-level  drift  is  generally  used,  and  the  main- 
haulage  entry  is  opened  at  the  lowest  accessible  point  on  the  outcrop,  which 
insures  free  drainage  and  a favorable  grade  for  haulage.  When  the  outcrop 
dips  into  the  hill,  the  drift  is  usually  commenced  a few  feet  below  the  out- 
crop terrace,  and  driven  on  a slight  up  grade  until  the  normal  dip  is  reached. 

When  the  inward  dip  is  too  strong,  the  better  plan  is  to  sink  a shaft  in  the 
center  of  the  basin,  provided  the  depth  is  not  too  great  and  the  amount  of 
water  to  be  pumped  is  comparatively  small.  If  the  inward  dip  to  the  center 
of  the  basin  does  not  exceed  a total  of  25  ft.  difference  in  level,  a drift  may 
be  used  and  drainage  be  effected  by  a siphon.  . 

Water-level  drifts  are  only  profitable  where  the  inclined  seam  is  exposed 
in  ravines  or  gorges  eroded  across  the  strike  of  the  measure,  or  where  the 
vein  can  be  reached  by  a short  tunnel  from  the  surface,  to  the  seam  across 
the  measures.  This  is  often  the  case  when  the  seam  dips  with  the  hill,  but 
when  the  dip  is  against  the  hill,  the  tunnel  is  generally  a long  one.  While 
the  expense  of  operating  a mine  opened  by  a long  tunnel  is  less  than  one 
opened  by  a slope  or  shaft,  owing  to  cheaper  drainage  and  haulage,  when 
the  coal  above  water  level  is  exhausted  the  tunnel  is  almost  worthless. 
When  the  seam  is  inclined  and  is  accessible  at  no  point  along  its  outcrop 
low  enough  to  furnish  sufficient  lift  or  breast  length,  it  should  be  opened 
by  a slope  or  shaft.  Or,  if  the  seam  is  flat  and  does  not  crop  on  the  tract, 
a shaft  is  the  only  method  of  working  it,  unless  it  lies  so  near  the  surface 
that  it  can  be  stripped. 

Where  a seam  has  a dip  of  20°  or  more,  and  is  brought  close  to  the  surface 
by  an  anticlinal  axis  or  “saddle,”  a “rock  slope,”  or,  in  other  words,  a 
tunnel  dipping  the  same  as  the  seam  may  be  started  from  the  surface,  and, 
when  the  seam  is  reached,  may  be  continued  to  the  desired  depth  in  the 


258 


OPENING  A MINE. 


seam.  In  sinking  slopes  for  coal  mines,  it  is  customary  to  sink  an  airway 
alongside  of  and  parallel  with  the  slope,  with  a pillar  of  about  10  yd.  between. 
The  slope  for  coal  mines  is  usually  sunk  so  that  there  is  a “lift”  of  from 
100  to  110  yd.,  and  then  gangways  are  turned  off  on  each  side.  The  term  - 
“lift”  in  this  connection  means  the  length  on  pitch  that  breasts  or  rooms, 
driven  at  right  angles  to  the  gangway,  can  be  driven  in  good  coal.  Subse- 
quent lifts  are  usually  from  80  to  100  yd.  long. 

Opening  Up  a Gold  Mine.— The  following  description  of  the  method  of  open- 
ing up  a gold  mine,  by  Mr.  S.  A.  Josephi  (“  Mines  and  Minerals,”  February, 
1900),  will  also  apply  in  general  for  the  opening  of  any  inclined  narrow  ore 
deposit:  The  equipment  for  the  top  of  shaft  for  the  preliminary  work  con- 
sists of  three  pieces  of  timber,  either  sawed  or  rough  hewn,  12  to  16  ft.  long, 

8 to  10  in.  in  diameter,  arranged  as  a tripod;  they  should  be  strongly  bolted 
together,  a pulley  hung  from  the  center,  through  this  a rope  passed  with  a 
bucket  fastened  to  the  end  entering  the  shaft,  and  a horse  hitched  to  the 
other  end  This  equipment  is  called  a whip , and  is  sufficient  for  the  first 
100  ft.  in  depth.  In  locating  the  shaft,  care  should  be  exercised  in  placing 
it  where  there  is  ample  dump,  or  ground  for  waste  or  valueless  vein  matter. 
Should  the  character  of  the  surface  not  admit  of  sufficient  ground  for  this 
purpose,  have  collar  (or  top)  of  shaft  elevated  10  or  12  ft.,  aDd  throw  waste 
around  the  outside  of  same  until  filled  up  solid. 

The  timbers  should  be  square  sets  made  of  rough  or  square  timbers, 
preferably  the  latter,  8 in.  X 8 in.;  divide  the  shaft  into  two  compartments 
4 ft  X 4 ft.  each,  one  for  the  bucketwav,  the  other  for  the  ladderway.  Where 
air  is  bad,  board  up  the  ladderway  to  aid  the  circulation.  The  sets  should 
be  not  less  than  4 ft.  and  not  over  6 ft.  apart,  in  the  clear. 

Sink  on  the  dip  of  the  vein,  and  keep  a careful  record  of  the  location, 
width  and  value  of  ore  bodv,  until  the  depth  of  100  ft.  is  attained;  here 
place  station  sets  8 ft.  high,  start  levels  each  side  of  shaft,  and,  if  there  is 
water  in  the  shaft,  a sump  16  ft.  to  80  ft.  deep  should  be  sunk.  The  sump 
should  be  built  in  the  same  manner  as  the  shaft,  so  that  it  will  serve  as  a 
continuation  of  same  when  greater  depth  is  wanted. 

Levels  should  be  run  on  both  sides  of  the  shaft  sufficiently  long  to  deter- 
mine length  of  the  ore  chute,  and  also  to  determine  the  existence  of  other 
ore  chutes  in  the  vein.  This  development  work  should  be  an  indicator  . of 
the  strength,  value,  and  permanence  of  the  property;  it  is  now  ready  for 
another  examination  by  competent  authorities,  to  determine  the  above 
conditions.  Should  their  verdict  be  favorable,  continue  the  shaft  to  the 
depth  of  an  additional  100  ft.;  if  w ater  is  found  in  but  small  quantities,  this 
can  best  be  done  by  replacing  the  whip  with  a whim;  this  runs  by  the  same 
horsepower,  costing  in  the  neighborhood  of  $100.  It  is  well  adapted  to  put 
the  shaft  down  250  ft.  A , ., 

When  the  shaft  is  down  200  ft.,  start  levels  as  at  the  100-ft.  depth,  provide 
sump,  and  drift  both  wavs  upon  the  vein,  proving  up  ore  bodies  as  before. 

Thus  far  the  cost  has  been  slight.  The  shaft,  including  timbers,  supplies, 
and  contingent  expenses,  should  not  cost  over  $20  a foot,  a total  of  $4,000;  the 
drifts  $6  a foot,  say  200  ft,  each  way  from  shaft  on  both  levels,  a total  of 
800  ft,  or  $4,800;  total,  $8,800,  less  amount  received  from  mineral  extracted  in 
sinking  and  drifting,  wThich  is  usually  small. 

Now  it  is  to  be  decided  what  further  amount  the  owners  are  willing  to 
expend,  and  how  extensively  they  desire  the  mine  opened  up  betore  the 
actual  extraction  of  ore  is  to  commence.  M e will  put  the  depth  of  shaft  at 
500  ft.,  the  drifts  the  full  length  of  the  claim  usually  1 £00ft. 

For  this  purpose,  a shaft  house  should  be  built,  say  40  ft.  X 60  ft.,  w ith  ore 
house,  say,  40  ft.  X 40  ft,  The  equipment  should  be  a 40  H.  P.  engine  and  a 60 
H.  P.  boiler  (if  a large  flow  of  water  is  encountered,  an  additional  boiler  and 
pump  must  be  provided),  the  shaft  continued  to  the  above  stated  depth,  and 
levels  extended  at  each  100  ft.  It  will  also  be  advisable  to  make  upraises  at 
the  farthest  point  practical  from  the  shaft,  on  each  side,  connecting  each 
level  with  the  other,  and  extending  to  the  surface.  These  upraises  should 
be  made  in  ore,  and  are  valuable  both  for  ventilation  and  escape  for  men, 
in  case  of  accident  to  or  near  the  shaft.  They  should  be  furnished  with 
ladders.  The  machinery  shaft  house,  and  skip,  with  which  all  incline  shatts 
should  be  equipped,  will  cost  about  $4,500.  The  additional  300  ft.  of  shaft, 
including  contingent  expenses  of  engineers,  fuel,  etc.  will  cost  $40  a toot,  or 
$12,000;  the  drifts,  $6  a foot.  The  upraises,  being  on  ore,  should  pay  for  the 

labor  . 

It  is  prudent  to  estimate  the  cost  of  thoroughly  opening  up  a gold  mine  to 


SHAFTS. 


259 


be  between  $40,000  and  $50,000,  which  fact  probably  originated  the  remark 
that  “it  takes  a gold  mine  to  make  a goldmine.”  This  is  practically  true, 
and  no  one  should  attempt  to  engage  in  the  mining  business,  as  a business, 
without  both  money  and  a willingness  to  use  it.  More  failures  can  be 
attributed  to  insufficient  capital  for  development  than  to  any  cause  save 
mismanagement.  


SHAFTS. 

Shafts  and  tunnels  may  be,  first,  temporary,  or  those  that  are  simply 
driven  for  exploration  purposes,  and  are  not  to  be  used  for  any  great  length 
of  time;  second , permanent,  or  those  that  are  driven  for  a specific  purpose 
and  usually  have  a definite  predetermined  capacity. 

Form  of  Shaft.— In  the  United  States,  shafts  are  usually  square  or  rectangu- 
lar in  form.  This  is  largely  due  to  the  fact  that  timber  is  used  in  lining 
such  shafts.  In  Europe,  round  or  oval  shafts  are  frequently  employed  with 
a lining  of  brick,  iron,  or  masonry.  _ . 

Compartments.— The  number  of  compartments  in  a shaft  and  their  arrange- 
ment depends  largely  on  the  use  to  which  the  shaft  is  to  be  put;  also  on  the 
number  of  shafts  at  the  property,  and  the  depth  of  the  shaft.  VS  here  the 
material  to  be  removed  is  comparatively  near  the  surface,  it  is  usuallv 
cheaper  to  sink  a number  of  2-  or  3-compartment  shafts  than  it  is  to  tram  all 
the  ore  to  one  large  shaft;  while,  in  the  case  of  very  deep  mines,  large  4-  or 
6-compartment  shafts  are  sunk,  and  the  underground  haulage  extends  over 
a greater  area.  When  the  shafts  are  lined  with  timber,  a stronger  con- 
struction can  be  obtained  by  placing  the  compartments  side  by  side,  as 
shown  in  Fig.  1,  than  by  placing  them  in  the  solid  block,  as  shown  in  Fig.  2. 
When  a body  of  material  compara- 
tively near  the  surface  is  being  re- 
moved through  a number  of  shafts, 

2-compartment  shafts  are  frequently 
employed,  both  compartments  being 
used  for  hoisting,  and  separate 
shafts  being  provided  for  the  pump 
column  and  ladderways.  This  re- 
duces both  the  size  of  the  shaft  and 
the  timbering  necessary,  and  also 

does  away  with  the  special  danger  from  fire  that  always  exists  when  there 
is  a ladderway  in  the  shaft,  for  it  is  always  difficult  to  fight  fire  in  these 
special  compartments. 

Shaft  Sinking.— As  a general  thing,  the  loose  material  or  wash  above  bed 
rock  is  not  thick  enough  to  cause  any  serious  trouble,  and  ordinary  cribbing 
of  heavy  timber  or  a masonry  curbing  is  sufficient.  But  when  the  surface  is 
very  thick  or  loose,  and  runs  like  quicksand,  considerable  difficulty  is 
experienced.  The  general  method  of  overcoming  this  difficulty  in  the  past 
was  to  at  once  divide  the  shaft  into  the  required  number  of  compartments 
by  heavy  timbers  alternating  or  placed  “skin  to  skin,”  which  had  the  effect 
of  bracing  the  cribbing  against  the  lateral  pressure  of  the  loose  material. 
This  method  is  effectual  where  the  wash  will  remain  solid  or  stand  long 
enough  to  allow  the  timbering  and  cribbing  to  be  put  in.  But  when  the 
surface  is  thick,  loose,  or  watery,  or  of  quicksand,  some  one  of  the  following 
special  methods  of  sinking  must  be  adopted: 

Forepoling.” 


Fig.  1. 


Fig.  2. 


Quicksand 


Rock  (hard  or  soft,  but  very  wet)  

Rock  (hard  or  soft,  but  not  very  wet)  — 


Metal  linings. ’ ’ (Forced 

down  without  the  use  of 
compressed  air.) 

l4Pneumatic”method.  (Limited 
to  about  100  ft.  in  depth.) 

“Poetsch”  process.  (Freezing 
method.) 

“Kind-Chaudron”  method. 

“ Continuous, ”or“Long-Hole,M 
method. 


Size  of  Shafts.— Shafts  vary  greatly  in  size,  depending  on  the  number 
of  compartments  desired  and  the  size  of  the  compartments.  For  coal 
mines,  they  are  generally  from  10  to  12  ft.  wide  inside  of  timbers,  and  each 


OPENING  A MINE. 


2 0 


compartment  is  from  6 to  7 ft.  wide  inside  the  guides.  This  would  make  the 
outside  dimensions  of  a double-compartment  shaft  about  13  to  15  ft.  wide,  17 
to  18  ft.  long,  and  a triple-compartment  shaft  from  24  to  25  ft.  long.  Shafts  at 
metal  mines  are  generally  smaller  than  those  at  coal  mines,  but  the  prac- 
tice in  different  localities  varies  so  that  it  is  impossible  to  give  general 
dimensions  that  would  be  of  value. 

The  table  on  opposite  page  gives  the  dimensions  of  a few  well-known 
shafts  in  different  localities. 

Forepoling. — When  the  ground  is  so  bad  that  it  will  not  stand  for  several 
days  between  excavation  and  the  completion  of  the  lining,  it  becomes 
necessary  to  carry  the  timber  to  the  bottom  of  the  work.  This  may  be 
accomplished  by  using  square-set  shaft  timbering  and  driving  laths,  or 
forepoling  behind  the  timber  so  as  to  keep  the  soft  material  from  running 
into  the  opening.  The  advantages  of  forepoling  are  that,  if  the  shaft  is 
being  lined  with  square  sets,  it  can  be  commenced  at  any  point,  and,  if  the 
ground  is  not  too  bad,  the  work  can  be  continued  by  this  means  until  solid 
material  is  encountered.  When  the  ground  is  particularly  bad,  it  may 
become  necessary  to  use  breast  boards,  which  are  simply  boards  braced 
against  the  bottom  of  the  shaft  so  as  to  keep  the  material  from  rising  into 
the  opening,  only  one  board  at  a time  being  removed  while  the  material 
behind  it  is  excavated. 

In  particularly  bad  ground,  where  breast  boards  have  to  be  used,  tne 
progress  made  is  very  slow.  After  the  shaft  has  been  put  down  by  fore- 
poling; it  is  sometimes  very  difficult  to  repair  or  replace  the  lining.  When 
the  forepoling  method  is  employed  in  quicksand,  there  is  considerable  risk 
of  losing  the  shaft  altogether,  owing  to  sudden  rushes  or  “boils”  of  the 
material  that  throw  the  timbering  out  of  line  and  fill  up  the  shaft. 

Metal  Linings  Forced  Down. — Metal  linings  forced  down  without  the  use  of 
compressed  air  are  rarely  resorted  to,  though  in  some  cases  they  have  been 
quite  successful.  If  the  formation  contains  but  few  boulders,  it  is  some- 
times possible  to  force  the  lining  down 
by  flushing  out  the  material  from  the  in- 
side with  jets  of  water.  At  other  times, 
men  enter  the  shaft  and  excavate  the  ma- 
terial as  the  work  progresses. 

The  pneumatic  method  of  shaft  sinking  was 
developed  from  the  system  in  use  for  put- 
ting down  foundations  for  bridge  piers. 
At  the  bottom  of  the  shaft  there  is  a small 
chamber  called  a caisson,  in  which  a suffi- 
cient air  pressure  is  maintained  to  exclude 
the  water  at  all  times.  The  shaft  lining 
is  built  on  above  this  chamber,  and  grad- 
ually forced  down  into  the  soil.  Men 
enter  the  chamber  and  excavate  the  mate- 
rial from  under  the  caisson  as  it  descends. 

By  this  method  the  sinking  commences 
at  once  and  is  continued  without  interrup- 
tion until  the  lining  is  completed  to  bed 
rock,  to  which  the  lining  is  joined,  as 
shown  in  Fig.  3.  An  air  compressor,  which 
is  subsequently  used,  is  the  only  auxiliary 
machine  necessary,  while  in  the  freezing 
process  an  ice  machine  is  required. 

It  is  best  to  use  electric  lights  in  the 
caisson;  hence,  it  may  be  necessary  to 
Fig.  3.  install  a small  dynamo  if  the  company 

does  not  have  an  electric-light  system 
in  operation.  In  the  pneumatic  system,  the  bottom  of  the  shaft  is  always 
exposed  to  view,  and  the  workmen*  know  when  they  reach  a solid  founda- 
tion; while,  in  the  freezing  process,  it  is  sometimes  difficult  to  tell  to  what 
depths  the  pipes  should  be  sunk  so  as  to  reach  below  any  fissures  or  seams  in 
the  bed  rock.  In  the  pneumatic  process,  the  fine  material  is  aspirated  out 
of  the  caisson  by  the  air  pressure.  The  pneumatic  process  is  limited  to  a 
depth  of  about  100  ft.,  as  it  is  impossible  for  men  to  work  under  a greater  air 
pressure  than  that  which  corresponds  to  about  100  ft.  of  hydrostatic  pressure. 

By  the  freezing  process,  pipes  are  sunk  in  the  ground  about  the  area  to  be 
frozen,  as  a rule,  not  more  than  3 or  4 ft.  apart.  The  lower  ends  of  the  pipes 


Table  of  Well-Known  Shafts. 


SHAFT  SINKING. 


261 


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262 


OPENING  A MINE . 


are  sealed  or  closed,  and  an  inner  tube  introduced  so  that  a freezing  mixture 
may  be  caused  to  circulate  down  through  the  inner  tube,  and  up  through 
theouter  tube.  This  freezing  mixture  may  be  either  liquid  ammonia  gas, 
which  is  allowed  to  expand  in  the  outer  tube,  or  it  may  be  a solution  of 
calcium  chloride  that  has  previously  been  reduced  to  a very  I9W  tempera- 
ture by  means  of  an  ordinary  refrigerating  machine.  The  circulation  is 
maintained  in  the  pipes  until  the  ground  between  them  is  frozen  solid,  after 
which  the  work  may  be  continued  as  though  the  formation  were  solid  rock, 
the  material  being  blasted  and  hoisted  in  buckets.  The  freezing  process 
mavTe  applied  to  any  wet  formation,  whether  hard  or  soft  while  the 
pneumltfc  process  is  applicable  only  to  soft  formations  The.  freezing 
process  may  be  carried  to  practically  any  depth.  As  a rule,  the  freezing  pipes 
are  never  sunk  inside  of  the  shaft  area.  , . 

The  Kind-Chaudron  method  is  applicable  only  to  round  shafts,  and  is 
suitable  for  shafts  passing  through  very  wet  and  at  the  same  time  com- 
paratively soft  formations.  The  excavation  is  carried  on  by  means  of  a 
large  set  of  boring  tools  armed  with  steel  teeth,  and  operated  in  a manner 
sinnlar  to  that  employed  in  drilling  wells  by  the  percussive  system  first, 
a pit  or  shaft  4 or  5 ft.  in  diameter  is  drilled;  this  is  followed  by  a reaming  bit 
that  enlarges  the  hole  to  the  desired  diameter,  or  the  work  may  be  accom- 
plished in  three  stages  by  using  two  reaming  bits.  The  material  removed  by 
the  first  bit  is  hoisted  out  by  means  of  a sand  bucket,  or  sludger  while  that 
removed  by  the  succeeding  tools  is  hoisted  out  by  buckets  that  are  placed 
in  the  bottom  of  the  first  pit  and  kept  there  while  the  tools  are  m operation. 
No  water  is  pumped  from  the  shaft  while  it  is  being  excavated  or  lined, 
and  hence  practically  all  the  tendency  that  tbe  s].des  w.ould  have  to  cave 
is  removed.  After  the  shaft  has  been  excavated  down  to  and  into  a solid 
formation,  it  is  lined  by  lowering  cast-iron  tubbing  into  the  hole  and  making 
a tight  ioint  against  the  bottom  by  means  of  an  expansive  packing  that  is 
forced  out  by  the  weight  of  the  tubbing,  or  lining.  After  the  lining  is  m 
place  the  space  between  it  and  the  sides  of  the  excavation  is  filled  with 
cement.  When  the  cement  is  thoroughly  hardened,  the  water  is  pumped 
from  the  inside  of  the  lining,  and  men  descend  and  examine  the  joint  at 
bed  rock.  In  this  method,  no  workmen  enter  the  shaft  until  it  is  lined 
through  the  troublesome  formation.  . 

Lone-Hole  Process.— The  long-hole  process  consists  m the  drilling  of  a 
series  of  diamond-drill  holes  over  the  area  of  the  proposed  shaft,  then  filling 
the  holes  with  sand,  after  which  the  work  progresses  by  removing  the  first 
5 or  6 ft  of  sand  from  the  holes  in  the  interior  of  the  shaft,  charging  these 
holes  with  explosives,  and  firing  them  by  electricity.  Next,  the  holes 
around  the  boundary  of  the  shaft  are  charged  and  fired  m the  same  manner, 
and  the  process  is  continued  until  the  bottoms  of  the  diamond-drill  holes  are 
reached.  This  method  is  especially  applicable  to  work  m hard  rock  where 
great  speed  in  sinking  is  desired,  for  all  the  drilling  is  accomplished  at  one 
dperation,  after  which  the  sinking  progresses  by  simply  cleaning  out  the 
drill  hole  and  blasting  the  material. 

General  Comparison  of  Methods  of  Shaft  Sinking.  Where  a shaft  is  sunk  by 
forepoling,  it  is  usually  made  rectangular  in  form.  The  pneumatic  method 
mav  be  used  for  either  round  or  rectangular  shafts,  and  the  lining  may  be 
either  of  metal  or  wood.  The  freezing  process  may  be  used  for  either  round 
or  rectangular  shafts,  and  the  lining  may  be  either  timber,  metal,  or  masonry, 
as  the  entire  opening  can  be  left  open  until  the  solid  rock  is  reached,  when 
the  lining  can  be  built  upon  it.  The  Kind-Chaudron  method  is  applicable 
only  to  round  shafts,  on  account  of  the  fact  that  the  hole  is  bored.  The 
long-hole  process  is  applicable  to  either  round  or  rectangular  shafts,  but  .was 
originally  introduced  for  sinking  rectangular  shafts.  . 

Sinking  Head-Frames.— Head-frames  of  very  simple  form  are  used  for  sink- 
ins  The  skeleton  of  the  frame  is  formed  of  heavy  squared  timber  (10"  X 10" 
or 12"  X 12")  mortised  and  pinned  together,  and  braced  by  diagonal  braces. 
A good  height  from  the  surface  to  the  center  of  the  sheave  is  from  20  to  25  ft. 
The  sheave  should  be  from  6 to  8 ft.  in  diameter.  The  sinking  bucket  should 
be  of  boiler  iron,  or  of  heavy  hard  wood  strengthened  by  iron  bands,  about 
3 ft.  in  diameter  at  the  top  by  from  2i  to  3 ft.  deep.  It  should  be  suspended 
bv  a handle  pivoted  a trifle  below  the  center,  and  it  should  have  a pm  on 
the  rim  of  the  bucket  that  will  hold  it  in  an  upright  position  when  a loose 
ring  on  the  handle  is  slipped  over  it.  A chain  fastened  to  the  top  of  the 
head-frame,  with  a hook  on  its  loose  end,  is  suspended  so  that  when  hang- 
ing plumb,  it  is  over  a chute  leading  to  the  dump  car.  As  the  bucket  is 


SHAFT  SINKING. 


263 


hoisted  out  of  the  shaft,  this  chain  is  attached,  and  the  engine  reversed. 
The  bucket  swings  over  the  chute,  the  ring  holding  it  upright  is  knocked  off 
the  pin,  and  the  rock  is  dropped  into  the  chute.  Rocks  too  large  for  the 
bucket  are  suspended  in  chains  and  are  hoisted  in  that  way,  and  removed 
on  a truck  that  runs  on  a track  inside  of  the  head-frame,  the  gauge  of 
which  is  sufficiently  wide  to  give  plenty  of  clearance  for  the  bucket. 

Sinking  Engines.— Most  shafts  and  slopes  are  sunk  with  old  engines,  or 
else  by  engines  especially  designed  for  such  work,  and  so  constructed  that 
they  can  easily  be  moved  from  place  to  place.  In  some  cases  where  an  old 
engine  can  be  readily  had,  it  is  set  up  on  temporary  timber  foundations  and 
used  until  the  shaft  or  slope  is  finished,  when  it  is  replaced  by  the  perma- 
nent engines,  and  the  old  one  is  dismantled  and  disposed  of  to  the  best 

a<1  Tod^— The  old  method  of  hand  drilling  is  still  adhered  to  in  many 
instances,  but  it  is  gradually  giving  way  to  machine  drilling,  especially  in 
deep  shafts.  When  properly  managed,  the  work  is  done  much  more  rapidly 
and  economically  by  the  several  excellent  types  of  rock  drills  now  on  the 
market.  They  are  constructed  in  a variety  of  shapes  by  the  makers,  and 
there  are  so  many  convenient  accessories  in  the  shape  of  fittings,  etc.  that 
all  contractors  prominent  in  the  various  coal  fields  possess  one  or  more  of 
their  favorite  type  of  drills.  These  drills  are  run  either  by  compressed  air, 
steam,  or  electric  power,  and  in  large  shafts  two  are  usually  employed,  so 
that  work  may  not  be  delayed  by  a breakdown  of  one  drill.  The  center  or 
one  side  of  the  shaft  is  usually  kept  in  advance  of  the  rest,  so  as  to  furnish 
a sump  for  the  collection  of  the  water.  The  holes  are  drilled  from  3 to  6 ft. 
apart,  and  the  depth  varies  with  the  character  of  the  rock.  When  a suf- 
ficient number  of  holes  are  drilled,  the  drill  is  removed,  and  a cartridge 
made  of  dynamite,  dualine,  or  some  other  form  of  high  explosive  is  tamped 
in  each  hole.  These  are  all  fired  simultaneously  by  an  electric  battery, 
detonating  caps  being  placed  in  each  charge. 

To  keep  the  shaft  the  required  shape,  if  rectangular,  a plumb-bob  is  sus- 
pended in  each  corner,  either  from  the  flooring  on  top,  or  from  a beam  laid 
across  the  cribbing,  and  these  guide  the  miner  in  squaring  the  corners  and 
sides.  If  the  shaft  is  a circular  one,  a plumb-line  is  let  down  in  the  center, 
from  time  to  time,  and  a rod  cut  the  exact  radius  is  revolved  around  it.  If 
it  strikes  the  rib,  the  miner  knows  that  at  that  point  the  shaft  is  not  true. 

Drainage  and  Ventilation.— When  only  a small  amount  of  water  is  encoun- 
tered while  sinking,  the  best  plan  is  to  allow  it  to  collect  in  a depression  and 
bail  it  from  there  into  the  bucket,  hoisting  it  the  same  as  the  rock.  Where 
the  water  is  excessive  in  quantity,  a steam  pump  is  necessary.  All  the 
leading  pump  works  make  pumps  especially  designed  for  sinking  purposes, 
and  it  is  not  in  the  province  of  this  work  to  mention  the  advantages  pos- 
sessed by  one  over  the  other. 

When  the  shaft  is  of  moderate  depth,  a fire  burning  m one  corner  will 
supply  ample  ventilation.  To  rapidly  clear  away  smoke,  a good  plan  is  to 
burn  a bundle  of  straw  or  shavings  in  one  end  of  the  shaft,  and  throw  a 
couple  of  buckets  of  water  down  the  other  end.  When  the  shaft  is  very 
deep,  or  when  the  sectional  area  is  small,  ventilation  is  produced  either  by  a 
steam  jet,  or  by  a small  fan  turned  either  by  steam  or  by  hand.  In  some 
cases,  a fire  is  used  that  draws  into  a board  pipe. 

Speed  and  Cost  of  Sinking.— Any  attempt  at  a general  estimate  regarding 
the  speed  and  cost  of  sinking  is  impossible,  for  many  reasons  appreciated  by 
the  practical  miner.  Shafts  vary  so  much  in  size,  and  in  the  character  of  the 
material  through  which  they  pass,  that  even  if  there  were  no  other  items  to 
be  considered,  a general  estimate  could  not  be  made.  But  if  the  ground  is 
pretty  well  known,  and  the  sectional  area  and  the  depth  given,  the  experi- 
enced contractor  knows  how  much  he  can  drive  in  a given  time,  and 
he  can  consequently  form  a good  estimate  for  each  separate  shaft.  The 
range  of  cost  is  so  great  that  it  may  be  anywhere  from  SI  to  S10  per  cubic 
yard  of  material  excavated.  , . , . 

Slope  Sinking.— A slope  is  an  inclined  plane  driven  down  on  the  bed  of  the 
seam,  and  is  generally  through  coal  or  ore,  though  sometimes  they  are 
driven  through  rock  across  measures  to  cut  the  seam  that  cannot  be  conve- 
niently worked  bv  a slope.  In  the  latter  case,  it  is  merely  an  “inclined 
tunnel.”  In  the  former  it  might  be  termed  an  “inclined  gangway.” 

A slope  and  an  inclined  plane,  when  mentioned  hereafter,  will  mean  an 
inclined  opening  in  coal  or  ore , used  as  a passageway  for  mine  cars. 

When  tne  location  of  the  slope  has  been  decided  on,  erect  a temporary 


264 


OPENING  A MINE. 


sinking  plant;  an  old  engine  is  generally  used.  For  a short  distanee, varying 
with  the  nature  of  the  ground,  but  usually  ranging  from  10  t<3  20 > ft. on  the 
pitch,  an  open  cut  is  made,  and  the  earth,  rock,  or  crop  coal  is  town ^out 
by  hand.  As  soon  as  sufficient  cover  is  reached,  the  work  of  undermining 
and  timbering  is  commenced,  and  at  the  same  time  a double  or  single  track 
is  laid,  so  that  the  material  can  be  taken  out  in  a car  or  self-dumping  skip. 
When  the  latter  is  used,  the  track  is  continued  up  a trestle  some  distance 
above  the  surface,  and  a head-sheave  so  placed  as  to  draw  the  skip  up  the 
required  distance  and  dump  the  material  in  a chute  beneath  tke  tres^mg. 

The  width  of  the  slope  depends  on  the  size  of  the  cars  and  the  number  of 
compartments.  The  most  common  arrangement  is  to  divide  the  slope  into 
three  compartments;  two  large  ones  for  hoistways,  and  a smaller  one  for 
pump  rod,  column  pipe,  steam  pipe,  and  traveling  way.  This  last  is  also 
used  as  an  airway  while  sinking  is  going  on. 

In  some  instances,  slopes  have  but  one  hoistway,  laid  with  three  ratio 
and  a turnout  at  the  middle  of  the  hoist,  and  some  have  single  track  with  a 
central  turnout.  This  may  be  economy  in  first  cost,  but  is  uot  ni  the  long 
run.  Collisions  are  apt  to  occur,  and  the  breaking  of  a rope  or  the  falling  ol 
coal  from  an  ascending  car  is  apt  to  cause  more  damage  than  when  two 

C°1Whenn Sveral  lifts  are  simultaneously  worked,  a single-track  slope  is 
used;  but  unless  the  pitch  is  light  and  several  cars  can  be  hoisted  at  once, 
this  method  produces  a comparatively  small  output.  . , , , 

When  the  dip  of  a slope  is  under  40°,  the  height  of  the  should  be 

about  7 ft.  in  the  clear.  When  the  slope  dips  more  than  40°,  unless  self- 
dumping  skips  or  gunboats  are  used,  a cage  is  necessary,  and  then  the 
height  must  be  made  greater.  . . , 4,  , n , „ QTw1 

The  sinking  of  a slope  is  similar  to  gangway  driving,  and  the  tracks  and 
timbering  are  kept  well  up  to  the  face.  . . . „„noTOj 

The  timbering  is  very  similar  to  gangway  timbering,  except  that  squared 
timber  is  more  frequently  used  (but  it  is  not  necessary)  and  .^e  jmito  are 
cut  with  more  care.  On  steep  pitches,  a heavy  mud  all  is  let  into  the  nb 
on  each  side,  to  prevent  the  road  from  slipping  down  the  pitch. 

The  Sump.— When  the  shaft  or  slope  is  completed,  among  the 
necessary  is  a sump  in  which  to  collect  the  drainage  of  the  mine.  This  is  an 
openingTower  in  the  vein,  when  it  is  a pitching  one,  or  in  the  rock  when  it 
is  a flat  seam  reached  bv  a shaft.  It  should  be  large  enough  to  hold  an\ 
excess  of  water  that  the  pumps  cannot  handle;  and  the  pumping  machinery 
should  be  powerful  enough  to  handle  the  ordinary  drainage  by  running  not 
over  10  hours  per  day.  When  this  is  the  case,  m an  emergency,  the  pumps 
ran  be  run  continuouslv,  and  thus  handle  the  surplus  w ater. 

Drivine  the  Gangway.— in  bituminous  coal  seams,  the  height  of  the  gangway 
is  governed  bv  tlie  thickness  of  the  seam,  and  this  is  also  true,  m a certain 
sense  in  the  anthracite  regions.  But  in  the  anthracite  regions  thej  are  very 
Hfdom  less  than  6 ft.  in  height.  In  the  larger  seams  they  are  ^m  6 ft  6 in 
to  7 ft.  6 in.  high  in  the  clear,  and  from  10  to  Id  ft.  wide  The  gauge  oftrack 
varies  from  24  to  48  in.  The  grade  should  rise  at  least  4 in.  in  100  ft.,  and 
a cutter  3 ft  wide  bv  18  in.  deep  should  be  cut  in  the  coal  on  the  low  side. 
Tfis  gutter  should  be  a gutter,  and  not  a receptacle  for  refuse.  There  is  no 
ecoSln  a sMlow^tter/or  in  neglecting  it  ^n^t  costs  a few  cents 
a dav  to  keep  it  open.  Some  authorities  advise  a rise  of  from  6 in.  to  1 ft. in 
oVerV  100  ft.,  but  thev  evidently  do  not  take  into  consideration  that ^g^ 
a riSe  means  a loss  of  from  26  to  53  ft  in  lift  at  ££ 

lone  or  in  other  words,  in  the  loss  of  from  68,000  to  13/, 000  sq.  ft.  of  tne  area 
LHoaT^o  be  reached  by  the  gangway.  This  app lies  to  Puffing  seams^ 
Where  the  seam  is  fiat,  or  nearly  so,  the  gangway  must,  of  course,  be  cmven 
on  a grade  that  best  suits  the  formation  Turnouts  oneach  side 

of  the  shaft  or  slope,  of  a suitable  length,  are  a necessity,  if  the  slope  or  snait 
to  be  ke  pt constantl v supplied  with  coal.  These  turnouts  vary  m length 
de^ndingonTe  length  of  the  cars,  and  the  number  necessary  to  keep  the 
machinery  in  motion  between  trips.  They  should  ^^?e  enough^abffiw 
at  least  3 ft.  in  the  clear  between  the  bodies  of  the  cars,  5 ft.  is  even  oette  . 
When  possible  to  avoid  it,  there  should  be  no  center  props  between  the 

^Levels  in  Metal  Mines.— The  cross-section  of  the  level  depends  largely  on 
the  character  of  the  ore  mined,  and  the  desired  output  from  the  deposit.  In 
.i.  _ mnfni  minoc  tytwI n pi n tr  hi eh-grade  mineral  from  narrow 


lixt;  cuaiauici  ui  me  uic  , — ~ , 

the  case  of  precious  metal  mines,  producing  high- 
veins,  the  levels  are  driven  as  small  as  possible. 


•grade  mineral  from  narrow 
Immediately  adjoining  the 


MINE  TIMBER  AND  TIMBERING. 


265 


shaft  there  is  a plat  or  station  the  full  width  of  the  shaft.  This  is  heavily 
timbered  and  provided  with  a double  track,  but,  as  a rule,  the  levels  have 
but  a single  track,  and  in  some  cases  there  is  but  a single  track  at  the  shaft, 
there  being  a turnout  or  switch  in  the  level  a short  distance  from  the  shaft. 
In  this  class  of  mines,  5 ft.  X 6£  ft.  in  the  clear  would  probably  be  the  average 
size  of  a level,  it  being  driven  as  small  as  possible.  In  the  case  of  mines 
producing  lower  grade  material  and  handling  heavy  tonnages  from  large 
deposits,  as,  for  instance,  in  some  of  the  iron  and  copper  mines,  the  levels  are 
driven  larger,  and  in  some  instances  are  double-tracked,  being  from  7 ft.  to 
8 ft.  high  in  the  clear,  and  from  7 ft.  to  12  ft.  wide  inside  timbers;  but,  even  m 
this  class  of  mines,  in  most  cases  single-track  levels  7 ft.  X 7 ft.  to  8 ft.  X 8 ft. 
in  the  clear  are  employed  with  turnouts  or  passing  points  at  intervals,  and 
a double  or  triple  track  at  the  shaft.  The  levels  are  usually  driven  with  a 
slight  grade  away  from  the  shaft,  so  that  they  will  drain  to  the  shaft,  and 
the  grade  will  be  in  favor  of  the  loaded  car.  In  some  mines  where  electric 
tramming  is  employed,  the  levels  are  so  driven  that  the  motor  makes  a 
circuit  through  the  mine,  following  the  foot-wall  in  one  direction,  and 
returning  along  the  hanging  wall,  or  one  of  the  drifts  may  be  in  the 
country  rock.  Such  systems  as  this  are  employed  only  in  large  properties 
handling  a very  great  tonnage.  

TUNNELS. 

Mining  tunnels  are  usually  of  small  cross-section  compared  with  those  that 
occur  in  railroad  work,  it  being  rare  that  their  size  is  such  that  they  cannot 
be  driven  in  full  section,  and  if  the  ground  is  firm  the  operation  of  placing 
the  lining  may  follow  behind  the  work  of  driving.  They  are  generally 
lined  with  timber,  and  in  case  the  ground  is  of  a soft  or  treacherous  nature, 
bridged  square  sets  and  forepoling  are  employed,  with  or  without  breast 
boards,  as  the  necessity  of  the  case  demands.  When  the  material  is  firm 
rock,  the  tunnel  is  sometimes  not  lined,  the  roof  being  given  an  arched 
form.  The  various  forms  of  timbering  employed  as  tunnel  linings  are 
shown  in  the  sections  on  Timbering. 


MINE  TIMBER  AND  TIMBERING. 


Choice  of  Timber.— Timber  used  for  underground  supports  in  mines  should 
be  long-grained  and  elastic,  and,  at  the  same  time,  should  not  be  too  heavy. 
Oak,  beech,  and  similar  woods  are  very  strong,  but  are  heavy  to  handle,  and 
when  set  in  place  are  treacherous,  owing  to  the  fact  that  they  are  short- 
grained and  not  elastic,  so  that,  though  strong,  when  they  do  break,  they 
break  without  warning.  Mine  timber  is  placed,  not  with  the  intention  of 
ultimately  resisting  the  great  pressure  of  the  earth,  but  so  that  it  may  keep 
any  loose  pieces  in  place  and  also  to  give  warning  to  the  workmen,  thus 
enabling  them  to  escape  before  a fall  occurs.  For  this  reason,  pine  and  fir 
are,  as  a rule,  better  for  mine  timbering,  as  they  combine  a fair  amount 
of  strength  with  considerable  elasticity,  and  hence  give  warning  long  before 
they  break.  Very  elastic  timbers,  such  as  cypress,  willow,  etc.,  are,  as  a rule, 
to  be  avoided,  on  account  of  the  fact  that  they  will  simply  bend  like  a bow, 
without  offering  the  necessary  resistance  to  hold  the  material  in  place  for  a 
short  time. 

Preservation  of  Timbers.— The  character  of  the  ventilation  in  a mine  has 
considerable  effect  on  the  life  of  any  timber  supports.  Damp  stagnant  air 
will  cause  mold  and  fungus  growth,  which  will  be  followed  by  the  destruc- 
tion of  the  timber  through  decay  or  dry  rot.  All  timbered  openings  should 
be  well  ventilated,  and  provision  made  for  the  speedy  removal  of  damp  hot 
air,  such  as  commonly  occurs  around  pump  rooms  and  along  steam  lines.. 

Water  is  a good  preservative,  as  it  washes  off  the  spores  of  the  fungi  as 
fast  as  they  are  formed,  and  sometimes  shaft  timbers  are  kept  wet  on 
account  of  the  preservative  action  of  the  water. 

Timber  may  be  also  preserved  (1)  by  a solution  of  common  salt  and 
water;  (2)  by  impregnating  the  wood  with  such  metallic  substances  as  sul- 
phates of  copper,  iron,  etc.;  (3)  by  impregnation  with  the  chloride  of  mag- 
nesium or  zinc;  (4)  by  creosoting;  (5)  by  coal  tar;  (6)  by  carbolineum. 

A solution  of  1 lb.  of  salt  in  4 or  5 gal.  of  water  gives  a cheap  and  easily 
armiied  preservative  with  which  the  timber  should  be  thoroughly  soaked. 


266 


MINE  TIMBER  AND  TIMBERING. 


Sulphate  of  iron  is  economical  and  effective.  In  the  zinc  process,  ablution 
of  1 gal.  of  liquid  chloride  of  zinc  (Sp  Gr.  1.5)  mixed  with  So  gal.  of 
is  forced  into  the  wood  by  pressure.  Impregnation  with  crude  CTe^ote 
oil  is  effective,  but  it  has  the  disadvantage  of  making  the  timber  very 
inflammable.  Creosote  acts  in  a threefold  manner:  (1)  WAhsthe  pores 

and  prevents  saturation  by  water;  (2)  it  destroys  organic  life,  ^ car- 
bolic acid  that  it  contains  coagulates  the  albuminoids  and  Pr^Y^^^cay. 
Painting  with  liquid  tar  is  effective,  but  makes  the  wood,  very  mflMomable. 
Painting  with  ordinary  whitewash  is  also  said  to  give  good  results.  Car- 
bolineum  is  said  to  be  effective  but  is  quite  expensive.  It  is  applied  with 
a brush,  or  bv  steeping  in  a tank;  1 gal.  will  cover  300  to  400  ft.  of  timber. 

Professor  Louis,  of  England,  has  shown  that  preservatives  decrease  the 
strength  of  timber  from  84  to  204,  depending  on  the  P^ce^used. 

The  following  table  gives  the  results  of  tests  made  by  different  methods 
of  treating  wood  at  Saint  Elroy,  France,  and  recorded  in  1890: 


Tests  of  Preservatives  for  Mine  Timber. 


Relative  Preservative  Effect. 


Name  of  Preservative. 

Oak. 

Fir. 

1 

Pine. 

Beech. 

Birch. 

Poplar. 

Tar 

Chloride  of  2dnc 

Sulphate  of  copper 

Sulphate  of  iron 

Creosote  

27.8 

10.5 

42.1 

18.0 

1.7 

263.5 

50.0 

12.0 
12.5 

2.5 

87.5 

26.3 

8.0 

4.2 

4.4 

105.4 

18.6 

1.8 

4.7 

0.6 

26.2 

52.5 

2.5 

3.7 

3.3 

150.5 

34.7 

15.5 

2.9 

1.3 

The  simple  removing  of  the  bark,  under  some  circumstances  seems  to  be 
advantageous,  but,  in  some  woods,  if  the  bark  is  removed,  the  sap  ’wood 
should  also  be  removed.  In  many  cases,  the  sap  wood  of  coniferous  trees 
is  as  strong  or  stronger  than  the  heart  wood,  and  for  this  reason  it  should 
not  be  removed.  Also,  in  the  case  of  many  coniferous  trees,  the  bark  seems 
to  act  as  a protection  to  the  timber  in  the  underground  workings.  If  it 
becomes  necessarv  to  reduce  the  size  of  the  individual  sticks,  it  is  usually 
better  to  split  them  than  to  saw  them,  especially  in  the  case  of  wood  from 
coniferous  trees,  as  this  does  not  destroy  the  sap  wood  or  unduly  injure  the 
grain  or  fibers  of  the  stick.  Generally  speaking,  mine  timbers  last  longer 
when  kept  wet,  and,  on  this  account,  some  of  the  mines  m Europe  have 
introduced  a system  of  pipes  for  spraying  the  timbers  m dry  portions  of  the 
mine  When  timbers  are  alternately  wet  and  dry,  they  are  destroyed  with 
amazing  rapiditv.  Timber  should  be  probed  from  time  to  time  to  ascertain 
its  condition,  as’ timbers  may  appear  sound  on  the  outside  when  the  heart  is 
completely  destroyed  bv  dry  rot.  In  selecting  props,  the  principal  points  to 
be  observed  are:  Straightness,  slowness  of  growth  as  indicated  by  narrow 
annular  rings,  freedom  from  knots,  indents,  resin,  gum,  and  sap.  They 
should  also  be  well  seasoned  before  use.  With  these  ^cautions  and  proper 
mine  ventilation,  fungus  growth  may  generally  be  obviated  and  durability 

^Pladne  of  Timber.— The  individual  sticks  should  never  be  weakened  by 
cutting  mortise  and  tenon  joints.  The  pressure  should  be  evenly  distributed 
over  a number  of  sticks,  and  not  concentrated  or  centered  at  one  point. 
Centers  of  revolution  should  be  avoided.  The  individual  sticks  should  be 
placed  in  the  direction  of  the  strain  that  they  are  to  resist,  so  thatthey  will 
be  subject  to  compression  along  their  length  rather  than  to  a transverse 
strain  J The  individual  sticks  should  be  so  placed,  and  the  joints  so  formed, 
that  the  pressure  tends  to  strengthen  rather  than  weaken  the  stm.cture  up  to 
the  crushing  strength  of  the  timber.  In  the  case  of  large  tlie  timber- 

ing should  be  done  according  to  some  regular  system,  while  at  the  face  of 
coal  mines,  single  props  or  posts  are  usually  found  better,  owing  to  the  fact 
that  “duty  is  only  to  support  the  loose  portion  of  the  roof  for  a lifted 
time.  Probably  the  most  important  point  is  to  timber  in  time,  before  the 
rock  becomes  broken  or  begins  to  settle. 


MINE  TIMBER  AND  TIMBERING . 


267 


It  seems  generally  agreed  that  the  main  weight  in  mines  comes  nearly  at 
right  angles  to  the  bedding,  and  that  the  props  should  be  mainly  set  in  that 
direction.  If  the  deposit  is  horizontal,  the  weight  generally  comes  vertically; 
but  if  the  deposit  is  inclined,  the  weight  comes  at  a right  angle  to  the  inclina- 
tion. Some  authorities  hold  it  as  a principle  that  all  props  should  be  set  at  a 
rectangle  against  the  main  pressure.  Others,  in  order  to  guard  against 
possible  side  thrusts  and  a tendency  of  the  ordinary  weight  to  ride  to  the  dip 
m inclined  deposits,  purposely  cause  a sufficient  number  of  props  to  be  set 
slightly  deviating  from  the  common  axis. 

Sawyer  fixes  a maximum  and  minimum  slope  for  the  props,  varying  with 
the  rate  of  dip.  He  makes  this  maximum  slope  of  the  props  one-sixth  that 
of  the  dip,  ana  the  minimum  slope  one-third  of  the  one-sixth. 

Props  are  usually  set  with  the  butt  end  downwards,  but  not  always.  Hav- 
ing the  butt  end  upwards  adds  a trifle  to  the  weight  on  the  lower  end,  but 
the  larger  size  at  the  top  should  lessen  the  liability  of  its  being  split  by  a 
coupling  resting  on  it,  and  also  gives  more  surface  for  abrasion  in  hammer- 
ing up  against  a rough  roof.  Both  ways  may  therefore  have  advantages 
according  to  the  circumstances.  The  butt  end  downwards,  with  air  circu- 
lating, is  the  way  Molesworth  recommends  for  stocking. 

Size  of  Timber.— The  general  tendency  at  all  metal  mines  at  present  is 
toward  the  use  of  systematic  frames  composed  of  small  sizes  of  timber,  rather 
than  toward  the  use  of  large  individual  sticks.  The  advantages  are:  (1)  the 
small  timber  is  cheaper  and  easier  to  procure;  (2)  it  is  easier  to  handle,  and 
hence  costs  less  to  place  in  position.  By  making  the  frames  according  to 
some  regular  system,  the  individual  sticks  can  be  framed  on  the  surface  by 
machinery  so  that  better  joints  are  secured.  The  setting  of  timber  can  be 
done  by  less  experienced  help  when  it  is  all  alike. 

Joints  in  Mine  Timbering. — In  all  mine  timbering,  the  object  is  to  so  form 
the  joints  that  no  fastenings  will  be  necessary  and  that  the  shape  of  the 
pieces  will  be  such  that  the  pressure  from  the  surrounding  material  will 
keep  the  joints  tight.  The  reason  for  this  is  that  any  metal  joints  usually 
corrode  rapidly  in  mines,  and  that,  when  it  becomes  necessary  to  replace 
timbering,  this  can  be  done  with  greater  ease  if  the  sticks  are  so  framed 
that,  by  relieving  them  temporarily  of  the  pressure  from  the  sides  and  top, 
they  can  be  simply  lifted  out  of  place  and  new  ones  substituted.  The  use 
of  a framing  machine  renders  it  possible  to  frame  the  joints  more  exactly 
than  with  hand  framing.  With  hand-framed  timbers,  the  joints  are  always 
cut  a little  free  to  allow  for  any  unevenness  in  the  surface,  but,  if  machine- 
framed,  they  are  sure  to  be  of  the  same  size.  As  timber  does  not  shrink  in 
the  direction  of  its  grain,  it  is  evident  that  where  the  posts  meet,  if  the 
caps  shrink  slightly,  they  will  become  loose  in  the  space  between  the  shoul- 
ders; hence,  if  timbers  are  cut  green  and  framed  to  the  exact  size,  subse- 
quent shrinking  may  open  some  of  the  joints.  This  may  be  obviated  by 
keeping  the  timber  moist.  . 

The  method  of  taking  timbers  into  a mine  depends  on  the  size  and 
number  of  timbers  used  and  on  the  character  of  the  opening  into  the  mine. 
In  drift  or  tunnel  mines,  timbers  are  sent  in  on  flat  cars  built  especially  for 
the  purpose,  or  in  the  regular  mine  cars.  In  vertical  shafts,  they  are  usually 
stood  on  end  on  the  floor  of  the  cage,  and  lashed  together  and  also  to  the 
supports  of  the  cage.  Where  the  opening  is  an  incline,  it  is  the  common 
practice  to  load  the  timbers  into  a skip  and  thus  lower  them  into  the  mine. 
Timber  should,  wherever  possible,  be  framed  on  the  surface. 

Undersetting  of  Props.— Props  at  the  working  face  should  not  be  set  at 
right  angles  to  the  inclined  floor  of  the  seam,  but  should  be  underset,  and 
the  greater  the  inclination,  the  greater  the  underset.  The  amount  of  under- 
set should  vary  with  the  inclination  of  the  seam,  and  should  not  be  so 
great  that  the  props  will  fail  out  before  the  roof  has  tightened  them. 

Forms  of  Mine  Timbering  and  Underground  Supports. — The  timbering  of  a mine 
maybe  divided  into  two  heads:  (1)  timbering  the  working  faces;  (2)  tim- 
bering the  roads. 

The  roof  may  be  supported  (a)  by  packing  the  waste  places  entirely 
where  sufficient  material  is  obtainable  for  the  purpose,  and  timbering  the 
faces  and  roads;  (ft)  by  partially  packing  the  waste,  by  buildings  or  stone 

Sillars  with  intervening  spaces,  and  by  timbering  the  face  and  roads;  (c) 
y timbering  the  face  and  roads  and  supporting  the  roof  in  the  waste  places 
by  wooden  or  stone  pillars,  but  without  any  packing;  ( d ) by  timbering  alone 
without  any  packs  or  walls  whatever;  ( e ) by  supporting  the  main  roads 
With  brick  arching,  or  by  steel  or  iron  supports. 


268 


MINE  TIMBER  AND  TIMBERING. 


The  accompanying  plates  include  all  the  common  forms  of  mine  timber- 
ing and  underground  supports.  _ . . . . 

Fig  1 shows  a post  a and  breast  cap  b.  The  breast  cap  b is  also  sometimes 
called’ cap,  head-block , headboard , lid,  or  bonnet  Sometimes  the  posts  are 
placed  upon  blocks  of  wood  similar  to  the  head-blocks  or  headboards,  the 
block  being  called  a sole;  at  other  times,  two  or  more  posts  may  be  set  upon 
one  long  block  of  timber  called  a sill.  When  posts  are  used  m inclines, 
they  should  not  be  set  perpendicular  to  the  foot  and  hanging  walls,  but 
should  be  underset  slightly,  so  that  any  tendency  of  the  hanging  wall  to 
settle  will  bring  the  posts  nearer  at  right  angles  to  the  walls,  and  so  tighten 
them-  the  amount  of  underset  should  never  be  more  than  one-sixth  the 
Ditch’ of  the  deposit.  Where  posts  are  set  at  an  angle,  they  are  usually 
Dlaced  on  wedges,  and,  as  the  pressure  comes  on,  the  wedges  are  tightened 
Fig  2 represents  a stull  a,  which  is  used  either  to  keep  the  walls,  of 
perpendicular  or  steeply  inclined  beds  or  veins  apart,  to  support  planking 
or  lagging  as  a working  platform,  or  as  a platform  upon  which  to  pile 
or©  or  rock 

Fig.  3 represents  cockermegs,  which  are  simply  timber  frames  employed 
in  coal  mines  for  holding  the  face  of  the  coal  in  place  while  it  is  being 
undercut  They  are  composed  of  a pole  c extending  along  the  face  and 
supported  by  short  stulls  or  braces  a,  the  whole  being  tightened  into  place 

by  the  long  stulls  b.  ......  „ ..  , , 

Fig.  4 shows  a crib,  cog,  chock,  pillar,  or  shanty  built  up  of  timbers  and 
filled  with  waste  rock.  It  is  intended  to  serve  as  a pillar  and  to  withstand 
great  vertical  pressure,  doing  away  sometimes  with  the  necessity  of  leaving 

pil  7^is  ^cribbing  framed  from  round  timbers  laid  skin  to  skin,  and  used 

in  raises  or  ore  chutes.  , , . r , 

Gangway  or  Level  Timbers.— Fig.  5 is  a set  employed  m the  case  of  an  extra- 
wide  gangway,  there  being  a center  post  under  the  middle  of  the  cap.  This 
form  of  set  may  be  provided  with  a sill  when  the  floor  of  the  drift  or 

gangway s^so^  ^ form  Qf  drift  set  surrounded  by  bridging  and  used  where 
such  bad  ground  is  encountered  as  to  necessitate  forepoling.  A are  the 
posts,  B the  caps,  and  C the  sill  of  the  regular  set;  D are  upright  bridge 
pieces;  E a horizontal  bridge  piece  separated  from  the  set  proper  by  blocks 
F so  as  to  provide  spaces  H around  the  regular  set  through  which  the  spiles 
or  forepoles  can  be  driven.  , . , 

Fig  8 shows  a form  of  drift  set  sometimes  employed  m very  heavy  or 
swelling  ground.  This  method  of  framing  the  timbers  shortens  each  piece 
and  reduces  the  transverse  strain  on  all  the  timbers. 

Fig.  9 shows  an  ordinary  drift  set  provided  with  a sollar  for  ventilation 
purposes.  An  additional  brace  b is  placed  parallel  to  the  cap  c,  and  this  is 
covered  with  plank  lagging  a,  so  as  to  provide  a passage  above  the  regular 
drift,  which  may  be  used  as  a return  air-course. 

Fig.  10  is  a simple  form  of  drift  set  employed  when  the  roof  and  walls  are 
of  soft  material,  but  the  floor  material  firm.  It  is  composed  of  posts  l,  upon 
which  is  placed  the  cap  c.  The  joggle  cut  into  the  cap  to  receive  the  heads 
of  the  post  should  never  be  less  than  1 in.  nor  more  than  one-third  the 
thickness  of  the  cap.  The  cap  is  usually  made  of  such  a length  that  the 
posts  l have  an  inclination  or  batter  as  shown  in  the  illustration,  thus  giving 
greater  strength  to  resist  side  pressure  without  decreasing  the  floor  area  of 
the  drift,  which  may  be  necessary  for  drains,  ditches,  water  pipes,  etc.  at  the 
sides  of  the  track.  When  the  floor  is  not  composed  of  solid  material,  the 
posts  l may  be  set  upon  a sill  that  is  framed  to  fit  the  legs  in  a manner 
similar  to  that  shown  for  the  cap.  The  joggle  cut  in  the  sill  should  never  be 
less  than  1 in.  nor  more  than  one-third  the  thickness  of  the  sill.  The  sill  is 
usually  composed  of  lighter  material  than  the  cap,  is  flattened  .on  one 
or  both  sides,  and  is  sometimes  used  as  one  of  the  ties  to  receive  the 
t;rack 

Fig.  11  shows  a post  l and  the  cap  or  collar  c,  used  where  one  wall  is  of 
firm  material.  On  one  end  the  cap  is  placed  in  a hitch.  When  the  collar 
is  supported  in  a hitch,  it  is  sometimes  said  to  be  needled,  the  operation  being 
called  “ needling.”  The  bottom  of  the  post  a is  also  secured  m a hitch,  in 
case  there  is  any  side  pressure.  To  keep  the  surrounding  material  in  place, 
lagging  is  necessary,  as  shown  behind  the  timbers  in  Figs.  5, 10,  and  11.  In 
the  case  of  running  ground,  the  lagging  is  usually  made  from  sawed  material 
apd  driven  close  together. 


MINE  TIMBER  AND  TIMBERING. 


269 


270 


mine  timber  and  timbering. 


Fie.  13  illustrates  a method  of  spiling  or  forepoling.  a are  the  I*>sts  of  the 
regular  set,  b the  caps,  and  e the  top  bridging.  The  front  ends  of  the  spiles 
from  any  given  set  rest  on  the  bridging  of  the  next  advanced  set,  and  the 
spiles  for  advancing  the  work  are  driven  between  the  bridging  and  the  set, 
as  shown  in  the  illustration.  To  force  the  spiles  out  into  the  ground,  so  as 
to  provide  room  for  the  placing  of  the  next  set,  tail-pieces  i are  employed, 
these  are  placed  behind  the  back  end  of  the  spiles  as  they  are  being  driven. 
After  the  spiles  have  been  driven  forward  the  desired  amount^another  set 
is  placed,  the  tail-pieces  knocked  out,  and  the  front  end  of  the  spiles  allowed 
to  settle  against  the  bridging  of  a new  set.  Where  the  face  is  composed  of 
extremely  bad  material,  it  may  be  necessary  to  hold  it  in  place  with  breast 
boards , asshown  at  k,  the  breast  boards  being  held  in  place  hy  props  ^ which 
rest  against  the  forward  set.  When  breast  boards  are  used,  it  is  usually 
necessary  to  employ  foot  and  collar  braces  between  the  sets,  so  as  to  transfer 

the  pressure  of  the  breast  back  through  several  sets.  ^ 

Fig.  14  shows  a method  of  placing  drift  sets  m the  case  of  very  heavy  or 
swelling  ground,  a are  the  posts,  c the  sills,  b the  caps,  d are  the  collar 
braces  that  bear  against  both  the  caps  and  the  posts,  while  e are  foot  oj  hM 
braces  that  bear  against  both  the  sills  and  the  posts;  / are  diagonal  braces  that 
are  halved  together  and  placed  as  shown.  . . . , , 

Shaft  Timbering.— Fig.  12  shows  square-set  timbering,  sometimes  employed 
for  shaft  lining.  A are  the  wall  plates,  B the  end  plates,  C the  buntons, 
and  D the  posts.  The  method  of  framing  the  different  parts  is  plainly 

Sh°Fig*  15  represents  cribbing  sometimes  employed  for  shafts.  It  is  composed 
of  heavy  sawed  material  halved  together  at  the  ends  ^ 
pieces  a are  called  wall  plates , and  the  short  pieces  b end  plates  Between  the 
compartments  a partition  is  built  up  of  pieces  c called  buntons  The  end of 
the  buntons  are  let  into  the  wall  plates  an  inch  or  so,  as  shown  m tne 
illustration  and  should  be  so  placed  that  they  will  break  joints  with  the 
individual  pieces  of'  the  wall  plates,  thus  preventing  the  timbers  of  any 

6infg.1f,  sh“wsla^tfJr  Method  of ' framing.  ^times  em^oyed  for  the 

formed  at  I).  This  construction  necessitates  the  cutting  of  a j^non  onthe 
the  Dost  F as  shown.  S is  a 2"X  2"  strip  nailed  along  the  center  of 
the  back  of  the  wall  and  end  plates  as  a support  f^^c  lag^ng  tha  is 
placed  outside  of  the  sets.  The  lagging  is  usually  composed  of  2 or  3 

^ 18  shows  the  use  of  hangers  between  the  individual  square  sets.  The 

it 

timber,  to  the  sinking  of  a small  prospecting  mld^from 

wS,t^"ted  down  by 

about  45°. 


272 


MINE  TIMBER  AND  TIMBERING . 


Landings  Plats  or  Stations.— Fig.  22  is  one  method  of  timbering  a pjat  or 
station.  The  regular  square-set  timbering  of  the  shaft  is  continued  past 
the  station  and  the  heavy  stull  or  reacher  a put  across  at  the  bottom  of  the 
station.  The  posts  b are  bolted  against  the  posts  of  the  sets  and  the  cap  c 
placed  on  top  of  them.  After  this,  the  wall  plates  are  cut  out  between  the 
posts  b and  the  station  opened  and  timbered  as  shown  in  the  illustration. 
The  height  of  the  station  is  gradually  reduced  to  that  of  the  drift  or  level 

COIFigCt23^epresents  a method  of  timbering  a level  in  a slope  where  the 
ground  is  so  firm  that  only  stulls  are  employed  m the  slope  and  at  the 
station  the  timbers  all  being  secured  in  hitches  or  by  stulls.  a represents 
the  stulls  and  c the  timbers  that  are  spiked  to  the  stulls  and  carry  the 
stringers  for  the  car  track,  b represents  the  car  track  from  the  level  that  is 

brought  across  above  the  skip  track.  , . , 

Special  Forms  of  Supports.— Fig.  24  shows  a stone  arch  which  as  a stull 
RiiTYDorts  the  waste  material  in  the  level.  . 

Fig.  25  shows  a stone  arch  when  one  wall  of  the  formation  requires 

SU^ig.*26  illustrates  a passage  lined  by  a combination  of  stone  or  brick  walls 

with  wooden  caps  and  lagging  for  the  roof.  ' _ _ - . 

Fig  27  illustrates  the  lining  of  a drift  or  level  supported  by  means  of  iron 
or  steel  shapes  bent  into  the  form  of  an  arch  and  employed  for  the  support  of 

^Fig^28  illustrates  a cast-iron  post  or  stull  that  has  been  successfully  used 
as  a support  in  mines.  It  is  composed  of  two  pieces  a and  5,  held  together 
by  a collar  vC.  By  driving  c down  on  the  post,  f|he  two  pieces  can  be  taken 

a^^Figa  29  illus?rates  a masonry  shaft  lining  supported  by  means  of  cast-iron 
plates  C set  in  bell-shaped  cavities  cut  in  the  walls  of  the  shaft.  As  the 
masonry  of  a section  from  below  is  built  up  toward  that  above,  the  over- 
hanging portion  D is  cut  out  a little  at  a time,  and  the  masonry  from  below 
built  up  under  the  plate  so  that  the  lining  becomes  continuous. 

Fig  30  illustrates  masonry  shaft  linings,  supported  by  artificial  stone  or 
cement  foundations  built  in  bell-shaped  cavities  cut  m the  walls  of  the  shaft. 
The  blocks  of  artificial  stone  are  provided  with  inclined  bearings  C,  whicn 
serve  to  transmit  a portion  of  the  downward  thrust  of  the  lining  in  the 

direction^of  the^a  SuppQrts  _The  use  Gf  ir0n  or  steel,  either  for  vertical  or 

horizontal  supports  in  mines,  has  not  become  at  all  general.  In  America, 
timber  is  as  yet  comparatively  cheap  m most  mining  localities,  but  this  situ- 
ation is  fast  changing  and  the  timber  reserves  are  be^g  rapidly  cut  off, 
so  that  many  mines  now  using  wood  must,  m the  comparatively  near 
future,  resort  to  some  other  form  of  support.  Some  of  the  disadvantages  ot 
metal  supports  are  their  greater  initial  cost,  and  on  this  account  it  is  essen- 
tial that  all  such  supports  should  be  recovered.  As  very  little timber  is 
recovered  in  American  mining,  this  objection  is  one  toat  ^1  proMbly  co^ 
tinue.  The  mine  water  is  often  of  such  a character  that  it  v ill  dissolve  iron 
or  steel;  particularly  is  this  the  case  in  copper  mines,  and  ^ 
where  there  is  much  pyrites.  Metal  mines  keep  their  shaft  sets  open  but  a 
short  time  compared  with  the  pit  bottoms  of  large  coal  mines,  and  hence 
the  extra  cost  of  metal  construction  is  frequently  not  warranted.  The  dis- 
tricts in  which  metal  mines  are  located  are  more  likely  to  be  disturbed  than 
is  the  ground  over  a coal  mine,  and  if  timbering  is  crushed,  it  is  much  easier 
to  repair  than  iron  or  steel.  'Another  objection  to  metal  supports  is  the  fact 

that  they  cannot  be  as  easily  framed  and  worked  as  timber.  

On  the  other  hand,  the  life  of  metal  is,  under  ordinary  circumstances, 
much  greater  than  that  of  timber,  and  while  the  inital  cost  may  be  greater, 
whenever  the  metal  can  be  recovered  it  can  be  used  over  and  over  again, 
and  it  always  has  a certain  value  as  scrap  iron  or  steel.  After  a metal  beam 
has  bent,  it  can  still  be  used  by  simply  turning  ^ upside  down  Another 
advantage  for  steel  is  that  it  occupies  less  space  than  timber  or  masonry, 
and  thus  gives  a larger  effective  area  of  roadway  for  the  same  cost  of  driving, 

or  else  the  amount  of  excavation  may  be  reduced.  . 

Although  metal  has  not  been  greatly  used  for  props  or  upright  supports, 
it  has  been  quite  extensively  used,  both  in  America  and  abrosm,  for  sup- 
porting shaft  bottoms  and  landings,  and  m England  it  has  been  quite 
successfully  used  for  cross-bars  in  timbering  roads,  the  bar  tong  set  upon 
wooden  legs.  In  some  of  the  European  mines,  a complete  metal  casing  has 


MINE  TIMBER  AND  TIMBERING. 


273 


been  used.  In  locations  where  a constantly  increasing  pressure  comes  upon 
the  roof,  an  elastic  bending  material  must  be  used,  and  in  such  case,  soft 
steel  is  greatly  to  be  preferred  to  cast  iron. 


274 


MINE  TIMBER  AND  TIMBERING. 


Trestles.— Figs.  31  and  33  illustrate  the  various  timbers  and  methods  of 
cutting  the  joints  for  ordinary  railroad  trestles.  In  Fig.  33  the  portion  (a)  at 
the  left  illustrates  the  manner  of  framing  a pile  trestle,  while  the  portion  ( b ) 
at  the  right  represents  the  manner  of  placing  timbers  and  cutting  the  joint 
for  the  framed  trestle.  Fig.  31  represents  bents  of  a frame  and  pile  trestle 


HEAD  FRAMES. 


275 


and  the  side  elevation  of  a low  pile  trestle.  The  various  pieces  in  the  figures 
are  numbered,  and  the  accompanying  table  gives  the  names  of  the  parts. 


Fig  32  illustrates  a bent  of  a frame  trestle  that  is  fastened  together  entirely 
by  means  of  drift  bolts,  no  joints  whatever  being  cut. 

Figs  34  and  35  illustrate  one  manner  of  cutting  the  tenons  and  mortises 
on  the  ends  of  the  batter  braces  and  posts  and  frame  bents,  and  also  the  drain 
holes  that  are  bored  in  the  mortise  to  prevent  the  timber  from  rotting.  Usually 
the  sills  are  notched  or  boxed  to  receive  the  ends  of  the  timbers,  in  addition 
to  having  mortises  formed  in  them.  Figs.  36  and  37  show  such  joints  for 
receiving  the  batter  brace  and  post.  . 

Fig  38  illustrates  the  manner  in  which  a tenon  is  sometimes  formed  on 
the  top  of  the  pile  to  secure  the  cap.  When  the  cap  is  secured  by  a tenon, 
the  two  are  united  by  a wooden  pin  shown  in  the  lower  part  of  the  figure, 
and  known  as  a treenail. 

Fig.  39  illustrates  a manner  m which  the  cap  may  be  placed  upon  a pile 
trestle  by  splitting  the  cap  into  two  pieces,  a and  b with  the  tenon  c the  full 
width  of  the  pile  between  them.  . . . 

Fig.  40  illustrates  the  manner  in  which  the  cap  is  sometimes  secured  to  a 


pile  by  means  of  a drift  bolt,  and  Fig.  41  shows  the  manner  in  which  the 
same  thing  may  be  accomplished  with  the  use  of  a dowel. 

Figs.  42  and  44  show  two  methods  of  longitudinal  bracing  between  the 
bents  of  the  trestles  for  inclined  planes,  such  as  are  used  at  breakers  or 
concentrating  mills.  # _ , 

Fig.  43  is  an  elevation  of  a high  trestle,  showing  the  cross-bracing  and 
framing  of  the  structure.  „ „ , 

• Timber  Head-Frames  or  Head-Gears— Fig.  45  is  the  simplest  form  of  head- 
gear,  which  consists  of  a vertical  post  to  carry  the  weight  of  the  sheave,  etc., 
and  a diagonal  post  that  approximately  bisects  the  angle  between  the  rope 
from  the  drum  and  the  rope  hanging  down  the  shaft,  thus  taking  the 
resultant  pull  upon  the  axle  of  the  sheave.  There  is  usually  some  extra 
timbering,  as  shown,  to  support  the  cage  guides  and  form  a platform  about 
the  sheave  for  convenience  in  oiling. 

Fig.  46  shows  a modified  form  of  the  same  type  of  frame,  in  which  the 
main  upright  leg  is  vertical  and  in  which  there  is  also  another  vertical 


Bent , Framed,  1. 

Bent,  Pile,  2. 

Cap,  8. 

Cross-Tie,  4. 

Dapping , 5. 

Gaining,  see  Dapping,  5. 
Guard-Rail,  6. 

Jack-Stnnger,  7. 

Longitudinal  Brace,  8. 

Mortise,  9. 

Mud  Sill,  10. 

Notching,  Gaining,  Dapping,  5. 


Packing  Block,  11. 
Packing  Bolts,  12. 


Sill,  17. 

Stringer,  18. 

Sway-Brace,  19. 

Tenon,  20. 

Waling  Strip , see  Longitudinal 


Brace,  8. 


276 


MIKE  TIMBER  ASD  TIMBERING. 


member  on  the  opposite  side  of  the  shaft.  The  inclined  leg  is  also  braced 
and  connected  to  the  main  vertical  member. 

Fig.  47  is  a head-frame  for  an  inclined  shaft  where  the  ore  pocket  is  in  the 
structure  carrying  the  sheaves.  Such  head-frames  are  sometimes  enclosed 


49 


in  their  upper  portions  in  a building  so  as  to  protect  the  men  during  winter. 

Fig.  4S  is  a form  ot  framing  quite  common  in  the  anthracite  coal  fields  of 
Pennsylvania,  in  which  the  timbers  are  further  braced  bv  tie-rods,  as  shown. 

Steel  Shaft  Bottoms.— Fig.  49  is  a shaft  bottom  fitted  with  steel  supports, 
the  posts  being  Z-bar  columns  and  the  caps  being  replaced  by  I beams, 
which,  in  the  station  proper,  are  supported  on  stone  or  brick  walls.  This 
metal  construction  is  employed  throughout  all  the  portion  of  the  bottom 
landing  and  passages  where  the  cars  are  handled  after  they  are  brought 
from  the  workings  or  before  they  are  returned  to  the  workings. 

Undersetting  of" Props.— The  following  table,  from  Sawyers  “Accidents  in 
Mines.”  gives  the  maximum  and  minimum  angles  at  which  props  should  be 
set  for  varying  inclinations.  This  table  can  be  taken  as  a general  guide, 
but  it  does  n<7t  take  account  of  the  length  of  prop  nor  the  varying  amounts 
of  movement  of  the  top  rock  under  different  conditions. 


METHODS  OF  WORKING. 


277 


Undersetting  of  Props. 


Rate  of  Inclination  of 
Seam. 

Degrees. 

Angle  or  Underset  of  Props. 

Minimum 

Degrees. 

Maximum 

Degrees. 

6 

0 

1 

12 

0 

2 

18 

J- 

3 

24 

1 

4 

30 

2 

6 

36 

2 

6 

42 

2 

7 

48 

3 

8 

64  and  upwards 

3 

9 

METHODS  OF  WORKING. 


No  definite  rules  can  be  given  for  the  selection  of  a method  of  mining 
that  will  cover  all  the  conditions  that  may  exist  at  any  given  mine.  Each 
mine  is  a distinct  and  separate  proposition,  and  each  superintendent  must 
judge  how  he  will  adapt  the  general  principles  here  given  to  the  local 
conditions  at  his  own  mine.  Every  system  of  mining  aims  to  extract  the 
maximum  amount  of  the  deposit  m the  best  marketable  shape  and  at  a 
minimum  cost  and  danger.  


OPEN  WORK. 

Open  work  applies  to  the  working  of  all  deposits  that  have  no  overburden, 
or  to  those  in  which  the  overburden  or  overlying  material  is  stripped  from 
the  portion  of  the  deposit  to  be  removed  by  hand,  steam  shovels,  scrapers, 
etc.  It  includes  particularly  all  quarries  and  placer  workings,  and  can  be 
applied  to  many  mineral  and  coal  deposits. 

The  advantages  of  this  system  are  that  no  timber  is  required;  unprofitable 
underground  workings  do  not  have  to  be  kept  open  and  in  repair;  when 
required,  a simple  hoisting  plant  is  used;  there  is  less  danger  to  the  work- 
men from  falls  of  roof  and  from  blasting;  there  is  practically  no  danger 
from  fire;  artificial  lights  are  not  required;  mining  can  Be  done  more 
economically,  as  larger  faces  are  open,  larger  blasts  can  be  used,  and  the 
amount  of  work  accomplished  per  miner  is  greater,  and  better  superintend- 
ence can  be  had;  the  health  of  the  men  is  usually  much  better  when 
working  in  the  open;  the  deposits  can  be  more  easily  extracted  and  the  ore 
more  easily  and  more  perfectly  selected,  and,  under  proper  conditions,  the 
output  can  be  increased  almost  indefinitely. 

The  disadvantages  of  open  work  are:  A large  amount  of  overburden  often 
has  to  be  removed  and  a place  for  sorting  this  waste  material  provided;  the 
workmen  are  exposed  to  the  weather;  the  expense  of  open  work  increases 
rapidly  with  depth  of  covering. 

Open  work  may  be  divided  into  two  general  classes:  First,  where  the 
whole  or  a greater  part  of  the  deposit  is  of  value  and  has  to  be  removed,  as 
in  quarries  and  in  ordinary  mines;  second , where  the  valuable  portion  is  but 
a small  part  of  the  whole,  as  in  placers  or  fragmental  deposits  carrying  gold, 
platinum,  etc. 

Deposits  of  the  first  class  may  be  worked  as  follows:  (a)  The  deposit  is 
stripped,  if  necessary,  and  the  material  is  removed  by  hoisting  with  derricks 
or  a cableway,  or  by  drawing  out  in  cars  with  the  use  of  underground 
passages.  This  class  includes  practically  all  quarries  for  building  or  orna- 
mental stone,  slate  quarries,  and  most  of  the  open-pit  and  steam-shovel 
iron,  phosphate,  and  similar  mines.  ( b ) The  deposit  is  stripped,  and  drifts 
or  tunnels  are  extended  through  the  material  below  the  surface,  either  from 
adjacent  valleys  or  from  shafts  sunk  outside  of  the  deposit.  The  material, 


278 


METHODS  OF  WORKING. 


after  being  mined  in  the  open  pit,  is  thrown  through  openings  to  these  drifts 
or  tunnels,  through  which  it  is  trammed  to  the  surface  or  to  the  foot  of  the 
hoisting  shaft.  . „ . 

Steam -shovel  mines  are  those  in  which  the  material  is,  when  necessary, 
first  shaken  loose  by  big  blasts  of  low-grade  powder,  and  then  loaded  into 
railroad  cars  with  steam  shovels,  which  lift  the  ore  from  its  natural  bed  and 
deposit  it  in  cars  to  be  taken  directly  to  market  or  to  a concentrating  or 
washing  plant.  Mining  is  thus  done  very  cheaply,  but  the  steam  shovel, 
from  a mechanical  standpoint,  is  not  an  economical  machine  and  the  costs 
of  repairs  are  high.  T he  expense  for  hauling  material  from  the  steam  shovel 
increases  rapidly  with  adverse  grades.  Economy  in  steam-shovel  mining 
depends  on  the  shovel  being  kept  constantly  at  work.  An  output  of  2,000 
tons  per  day  for  a steam  shovel  and  one  locomotive  has  been  reached  and 
even  surpassed,  but  this  cannot  he  taken  as  an  average  for  a season  s work. 
Under  favorable  conditions,  there  is  probably  no  cheaper  method  of  mining 
The  cost  of  removing  97,854  yd.  of  material  over  a seam  of  anthracite  coal 
was  81  per  ton  of  material  stripped,  and  80.516  per  ton  of  coal  obtained.  The 
average  depth  of  the  stripping  was  75  ft.  and  about  two-thirds  of  the 
material  removed  was  rock.  The  cost  of  stripping  a bank  15  to  18  ft.  high  in 

Western  Pennsylvania  was  80.30  per  cu.  yd.  of  stripping. 

By  milling  system,  the  deposit  is  stripped,  shafts  are  sunk  outside  of  the 
boundaries,  and  drifts  are  extended  through  the  ore  some  distance  from 
the  surface.  From  these  drifts,  raises  are  put  up  to  serve  as  chutes,  after 
wrhich  the  material  is  simply  blasted  loose  and  worked  into  these  raises, 
through  which  it  passes  to  the  underground  passages,  and  is  trammed  to  the 
shafts  and  hoisted  to  the  surface.  The  advantages  of  this  system  over  the 
steam-shovel  methods  are:  It  is  not  necessary  to  make  any  long  cut  through 

the  overburden  to  bring  the  cars  on  the  surface  of  the  ore  body.  The 
mining  force  can  be  employed  underground  in  extending  drifts  and  driving 
new  raises  in  bad  or  stormy  weather.  Very  little  handling  of  the  material 
by  manual  labor  is  required,  the  men  simply  working  the  loosened  ore  into 
the  chutes  by  means  of  bars  or  shovels,  without  having  to  lift  any  of  it. 
Some  of  the  soft-ore  iron  mines  have  used  this  system  very  advantageously. 

Cableways  in  Mining— Cableways  are  extensively  used  for  stripping 
deposits,  for  transporting  material  after  it  has  been  quarried,  and  also  for 
mining  soft  or  loose  deposits,  such  as  clays,  phosphates,  and  gravels,  ine 
cost  of  removing  the  overburden  varies  greatly  with  the  nature  of  the 
ground,  and  depends  largely  on  the  distance  to  which  it  is  necessary  to 
carry  the  waste  material  before  dumping.  Frequently,  a cableway  can  be 
installed  spanning  both  the  place  of  mining  and  the  dumping  ground.  In 
other  cases,  one  end  of  the  cableway  is  fixed  and  attached  to  a washing  or 
gold-saving  plant,  while  the  other  end  revolves  about  this  fixed  point  m a 
circle  until  all  of  the  material  within  this  circumference  has  been  exca- 
vated; the  entire  plant  is  then  moved  to  another  location.  The  advantages 
of  cableways  over  steam  shovels  or  dredges  are  that  the  load  may  be 
delivered  at  a considerable  distance  from  the  point  of  excavation,  while  the 
entire  apparatus  rests  on  banks  entirely  clear  of  the  excavation. 

Cablewavs  have  been  constructed  with  single  spans  up  to  1,650  ft.,  han- 
dling 25-ton  loads,  and  delivering  an  average  daily  capacity  (10  hours)  of  617 
vd.  of  rock  Mr.  Spencer  Miller  places  the  following  limitations  on  the 
practical  applications  of  cableways:  Span  (sdnglej^.OOO  ft.;  load,  2o  tons, 

speed  of  travel,  1,800  ft.  per  minute;  speed  of  hoist,  900  ft.  per  minute.  The 
average  practice,  however,  is  about  as  follow’s:  Span,  600  to  1.200  ft.,  loads, 
3 to  7 tons,  speed  of  travel,  500  to  1,000  ft.  per  minute;  speed  of  hoist,  loO  to 

300  ft.  per  minute.  ...  _ , f 

Placer  or  fragmental  deposits  may  be  worked  by  means  of  a stream  of  water 
from  a pipe  or  nozzle  directed  against  the  bank  (hydraulic  mining),  or  the 
material  may  be  excavated  by  hand  or  by  mechanical  means,  such  as 
dredges,  steam  shovels,  etc.  , , , . _ 

Hydraulic  Placer  Mines.— The  material  is  broken  down  by  water  Sowing 
over  the  bank,  as  flume  waterfalls,  or  along  the  ground  so  as  to  ground-sluice 
the  material.  The  material  is  frequently  just  loosened  by  means  of  picks  or 
shovels,  the  current  being  depended  on  to  carry  it  away.  This  is  commonly 
called  ground  sluicing.  Another  method  of  excavating  the  matenaL  is  to 
direct  a stream  of  water  against  the  bank  from  a pipe  or  nozzle.  _ This  is 
true  hydraulicking.  After  the  material  has  been  loosened  by  the  water,  it  is 
allowed  to  flow  through  sluices  and  over  undercurrents  or  gold-saving 
tables  so  as  to  recover  the  valuable  portions. 


CLOSED  WORK. 


279 


Placer  Mines  Worked  by  Mechanical  Means— Where  water  is  scarce,  the 
material  may  be  excavated  by  steam  shovels  or  other  excavators,  such  as 
grab,  or  scooping,  buckets,  operated  by  cableways.  The  material  is  then 
washed  by  a limited  supply  of  water  that  is  frequently  used  over  and  over, 
or  it  may  be  passed  over  a dry  washer  or  concentrator.  Both  the  steam 
shovel  and  the  cable  excavator  have  proved  very  efficient  means  for 
working  certain  classes  of  deposits. 

Dredge  Mining.— Where  the  gold-bearing  material  lies  below  the  water 
level,  or  where  water  can  be  introduced  so  as  to  float  a boat,  a dredge  may 
be  employed.  > 

For  gold  dredging,  a dredge  should  fulfil  the  following  conditions: 
(1)  Speed  and  readiness  in  moving  and  taking  up  different  positions;  (2)  an 
adaptability  for  cleaning  up  rock,  and  for  digging  to  a maximum  depth; 
(3)  feasibility  of  working  and  of  the  banking  or  disposing  of  the  tail- 
ings; (4)  cheapness  in  working,  as  most  of  the  dredging  propositions  are  of 
low  grade.  , , ,, 

Three  types  of  dredges  have  been  used:  the  hydraulic  suction  dredge,  the 
shovel  dredge,  and  the  continuous-bucket  ladder  dredge.  The  first  of  these 
is  well  adapted  for  digging  very  small  gravel  and  sand,  but  is  not  suited  for 
boulders  or  even  large  stones  without  a great  loss  of  efficiency.  The  con- 
tinuous-bucket dredge  has  proved  the  most  successful  under  ordinary  cir- 
cumstances, as  it  is  controlled  by  lines  and  not  by  spiles  or  spuds,  and  hence 
can  be  shifted  more  rapidly  and  made  to  conform  to  irregularities  m the  bed 
rock  more  readily  than  the  dipper  type.  Also,  the  continuous-bucket 
dredge  furnishes  a constant  supply  of  material  to  the  apparatus  used  for 
recovering  the  gold.  „ ^ 

A continuous-bucket  dredge  can  operate  to  a depth  of  60  ft.  According 
to  Mr.  R.  H.  Postlethwaite’,  of  San  Francisco,  Cal.,  a decided  advocate  of 
continuous-bucket  dredges,  the  cost  of  working  a shovel  dredge  runs  from 
7 cents  per  cubic  yard  upwards;  but  he  claims  that  the  bucket  dredge  can  be 
worked  at  a cost  of  from  3 to  5 cents  per  cubic  yard,  including  a charge  of 
$100  per  week  for  depreciation.  The  cost  of  running  a small  gold  dredger 
should  not  average  over  $200per  week— that  is  allowing  $125  for  wages,  $50 
for  fuel,  and  $25  for  repairs,  etc.  If  the  dredger  handles  10,000  cu.  yd.  per 
week,  that  would  be  at  a cost  of  2 cents  per  cubic  yard.  If  the  material 
averaged  6 cents  per  cubic  yard,  there  should  be  an  approximate  profit  of 
$400  per  week  on  an  investment  of  from  $25,000  to  $40,000.  18  cu.  ft.  of  gravel 
in  place  will  weigh  2,000  lb.;  a cubic  yard  will  weigh  li  short  tons. 


4 CLOSED  WORK. 

Under  this  general  heading  it  is  customary  to  divide  the  methods  of 
mining  into  coal-mining  methods  and  metal-mining  methods.  This  classifi- 
cation is  not  entirely  logical,  for  identical  methods  are  applied  to  nat  bedded 
deposits  of  coal,  iron  ore,  clay,  salt,  etc.,  and  identical  or  very  similar 
methods  to  highly  inclined  coal  seams  and  mineral  veins.  A more  logical 
classification  is  one  based  on  the  position,  character,  and  thickness  of  the 
deposit,  but  the  older  classification  has  become  so  firmly  established  that  it 
is  not  advisable  to  give  it  up  entirely  in  a pocketbook. 

Bedded  Deposits.— The  typical  and  most  extensive  bedded  mineral .deposits 
are  of  coal  and  iron  ore,  and  of  these  the  former  is  by  far  the  more  extensively 
mined.  A description  of  the  several  methods  of  mining  coal  beds  will 
therefore  comprise  not  only  all  of  the  essential  points  in  the  mining  of  other 
bedded  deposits,  but  will  include  a number  of  points  not  usually  considered 
in  mining  such  deposits.  The  chief  of  these  is  the  presence  of  explosiwe  gas 
in  such  quantities  as  to  influence  the  choice  of  a method  of  mining,  r rom 
the  descriptions  of  the  methods  of  coal  mining  here  given  it  will  therefore 
be  a comparatively  simple  matter  for  the  miner  of  clay,  iron  ore,  etc.  to 
adapt  a method.  


COAL  MINING. 

General  Considerations.— The  elementary  causes  affecting  the  extraction  of 
coal  are  (1)  weight  of  overlying  strata  or  depth  of  the  deposit;  (2)  strength 
and  character  of  roof;  (3)  character  of  floor;  (4)  texture  of  bedded  material; 
(5J  inclination  and  thickness  of  bed;  (6)  presence  of  gas  in  the  seam  or  in 
adjoining  strata. 


280 


METHODS  OF  WORKING. 


Roof  Pressure.— Of  these  causes,  the  roof  pressure  is  the  most  impOTtant, 
and  a number  of  the  other  causes  are  directly  affected  by  it.  The  weight  of 
the  overlying  cover  will  give  a maximum  roof  pressure,  but  this  may  be  so 
variously  modified  that  the  determination  of  the  actual  pressure  is  practically 
impossible,  and  estimates  of  this  pressure  must  be  based  largely  on  practical 
experience;  hence,  rules  for  its  calculation  are  of  comparatively  little  value. 
One  very  essential  point,  however,  must  be  borne  in  mind,  1.  e.,  that  the 
direction  of  pressure  is  perpendicular  to  the  bedding  plane. 

Strength  and  Character  of  Roof.— The  strength  of  roof  refers  to  the  power  of 
being  self-supporting  over  smaller  or  larger  areas.  A strong  roof  permits 
larger  openings,  but  increases  the  load  on  the  pillars,  thereby  necessitating 
larger  pillars.  A weak  roof  requires  smaller  openings,  and  permits  smaller 


The  character  of  floor  influences  largely  the  size  of  pillars.  A soft  bottom 
requires  large  pillars  and  narrow  openings,  especially  when  the  roof  is  strong. 

Texture  of  Coal  and  Inclination  and  Thickness  of  Seam.— Soft,  friable  coal 
requires  large  pillars,  while  a hard,  compact  coal  requires  only  small  pillars. 
The  inclination  and  thickness  of  the  deposit  increase  the  size  of  pillars 
required,  and  also  influence  the  haulage,  drainage,  timbering,  method  of 
working,  arrangement  of  breasts,  etc. 

The  presence  of  gas  in  the  seam  or  in  the  enclosing  strata  affects  the  system 
of  working,  as  ample  air  passages  must  be  provided,  and  provision  must  fre- 
quently be  made  for  ventilating  separately  the  different  sections  of  the  mine. 
Where  the  gas  pressure  is  strong,  and  outbursts  are  of  frequent  occurrence, 
narrow  openings  are  necessitated  that  render  the  workings  safe  until  the 
gas  has  escaped.  ___ 

SYSTEMS  OF  WORKING  COAL. 

There  are  two  general  systems  of  working  coal  seams:  (1)  room-and-pillar, 

and  (2)  longwall.  There 
are,  however,  a great  num- 
ber of  modifications  of 
each,  and  it  is  often  diffi- 
cult to  exactly  classify  a 
given  method  under  either 
of  these  two  systems. 

The  room-and-pillar  sys- 
te/n,  also  known  as  the  pil- 
lar-and-chamber  or  bord- 
and-pillar.  and  which  may 
include  the  pillar-and-stall , 
svstem,  is  the  oldest  of  the 
systems,  and  the  one  very 
generally  used  in  the  mines 
of  the  United  States.  By 
this  system,  coal  is  first 
mined  from  a number  of 
comparatively  small  places 
called  rooms,  chambers, 
stalls,  bords . etc.,  which  are 
driven  either  square  from 
or  at  an  angle  to  the  haul- 
ageway. These  openings 
may  be  wide  or  narrow, 
and  may  be  either  a road- 
way, incline,  or  chute, 
according  to  existing  con- 
ditions. The  pillars  that 
are  left  between  the  open- 
ings in  the  original  work- 
ings support  the  roof,  and 
are  usually  subsequently 
removed.  All  forms  of 

room-and-pillar  workings  become  impracticable  when  the  ^lck^yef  ^ 
pillars  necessary  to  support  the  roof  pressure  much  exceeds  aouDie  me 
width  of  the  breast  openings. 


LONG  WALL  METHOD. 


281 


The  pillar-and-stall  system  is  similar  to  the  room-and-pillar  system,  but  in 
the  former  the  stalls  are  opened  off  from  the  entry  their  full  width,  while  in 
the  latter  the  rooms  or  chambers  are  turned  narrow,  and  widened  inside  to 
their  regular  width.  Fig.  1 shows  a typical  room-and-pillar  method  for 
working  an  approximately  horizontal  seam  of  coal  of  moderate  thickness 
(4  to  10  ft.),  and  with  a fairly  good  roof  and  bottom.  Main  headings  A are 
usually  driven  perpendicular  to  the  strike,  unless  this  direction  is  changed 
by  the  cleat  in  the  coal,  as  explained  later.  Cross-headings,  or  entries  B,  B, 
are  turned  off  at  regular  intervals,  and  at  an  angle  of  90  to  these  main 
headings,  the  distance  between  any  two  pairs  of  cross-entries  being  deter- 
mined, in  flat  seams,  by  twice  the  length  to  which  a room  can  be  driven, 
which  in  turn  is  determined  by  the  character  of  the  roof,  floor,  and  seam. 
The  rooms  are  turned  to  the  right  and  left  of  each  pair  of  butt  headings,  and 
driven  until  they  meet,  or  one-half  the  distance  between  two  pairs  of  entries. 
After  the  rooms  are  driven  up,  the  pillars  between  the  rooms  are  drawn,  and 
later  the  room  stumps  along  these  entries,  and  the  entry  pillars  themsel  ves, 
are  drawn,  unless  it  should  be  necessary  to  keep  some  of  these  cross-entries 
open  for  purposes  of  ventilation.  A large  chain  pillar  is  left  to  protect  the 

main  headings.  , , 

When  cross-entries  have  been  extended  a considerable  distance,  roads  are 
often  driven  between  them  parallel  to  the  main  heading  A.  The  object  of 
these  subroads  is  to  reduce  to  a minimum  the  air-courses  and  roadways  to  be 
maintained;  or  such  a subroad  may  be  necessary  on  account  of  a squeeze 
crossing  any  pair  of  cross-entries.  The  extent  of  the  territory  worked  out  to 
the  right  and  left  of  each  main  entry  is  a matter  for  local  determination. 

The  room  openings  are  made  suitable  to  prevailing  conditions,  and  Fig.  1 
shows  several  of  the  common  methods.  The  width  of  the  room  and  the  form 
of  the  opening  depend  on  the  character  of  the  roof  and  the  extent  to  which 
it  is  necessary  to  leave  a pillar  to  support  the  cross-heading,  it  being  advan- 
tageous, of  course,  to  open  out  the  room  to  its  full  width  at  the  earliest 

POTongwanMethod  of  Mining.-The  longwall  system  contemplates  the  extrac- 
tion  of  the  entire  seam  or  bed,  and  the  original  significance  of  the  term 
“longwall”  was  a continuous  line  of  breast.  No  portion  of  the  seam  is 
allowed  to  remain  after  leaving  the  vicinity  of  the  shaft.  The  method 
depends  on  producing  a uniform  and  gradual  settlement  of  the  root  a tew 
yards  behind  the  working  face.  Pack  walls  are  built  on  each  side  of  the 
roadways,  and  at  regular  intervals  in  the  gob  or  waste  area,  and  the  root 
settles  firmly  on  these  packs,  pressing  them  into  the  bottom,  or  compressing 
them  until  the  roof  subsidence  is  complete.  The  heignt  of  the  main  road- 
way is  maintained  by  “brushing”  the  roof  or  lifting  the  bottom.  Longwall 
may  be  advancing  or  retreating . In  longwall  advancing,  mining  begins  at  oi 
near  the  foot  of  the  shaft  and  advances  outwards  forming  a gradually 
widening  and  increasing  length  of  face  to  the  boundary.  The  passages  are 
made  through  the  excavated  portions  of  the  mine,  and  are  maintained  b> 
pack  walls  built  either  of  the  refuse  secured  in  mining  or  sometimes  from 
material  brought  in  from  the  surface.  In  longwall  ^fating  or  withdraw- 
ing,  entries,  gangways,  or  headings  are  first  driven  to  the  boundary  or  to 
other  convenient  distances  inbye,  and  the  pillars  between  these  entries  are 
then  drawn  back  toward  the  shaft;  this  is  also  called  working  home. 

Fig.  2 shows  a plan  of  combined  longwall  advancing  and  retreating,  in 
the  upper  arrangement,  or  Scotch  longwall,  the  face  is  semicircular  and  the 
roadsTe  turned  off  at  angles  of  45°  This  plan  issuitablefor  seams  up  to 
3 ft.  thick  with  a weak  top,  and  which  pitch  less  than  20  , and  situated  at 
almost  any  depth.  It  is  the  one  from  which  most  of  the  longwall  practice 
in  the  central  coal  basins  of  the  United  States  is  taken.  In  the  lower ^por- 
tion, which  shows  one  method  of  longwall  retreating,  narrow  Parallel 
headings  are  driven  in  pairs  to  the  boundary,  being  from  200  to  300  ft.  apart. 
Such  a combination  of  longwall  advancing  and  retreating  insures  an 
unvarying  supply  of  coal,  for  while  one  side  continually  leaves  the  shaft,  the 

Longwall  is  specially  adapted  to  flat  seams  or  those  having  a regular  and 
moderate  pitch,  and  which  are  free  from  faults;  to  hard  rather  than  to  soft 
coal;  and  to  the  use  of  undercutting  machines.  It  us  also  easy  of  venti- 
lation and  economical  in  timber,  explosives,  and  trank. 

In  all  longwall  work,  the  wreight  of  the  roof  is  made  to  act  upon  the  coal 
face,  which  is  undercut,  according  to  the  ability  of  the  miner  and  the  con- 
ditions of  the  seam,  from  2£  to  3 ft.  deep.  This  weighing  action  of  the  roof 


282 


METHODS  OF  WORKING. 


performs  the  work  of  the  powder  and  breaks  the  coal  in  a few  hours  or  less, 
after  the  sprags  have  been  removed.  The  time  required  to  break  the  coal 
will  be  greater  or  less,  according  to  conditions.  The  success  of  the  entire 
system,  as  will  be  readily  seen,  depends  on  a uniformly  regular  advance  of 
the  line  of  the  face  or  breast,  and  a uniform  system  of  setting  and  drawing 
timber  at  the  face;  also,  uniformity  in  the  pack  walls  along  the  roads,  and  in 
the  amount  of  gob  packing.  This  system  does  not  permit  of  long  idle  spells 
induced  by  strikes  or  other  causes.  The  coal  does  not  break  well,  either, 
when  some  of  the  men  are  out  a portion  of  the  time,  and  their  places  lie  idle. 
The  life  of  the  whole  system  consists  in  maintaining  what  miners  call  a 


Fro.  2. 


traveling  weight  upon  the  coal  face,  which  can  only  be  accomplished  satis- 
factorily by  uniformity  in  every  part  of  the  work. 

Longwall  advancing  is  better  suited  to  thin  seams  than  to  thick  ones,  to 
flat  rather  than  pitching,  and  to  good  roofs  and  hard  floors. 

Longwall  retreating  is  better  adapted  to  thicker  beds;  to  those  liable  to  gob 
fires;  to  seams  of  hard  coal  having  a considerable  pitch;  to  pockety,  or 
irregular  seams;  and  to  a soft  and  treacherous  top.  The  air-course  is  also  less 
broken  along  the  face,  and  better  haulage  installations  can  be  made.  Its 
chief  disadvantage  is  the  large  amount  of  dead  work  necessitated  before 
returns  are  received.  With  this  system  there  is  no  expense  in  keeping  up 
the  haulage  road  so  far  as  creep  or  falling  roof  is  concerned,  as  the  roads  are 
all  in  solid  coal,  nor  is  there  any  trouble  from  gob  fires  or  water;  and  little 


STARTING  LONGWALL. 


283 


detriment  to  the  working  face  is  caused  by  the  mine  having  to  stand  idle 
for  a time.  If  the  seam  is  high  enough  for  the  mules.  horses>  jo  rock 
whatever  will  need  to  be  taken  down.  The  coal  seam  will  be  proved  before 

^The Ventilation ^n  the  retreating  plan  is  as  near  perfect  as  it  is  possible  to 
get  it  in  practice.  All  the  airways  are  tight,  a thing  impossible  to  get  in  the 
advancing  plan;  and  it  is  a comparatively  easy  matter  to  shut  off  hre  or  to 
allow  a portion  of  the  working  face  to  remain  idle.  o,.  e 

Longwall  retreating  is  frequently  used  for  working  quite  limited  sections 
of  a mine  in  which  the  seam  of  coal  is  16  to  20  tt.  thick,  aQd  inclined  not 
more  than  10°.  A series  of  8 or  10  pairs  of  headings  are  turned  off  the  butt 
entry  and  driven  a distance,  dependent  on  local  conditions  where  the 
working  face  is  formed  by  driving  cross-cuts  from  one  to  the°tber* 
bice  is  carried  back  on  the  retreating  plan,  allowing  the  r^of^9  or 

settle  on  the  gob  as  the  work  approaches  the  butt  entry.  J1*  way,  any 
extra  weight  that  would  crush  and  rum  the  adjacent  coal  is  avoided.  This 
method  is  also  used  in  lower  seams  in  which  the  coal  is  soft,  <3r  ^eroof,  or 
bottom,  or  both,  are  of  such  a nature  as  to  give  trouble  m working  the ^oom- 
and-pillar  system.  Sometimes,  instead  of  driving  pairs  of  headings  at 
considerable7  distances  apart,  a number  of  single  headmgs  are  driven  com- 
paratively close  together,  and  connected  by  cross-cuts  froni  1C (to  20  yd. 
apart  When  the  limit  of  the  section  is  reached,  the  working  face  is  formed 
and  carried  back,  as  in  the  other  plan.  This  latter  method  is  more  suita- 
ble for  tender  roof,  or  a coal  in  which  the  face  and  butt  cleats  are  not 

Pr°S?artine  Longwall. — There  are  two  methods  of  starting  longwall  workings. 
In  the  first,  the  work  of  extraction  begins  at  the  shaft  itself,  the  coal  being 
taken  out  all  around  and  its  place  filled  with  solid  packs,  leaving  only  space 
for  the  roadways.  In  the  second  method,  a pillar  of  solid  coal  is 
port  the  shaft,  cut  only  by  the  roadways.  The  longwall  work  is  then 
started  uniformly  all  around  this  pillar.  Great  care  is nee(ie(i  iri  build, 
the  first  pack  walls  around  the  shaft  pillar,  to  see  that  they  are 
and  well  rammed,  in  order  to  break  the  roof  over  the  coal.  The  system  will 
not  work  rightly,  however,  until  the  breast  has  been  advanced  some  dis- 
tance from  the  pillar,  so  as  to  secure _ the  benefit  from  the  weighing  action  of 
the  roof  upon  the  coal  face.  The  mining  will  be  more  difficult  in  the  start, 
and  in  some  exceptional  cases  it  may  even  be  necessary  to  place  some  light 
shots;  which,  however,  should  be  avoided,  if  possible.  . . 

The  panel  system  divides  a mine  into  districts  or  panels  by  driving  entries 
and  cross-entries  so  as  taintersect  one  another  at  regular  intervals  of,  usually, 
about  100  yd.  Large  pmars  are  left  surrounding  the  workings  within  each 
panel,  and  any  method  of  development  may  be  used  for  each  panel.  This 
system  presents  the  following  advantages:  (1)  Better  control  of  the  ventila- 

tion, since  the  air  in  any  panel  may  be  temporarily  increased  or  decreased, 
as  required.  An  explosion  occurring  in  one  panel  is  less  liable  to  afreet  the 
other  workings.  (2)  Coal  may  be  extracted,  pillars  drawn,  and  the  panels 
closed  and  sealed  off  independently  of  each  other.  (8)  Greater  security  is 
afforded  against  creep  and  squeeze.  (4)  Coal  that  disintegrates  on  standing 
can  be  quickly  worked  out.  , _ x 

Bearing  In,  or  Undercutting.— In  any  method  of  mining  where  the  coal  is 
undermined,  advantage  should  be  taken  of  the  roof  pressure  to  assist  m 
both  breaking  down  the  coal  and  also  in  bearing  in.  The  fact  is  often 
overlooked  that  the  roof  pressure  upon  the  face  coal  makes  it  brittle  and 
more  susceptible  to  the  pick,  and  the  good  miner  starts  a shallow  mining  in 
the  under  clay,  or  lower  coal,  and  carries  it  the  entire  width  of  the  face. 
Bv  the  time  he  returns  to  the  side  of  the  breast  at  which  he  started,  the  roof 
pressure  has  made  the  coal  more  tender  and  susceptible  to  the  pick,  buch  a 
gradual  system  of  mining  throws  the  pressure  on  the  coal  face  gradually, 
and  the  coal  breaks  in  larger  pieces.  The  depth  of  the  undercut  depends 
on  the  thickness  of  the  seam  and  the  other  conditions.  Undercutting  by 
mining  machines  is  rapidly  replacing  hand  work  wherever  these  machines 

Ca^Bunffing^.’Pack  Walls,  and  Stowing.— Pack  walls  should  be  built  large  enough 
at  first  and  kept  well  up  to  the  face,  to  prevent  the  weight  coming  upon  the 
timber  and  also  to  permit  the  roof  to  settle  rapidly  when  the  timber  is 
taken  out  of  the  face.  Often  the  roof  will  not  stand  this 
without  breaking,  and  possibly  closing  in  the  entire  face.  The  face  should 
therefore  be  kept  in  shape,  and  just  as  soon  as  there  is  room  for  a prop  or 


284 


METHODS  OF  WORKING. 


chock,  it  should  be  put  in  immediately,  and  the  pack  walls  likewise  should 
be  extended  after  each  cut  or  web  is  loaded  out. 

As  a general  thing,  the  pack  walls  in  the  gob  are  not  so  wide  as  the  road- 
side ones,  particularly  when  the  seam  produces  enough  waste  material 
to  stow  the  “marches,”  “ cundies,”  or  “gobs,”  between  these  pack  walls. 
Usually  about  50/c  of  the  cubical  contents  of  the  solid  seam  taken  out  will 
stow  the  spaces  between  the  pack  walls  in  thick  pitching  seams,  where  the 
entire  gob  must  be  completely  filled  or  nearly  so.  No  waste  material,  except 
such  as  will  hasten  spontaneous  combustion,  should  be  taken  out  of  the 
mine  to  the  surface. 

Timbering  a Longwall  Face.— The  method  of  timbering  the  working  face 
depends  on  the  nature  of  the  roof,  floor,  coal,  etc.  The  action  of  the  roof  on 
the  coal  face  is  regulated  almost  entirely  by  timber;  consequently,  when  the 
coal  is  of  such  a nature  as  to  require  little  weight  to  make  it  mine  easily,  the 
roof  must  be  timbered  with  rows  of  chocks  and,  if  necessary,  a few  props. 

Control  of  Roof  Pressure.— The  working  face  of  a longwall  working  should 
advance  up  grade,  but  this  face  cannot  always  be  kept  parallel  with  the 
strike.  When  the  angle  at  the  line  of  face,  made  with  the  line  of  strike,  is 
less  than  90°,  the  greater  pressure  of  the  covering  rocks  is  thrown  on  the 
gob,  and,  when  this  angle  is  more  than  90°,  the  greater  pressure  comes  on 
the  coal.  The  angle  made  by  the  working  face  with  the  line  of  pitch  varies 
inversely  as  the  vertical  angle  of  pitch,  or  for  a high  pitch  this  angle  is 
small  and  for  a low  pitch  it  is  large.  Where  longwall  is  worked  in  adjacent 
sections,  care  must  be  taken  to  prevent  the  advancing  of  one  section  throw- 
ing a crushing  weight  on  any  of  the  others,  and  thus  producing  a crush  or 
an  uncontrollable  cave.  Where  the  rocks  are  pitching*  and  a greater  portion 
of  the  cracks  that  cut  them  run  in  lines  parallel  to  the  strike,  neither  stone 
nor  timber  can  efficiently  support  the  roof,  which  frequently  breaks  off  close 
to  the  working  face. 

The  ends  of  all  stone  packs  nearest  the  face  of  the  coal  should  be  in  line, 
and  the  ends  of  these  pack  walls  should  form  a line  parallel  to  the  face  of 
the  coal.  Timbers  set  at  equal  distances  and  in 
line  along  a longwall  face  are  much  more  efficient 
in  supporting  the  roof  than  irregularly  set  tim- 
bers. Fig.  3 shows  the  proper  way  of  locating 
the  pack  walls  and  the  face  timber. 

Number  of  Entries.— The  entries  in  a mine  may 
be  driven  single , double , triple,  etc. 

The  single-entry  system  is  only  advisable  under 
certain  conditions  and  for  short  distances,  since 
the  ventilation  must  be  maintained  along  the 
face  of  the  rooms,  and  there  is  but  one  haUlage- 
way,  which  may  easily  be  closed  by  a fall  or  creep.  Rooms  are  turned  off 
one  or  both  sides  of  the  entry. 

The  double-entry  system  is  most  commonly  used.  Two  parallel  entries 
are  driven,  separated  by  an  entry  pillar  whose  thickness  varies  with  the 
depth  of  the  seam,  and  connected  at  intervals  of  about  20  yd.  by  cross-cuts 
or  breakthroughs  to  maintain  ventilation. 

The  triple-entry  system  is  used  particularly  in  very  gaseous  seams  requir- 
ing separate  return  airways;  or,  at  times,  in  mines  where  the  large  output 
requires  ample  haulage  roads.  It  is  usually  applied  to  the  main  entries  only, 
but  sometimes,  also,  to  the  cross-entries.  In  gaseous  mines,  the  middle 
entry  is  usually  made  the  haulage  road  and  intake  airway,  and  the  outside 
entries  the  return  air-courses  for  either  side  of  the  mine,  respectively. 

A still  larger  number  of  entries  even  has  been  suggested  for  deep 
.'workings  where  it  is  difficult  to  keep  open  broad  passages,  but  these  have 
not  been  generally  adopted  or  tried  experimentally  to  any  great  extent. 

Direction  of  the  Face. — The  typical  room-andqflllar  plan,  Fig.  1,  shows  the 
main  headings  and  the  rooms  driven  parallel  to  the  direction  of  the  dip,  and 
the  cross-headings  parallel  to  the  strike,  but  in  most  coal  seams  there  are 
vertical  cleavages,  called  cleats,  which  cross  the  coal  in  two  directions  about 
at  right  angles  to  each  other.  Face  cleats,  as  they  are  called,  are  the  more 
pronounced,  while  the  end  or  butt  cleats  are  the  shorter,  less  pronounced 
joints.  The  direction  of  the  face  with  respect  to  the  cleats  is  of  prime 
importance  as  greatly  facilitating  or  retarding  the  mining  of  the  coal. 

Fig.  4 shows  the  different  positions  that  the  face  may  occupy  with  respect 
to  the  direction  of  the  cleats.  The  angle  of  the  breast  depends  on  the  hard- 
ness of  the  coal  and  freedom  of  the  cleats,  and  each  method  has  its  peculiar 


Fig.  3. 


PILLARS. 


285 


adaptation  to  the  varying  conditions  of  a coal  seam.  When  the  face  cleats 
are  working  free  and  the  coal  is  very  soft , it  may  be  necessary  to  drive  “ end 
on.”  The  end-on  method  is  best  adapted  to  a very  heavy  roof  pressure, 
while  for  a light  roof  pressure  the  short-horn  method  assists  in  breaking  the 
coal.  If  the  “ face  ” cleats  are  free  and  the  coal  breaks  readily  along  them, 
and  it  is  reasonably  hard , the  long-horn  method  is  adopted,  for  when  the 
coal  is  undercut  it  needs  more  support  than  it  gets  from  the  cleats,  and  its 
weight  must  be  thrown  somewhat  upon  the  end  cleats.  “ Face  on”  is 
adopted  when  the  face  cleats  are  not  as  free  or  numerous  as  the  butt  cleats. 
Unless  the  coal  at  the  face  re- 
ceives sufficient  support,  the 
undercutting  or  bearing  in  can- 
not be  thoroughly  done,  or  else 
the  amount  of  spragging  and 
the  risk  to  the  miner  are  in- 
creased. When  the  end  cleats 
are  less  pronounced  and  nu- 
merous, and  the  roof  pressure 
reat,  the  coal  will  probably 
reak  better  by  carrying  wide 
breasts  upon  the  ends  of  the 
coal,  and  it  is  then  an  advan- 
tage to  drive  double  rooms  with 
large  pillars  between  them.  In  pitching  seams,  the  pillar  should  have  very 
long  sides  perpendicular  to  the  strike,  if  the  principal  cleats  in  the  coal 
are  parallel  to  the  strike,  or  nearly  so.  , 

The  short-horn  method  is  adapted  to  heavy  roof  pressure  and  wide  room 
pillars,  as  the  face  cleats  are  here  quite  pronounced,  and  the  pillars  between 
the  rooms  thereby  weakened  to  a large  extent;  hence,  wide  pillars  are  more 
often  employed  when  working  on  the  ends  of  the  coal.  When  the  face 
cleats  are  less  pronounced,  and  the  end  cleats  are  working  freely,  a good 
breast  of  coal  is  carried  on  the  face,  and,  unless  other  conditions  require  it, 
a great  width  of  room  pillars  is  not  needed.  If  this  can  be  done  consistently, 
and  good  lump  coal  secured  at  the  same  time,  the  room  should  cross  the  pitch 
as  little  as  possible,  as  a side  pressure  upon  the  pillars  having  very  long  sides 
running  diagonally  across  the  pitch  is  destructive. 


PILLARS. 

Size  of  Pillars.— It  is  impossible  to  give  exact  rules  or  formulas  for  deter- 
mining the  proper  size  of  pillars.  Each  case  in  practice  requires  special 
consideration,  and  in  laying  out  the  pillars  in  a virgin  field  it  is  well  to  find 
out  what  the  current  practice  is  in  similar  fields.  In  general,  the  thicker 
the  seam  and  the  greater  its  depth  from  the  surface,  the  greater  should  be 
the  thickness  of  the  pillar.  Some  coal  deteriorates  rapidly  when  subject  to 
weight  and  to  the  disintegrating  effect  of  the  atmosphere,  and  pillars  of 
such  coal  must  be  larger  than  when  composed  of  a hard,  compact  coal. 
Permanent  pillars,  or  those  that  are  to  remain  for  a considerable  length  of 
time,  must  be  larger  than  those  that  are  to  be  promptly  removed.  Pillars 
about  the  bottom  of  a shaft,  or  along  main  haulage  roads,  should  be  left  large 
enough  to  provide  for  increasing  developments,  for  when  landings  are 
enlarged  or  when  haulage  systems  are  introduced,  the  original  pillars  fre- 
quently have  to  be  reduced  in  size  by  taking  a skip  off  of  them  or  by  taking 
out  chambers  for  engines  and  pumps.  . 

Shaft  Pillars.— Various  formulas  have  been  given  to  determine  the  size  of 
shaft  pillars,  and  the  results  given  by  these  several  formulas  are  very  diverse. 

Merivale. — S = X 22,  where  S equals  the  length  of  the  side  of  the 

pillar  in  yards,  and  D equals  depth  of  shaft  in  fathoms. 

Andre— Up  to  150  yd.  depth,  have  the  pillar  35  yd.  square,  and  for  greater 
depths  increase  5 yd.  on  each  side  for  every  25  yd.  of  increased  depth. 

Dron. — Draw  lines  enclosing  all  surface  buildings  that  it  is  necessary  to 
erect  about  the  head  of  the  shaft,  and  make  the  shaft  pillar  so  that  solid 
coal  will  be  left  outside  these  lines  all  around  for  a distance  equal  to  one- 
third  the  depth  of  the  shaft. 

Wardle.— Shaft  pillars  should  not  be  less  than  40  yd.  square  down  to  a 
depth  of  60  fathoms,  and  should  increase  10  yd.  on  a side  for  every  20 
fathoms  increase  in  depth. 


Fig.  4. 


286 


METHODS  OF  WORKING. 


Hughes. — Leave  1 yd.  in  width  of  pillar  for  every  yard  in  depth  of  shaft. 

Pa  mely.— Allow  a pillar  40  yd.  square  for  any  depth  up  to  100  yd.;  for 
greater  depths,  increase  the  pillar  5 yd.  for  every  20  yd.  in  depth. 

Calculating  the  size  of  pillar  from  each  of  these  authorities,  we  find  the 


Authority. 

For  Shaft  300  Ft.  Deep. 

For  Shaft  600  Ft.  Deep. 

Merivale 

4ndre  

22  yd.  square. 
35  yd.  square. 

31  yd.  square. 
45  yd.  square. 

Wardle 

Pamely  

Dron 

Hughes 

40  yd.  square. 

40  yd.  square. 
33i  yd.  square.* 
100  yd.  diameter. 

60  yd.  square. 

65  yd.  square. 
66f  yd.  square.* 
200  yd.  diameter. 

•Outside  of  buildings. 

None  of  these  formulas  takes  account  of  the  thickness  of  the  seam,  and 
the  following  formula,  which  takes  account  of  this  veiy  important  element, 
was  suggested  by  Mr.  R.  J.  Foster,  in  “ Mines  and  Minerals  . 

Radius  of  pillar  = Z\/  D X U 
in  which  D = depth  of  shaft;  t = thickness  of  seam. 

Pitching  seams  require  smaller  pillars  on  the  low  side  than  on  the  rising 

Sid RooV^PM Tars.— The  relative  width  of  pillar  and  breast  is  dependent  on 
the  weight  of  cover,  as  compared  with  the  character  of  the  roof  and  floor, 
and  the  crushing  strength  of  the  coal.  These  relative  widths  are  deter- 
mined largelv  by  practice.  Speaking  generally,  the  narrower  the  rooms 
or  chambers. ‘the  higher  the  cost  in  yardage,  the  greater  the  production  of 
slack  and  nut  coal,  the  greater  the  consumption  of  powder,  track  iron,  ties, 
etc.,  and  the  greater  the  cost  of  dead  work.  , 

For  bituminous  coal  of  medium  hardness  and  good  roof  and  floor,  a rale 
often  used  is  to  make  the  thickness  of  room  pillars  equal  to  1*  of  the 
depth  of  cover  for  each  foot  of  thickness  of  the  seam,  according  to  the 

expression  Wp  = ^ X A in  which  Wp  = pillar  width;  t = thickness  of 

seam-  D = depth  of  cover,  and  then  make  the  width  of  breast  or  opening 
equal’  to  the  depth  of  cover  divided  by  the  width  of  pillar  thus  tound, 

according  to  the  expression  W0  = where  W0  = width  of  room. 

Frail  coal  and  coal  that  disintegrates  readily  when  exposed  to  the  air,  and 
a soft  bottom,  may  increase  the  width  of  pillar  required  as  much  as  o0*  of 
the  amount  found  above;  also,  a hard  roof  may  increase  the  same  as  much 
as  254;  while  on  the  other  hand,  a frail  roof  or  a hard  coal  or  fl(x>r  may 
reduce  the  width  of  pillar  required  25*.  The  hardness  of  the  roof  affects 
both  the  width  of  pillar  and  width  of  opemng  alike,  which  is  not  the  case 
with  any  of  the  other  factors. 

Dunn’s  Tables  of  Size  of  Room  Pillars  for  Various  Depths. 

The  following  table  is  for  first  working,  with  the  design  of  afterwards 
taking  out  the  pillars,  the  width  of  the  principal  workings  being  5 yd.,  and 


Depth. 

Feet. 

Size  of 
Pillars. 
Yards. 

Proportion 

in 

Pillars. 

Depth. 

Feet. 

Size  of 
Pillars. 
Yards. 

Proportion 

in 

Pillars. 

120 

20  X 5 

.41 

1,080 

26  X 14 

.69 

240 

20  X 6 

.50 

1,200 

26  X 16 

.71 

360 

22  X 7 

.52 

1,320 

28  X 18 

.73 

480 

22  X 8 

.57 

1,440 

28  X 20 

.75 

600 

22  X 9 

.59 

1,560 

30  X 21 

.77 

720 

22  X 12 

.61 

1,680 

30  X 22i 

.78 

840 

26  X 15 

.63 

1,800 

30  X 24 

.79 

960 

28  X 16 

.66 

ROOM  PILLARS. 


287 


Extremely  large  pillars  must  often  be  left  as  a precautionary  measure  to 
protect  permanent  haulageways  and  surface  buildings,  or  to  avoid  any  pos- 
sibility of  a break  in  the  roof  that  would  cause  an  inflow  of  water. 


Table  Showing  Distance  From  Center  to  Center  of  Breasts  or 
Chambers  Measured  on  the  Entry  or  Gangway,  for 
Different  Angles. 


A I to 

I B 

© © 
0^© 


Distance  Measured  on  the  Entry  in  Feet,  When  Width  of 
Breast  + Width  of  Chamber  Is: 


03  r ' 

h q;  f-i  . 

20 

25 

30 

35 

40 

45 

50 

65 

60 

65 

70 

75 

90 

20.0 

25.0 

30.0 

35.0 

40.0 

45.0 

50.0 

■ 

55.0 

60.0 

65.0 

70.0 

75.0 

85 

20.0 

25.1 

30.1 

35.1 

40.2 

45.2 

50.1 

55.2 

60.2 

65.3 

70.3 

75.3 

80 

20.3 

25.4 

30.5 

35.5 

40.6 

45.7 

50.6 

55.8 

60.9 

66.0 

71.1 

76.2 

75 

20.7 

25.9 

31.1 

36.2 

41.4 

46.6 

51.2 

56.9 

62.1 

67.3 

72.5 

77.7 

70 

21.2 

26.6 

31.9 

37.2 

42.6 

47.9 

53.1 

58.5 

63.9 

69.2 

74.5 

79.8 

65 

22.0 

27.6 

33.1 

38.6 

44.1 

49.6 

55.1 

60.7 

66.2 

7L7 

77.2 

82.8 

60 

23.0 

28.9 

34.6 

40.4 

46.2 

52.0 

57.6 

63.5 

69.3 

75.1 

80.8 

86.6 

55 

24.4 

30.5 

36.6 

42.7 

48.8 

54.9 

60.9 

67.1 

73.3 

79.4 

85.5 

91.6 

50 

25.8 

32.6 

39.2 

45.7 

52.2 

58.7 

65.1 

71.8 

78.3 

84.9 

91.4 

97.9 

45 

28.2 

35.4 

42.4 

49.5 

56.6 

63.6 

^0.6 

77.8 

84.9 

91.9 

99.0 

106.1 

40 

31.1 

38.9 

46.7 

54.5 

62.2 

70.0 

77.6 

85.6 

93.4 

101.2 

109.0 

116.7 

35 

34.9 

43.6 

52.3 

61.0 

69.7 

78.5 

87.0 

95.9 

104.6 

113.4 

122.1 

130.8 

30 

40.0 

50.0 

60.0 

70.0 

80.0 

90.0 

100.0 

110.0 

120.0 

130.0 

140.0 

150.0 

25 

47.3 

59.2 

71.0 

82.8 

94.6 

106.5 

118.1 

127.2 

142.0 

153.8 

165.7 

177.5 

20 

58.5 

73.1 

87.7 

102.4 

117.0 

131.6 

145.9 

160.8 

175.5 

190.1 

204.7 

219.3 

15 

77.4 

96.6 

115.9 

135.3 

154.5 

]73.9 

192.8 

212.5 

231.9 

251.2 

270.5 

289.8 

10 

115.2 

144.0 

172.8 

201.6 

230.4 

259.2 

287.3 

316.7 

345.6 

374.4 

403.1 

432.0 

5 

229.5 

286.9 

344.2 

401.6 

459.0 

516.3 

572.5 

631.1 

688.5 

745.8 

803.2 

860.5 

In  the  following  table,  the  weight  thrown  upon  pillars  at  different  depths 
by  the  removal  of  different  proportions  of  coal  is  given: 

Weight  on  Pillars  in  Pounds  per  Square  Inch. 


Percentage  of  Coal  Left  in  Pillars. 


Depth 

Sean 

Feel 

90/. 

80/ 

70/ 

60/ 

50/ 

40/ 

30/ 

20/ 

10/ 

100 

Ill 

125 

142 

166 

200 

250 

333 

500 

1,000 

500 

555 

625 

710 

830 

1,000 

1,250 

1,665 

2,500 

5,000 

1,000 

1,111 

1,250 

1,428 

1,666 

2,000 

2,500 

3,333 

5,000 

10,000 

1,500 

2,000 

3.000 

4.000 

5.000 
10,000 

1,666 

2,222 

3,333 

4,444 

5,555 

11,110 

1,875 

2,500 

3,750 

5,000 

6,250 

12,500 

2,138 

2,956 

4,384 

5,912 

7,340 

2,496 

3,333 

4,999 

6,666 

3.000 

4.000 

6.000 
8,000 

3,750 

5,000 

7,500 

4,998 

6,666 

7,500 

15,000 

Chain  and  barrier  pillars  vary  in  size  even  more  than  shaft  pillars,  and  their 
widths  are  almost  entirely  determined  by  local  considerations.  In  some 
States,  the  minimum  width  of  barrier  pillars  is  regulated  by  law. 

Barrier  Pillars. — For  finding  the  width  of  barrier  pillars  in  anthracite 
seams,  the  following  formula,  adopted  conjointly  by  the  chief  mining  engi- 
neers of  the  Lehigh  & Wilkes-Barre  Coal  Co.,  Susquehanna  Coal  Co.,  D.,  L.  & 
W.  R.  R.  Co.,  Delaware  & Hudson  Canal  Co.,  and  the  State  mine  inspectors 
of  Eastern  Pennsylvania,  is  recommended: 

Formula  for  width  of  barrier  pillars:  (Thickness  of  workings  X 1 / of  depth 
below  drainage  level)  + (thickness  of  workings  X 5). 

Thus,  for  a seam  6 ft.  thick,  400  ft.  below  drainage  level,  the  barrier  pillar 
should  be  (6  X 4)  + (6  X 5)  — 54  ft. 


Depth  Below  Water  Level — All  Dimensions  in  Feet. 

Formula. — (Thickness  of  workings  X 1*  of  depth  below  drainage  level)  + (thickness  of  workings  X 5)  = width  of  barrier  pillar. 


288 


METHODS  OF  WORKING. 


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Each  adjoining  owner  is  to  leave  one-half  of  the  pillar  thickness  required. 


PILLAR  DR  A WING. 


289 


Compressive  Strength  of  Anthracite.— Attention  has  recently  been  called  by 
Mr.  William  Griffith,  of  Scranton,  Pa.,  to  the  advisability  of  testing  the 
strength  of  the  different  coals  and  of  using  this  data  as  a basis  for  the  proper 
proportioning  of  the  pillars  and  for  determining  the  probability  of  a squeeze. 
Jn  some  crude  experiments,  which  Mr.  Griffith  carried  on,  he  found  that 
different  coals  from  even  the  same  locality  varied  greatly  in  their  strengths. 
If  attention  were  given  to  this  matter,  probably  the  sizes  of  pillars  could 
be  calculated  on  a much  more  certain  basis  than  is  possible  at  present, 
and  the  liability  to  squeeze  lessened. 

The  table  on  page  290  gives  the  results  of  some  preliminary  and  crude 
tests  made  by  Mr.  Griffith,  which  supply  the  only  data  available  as  to  the 
crushing  strength  of  anthracite  coal. 

Drawing  pillars  is  about  the  most  dangerous  work  the  miner  has  to  perform, 
but  the  met  of  its  being  so  is  no  doubt  the  reason  why,  comparatively 
speaking,  so  few  serious  accidents  happen  in  it.  It  is  not  so  much  that  the 
best,  most  skilled  workmen  are  chosen  to  perform  pillar  drawing,  as  that 
the  men,  being  alive  to  the  dangers,  are  more  on  the  alert  and  careful  to 
protect  themselves. 

Sometimes,  if  not  very  often,  in  chamber  or  room-and-pillar  working  it  is 
the  custom  to  work  out  the  rooms  or  chambers  and  leave  pillars  all  the  way 
from  the  shaft  to  the  boundary  line  over  large  areas;  in  other  words,  the 
portion  of  the  roof  left  standing  on  pillars  is  very  extensive.  Mines  so 
worked  have  sometimes  been  spoken  of  as  mines  on  stilts.  To  this  mode  of 
proceeding  there  are  several  serious  objections.  By  leaving  the  pillars  until 
the  boundary  has  been  reached,  a large  number  of  airways  and  roadways 
have  to  be  kept  open  and  in  repair,  and  this  number  is  constantly  increasing 
until  the  limits  of  the  workings  have  been  reached.  This  circumstance 
renders  the  ventilation  more  difficult,  and  thereby  increases  risks  of 
accident.  Moreover,  the  length  of  time  during  which  the  old  rooms  and 
pillars  are  left  open  and  standing  increases  the  danger  of  squeeze  and  creep 


Fig.  5.  Fig.  6. 


setting  in,  by  which  a large  area  may  in  a short  time  be  overrun.  Also,  by 
this  method,  the  pillars  first  formed  are  last  removed,  and  hence  it  happens 
that  a large  number  of  them  crack  and  give  way  under  the  combined  action 
of  atmospheric  agencies  and  great  pressure.  Even  if  they  resist  these  actions 
well,  the  quality  of  the  coal  greatly  deteriorates  by  the  long  exposure. 

For  the  above  reasons,  it  is  the  best  practice  to  carry  on  the  two  workings 
(working  the  rooms  and  drawing  the  ribs  and  pillars)  simultaneously.  By 
so  doing,  the  length,  mean  duration  of  the  roadways,  etc.  are  reduced,  and 
the  pillar  coal  obtained  in  much  better  condition;  and,  in  order  to  concen- 
trate the  workings  as  much  as  possible,  the  two  operations  should  go  on  as 
closely  together  as  practicable.  With  fairly  thick  and  very  soft  coals,  the 
rapid  working  up  of  the  rooms  and  equally  quick  drawing  of  the  ribs,  as 
soon  as  the  rooms  are  driven  their  full  distance,  is  essential  to  economical 
working;  for  delay  in  extracting  ribs  and  pillars  in  such  circumstances 
results  in  their  getting  crushed  and  the  coal  lost  or  largely  ground  to  slack, 
waste  of  props  and  material,  disordered  ventilation,  and  shortened  life  of 
the  mine. 

Methods  of  drawing  pillars  vary  according  to  the  inclinations  of  the 
seams,  the  nature  of  the  roof  and  floor,  and  the  character  of  the  coal.  Figs. 
5 and  6 show  the  common  methods.  In  Fig.  5,  A,  B,  and  C,  the  drawing 
begins  by  cross-cutting  the  fast  ends  of  the  pillars  to  obtain  a retreating 
face.  A shows  a method  for  soft  coal  and  narrowing  pillars,  B for  wide 


Tests  of  Compressive  Strength  of  Sawed  Pieces  of  anthracite  Coal. 


290 


METHODS  OF  WORKING. 


Remarks. 

Checker  coal  from  Exeter. 

Checker  coal  M.  W.  coal  pile. 

Checker  coal  bottom  of  Clear  Spring  colliery. 

Clear  Spring  Pittston  vein  glassy  coal. 

Clear  Spring  Marcey  checker  coal. 

Clear  Spring  Marcey  checker  coal. 

Clear  Spring  Marcey  checker  coal. 

Clear  Spring  Marcey.  Very  good  test.  Checker  coal. 
Clear  Spring  Marcey.  Knot  in  block.  Not  fair  test. 
Clear  Spring  reddish  glassy  coal. 

Clear  Spring  reddish.  Not  fair  average  test. 

Crushing 
Weight.  Tons. 
Deduced. 

Per 
Cu.  In. 

CO  © I— J O')  © r-J  I-J  H<NOiP 
cir^T^^COiOCOiOT^CO' — 

4.67 

Per 
Sq.  In. 

SaOlOO^<Mr-4lOCOC<l^-N 
-<^0©COCOI>'^'^COi-HC- 
<^c4r-5©fHr-3iHCOCli— i' 

Breaking 
Weight.  Tons. 
Deduced. 

Per 
Cu.  In. 

ONClONOJN  . 

Oioooco^o 
— 'GO  <N  <N  <M  rH  CO 

2.70 

Per 
Sq.  In. 

co 

o io  i>  ao  © © 

O'-,  c^.  C^.  lO  © i“ 1 OO  lO  '-H 

^ ^ ' H H H rH 

Average 

Weight 

Sustained. 

Crush- 

ing. 

Tons. 

t'-»o>ia©ioioi>-©G003 

CO(MCOCOl>*CQ'MI>iOCOw 

Break- 

ing. 

Tons. 

28  (?) 
17  (?) 
30  (?) 
28  (?) 
30 
20 
22 
38 
32 
22 
30 

Dimensions  of  Test 
Piece. 

Height. 

r-tC4C<liO>COCO<Mi-lT-ICOC^ 

Width. 

Length. 

•«*CC©CO0OTt<''jHTt<Tt<i>lO> 

*1S9X  jo 
jaqxnnK 

i-HMCO''*iiO©t>CC©©^| 

1 

pillars,  the  end  being 
taken  in  two  lifts,  while 
C is  for  harder  coal  and 
shows  it  taken  in  three 
lifts.  D and  E show  the 
pillars  cut  into  stocks  to 
be  drawn  by  side  or  end 
lifts,  according  to  the 
character  of  the  coal,  the 
inclination  of  the  seam, 
thickness  of  the  cover, 
and  the  strength  or  weak- 
ness of  the  roof  and  floor. 
Fig.  6 shows  some  of  the 
methods  used  in  robbing 
the  pillars  in  steep  pitch- 
ing, thick  beds  of  anthra- 
cite. To  get  the  coal  out 
of  the  pillar  at  the  left 
of  A,  a skip  is  taken  off 
the  side,  as  shown.  Suc- 
cessive skips  are  thus 
taken  off  until  the  whole 
is  removed,  the  miner 
keeping  the  manway 
open  to  the  heading  be- 
low as  a means  of  retreat. 
The  pillar  between  A 
and  B is  very  similarly 
worked.  To  remove  that 
between  B and  C,  a nar- 
row chute  or  heading  is 
driven  up  the  middle, 
and  cross-cuts  put  to  the 
right  and  left  a few  yards 
from  the  upper  end. 
Shots  are  placed  in  the 
four  blocks  of  coal  thus 
formed,  as  shown,  and 
they  are  fired  simultane- 
ously by  battery.  This 
operation  is  repeated  in 
each  descending  portion 
unless  the  pillar  begins 
to  run.  A pillar  from 
which  the  coal  has 
started  to  run  is  shown 
to  the  right  of  C. 

To  secure  the  highest 
percentage  of  pillar  coal, 
a method  should  be 
adopted  that  will  pre- 
vent squeezing  or  crush- 
ing, if  possible.  All  the 
pillars  in  a panel  may  be 
taken  out  at  the  same 
time  by  end  lifts  in  such 
a way  as  to  keep  the  face 
of  all  the  lifts  in  line  and 
perpendicular  to  the 
sides  of  the  pillars,  or 
the  pillars  are  drawn  in 
lifts  of  three  or  more 
pillars  each,  the  centers 
of  the  face  of  the  lifts 
lying  in  a straight  line 
that  makes  an  angle  of 
about  40°  with  the  sides 


R 0 OM-AND-PILLA R METHODS. 


291 


of  the  pillars.  (See  also  “ Flushing  of  Culm,”  which  is  described  fully  on 
page  314.) 

Gob  fires  are  due  to  the  spontaneous  ignition  of  coal,  and  are  most  likely 
to  occur  in  pack  walls  and  gobs  where  there  is  an  insufficiency  of  air.  Ample 
ventilation  is  the  best  preventive. 

Spontaneous  Combustion.— According  to  Prof.  Able,  Dr.  Percy,  and  Prof. 
Lewes,  the  causes  of  the  spontaneous  ignition  of  coal  are:  First , and  chiefly, 
the  condensation  and  absorption  of  oxygen  from  the  air  by  the  coal,  which 
of  itself  causes  heating,  and  this  promotes  the  chemical  combination  of  the 
volatile  hydrocarbons  in  the  coal  and  some  of  the  carbon  itself  with  the 
condensed  oxygen.  This  process  may  be  described  as  self-stimulating,  so 
that,  with  conditions  favorable,  sufficient  heat  may  be  generated  to  cause 
the  ignition  of  portions  of  the  coal.  The  favorable  conditions  are:  A mod- 
erately high  external  temperature;  a broken  condition  of  the  coal,  affording 
the  fresh  surfaces  for  absorbing  oxygen;  a supply  of  air  sufficient  for  the 

Purpose,  but  not  in  the*  nature  of  a strong  current  adequate  to  remove  the 
eat;  a considerable  percentage  of  volatile  combustible  matter  or  an 
extremely  divided  condition.  Second , moisture  acting  on  sulphur  in  the 
form  of  iron  pyrites.  The  heating  effect  of  this  second  cause  is  very  small, 
and  it  acts  rather  by  breaking  the  coal  and  presenting  fresh  surfaces  for  the 
absorption  of  oxygen. 

Coal  Storage.— Prof.  Lewes  gives  the  following  recommendations  for  the 
storage  of  coal:  “ The  coal  store  should  be  well  roofed  in,  and  have  an  iron 
floor  bedded  in  cement;  all  supports  passing  through  and  in  contact  with 
the  coal  should  be  of  iron  or  brick;  if  hollow  iron  supports  are  used,  they 
should  be  cast  solid  with  cement.  The  coal  must  never  be  loaded  or  stored 
during  wet  weather,  and  the  depth  of  coal  in  the  store  should  not  exceed 
8 ft.,  and  should  only  be  6 ft.  where  possible.  Under  no  condition  must  a 
steam  or  exhaust  pipe  or  flue  be  allowed  in  or  near  any  wall  of  the  store, 
nor  must  the  store  be  within  20  ft.  of  any  boiler,  furnace,  or  bench  of  retorts. 
No  coal  should  be  stored  or  shipped  to  distant  ports  until  at  least  a month 
has  elapsed  since  it  was  brought  to  the  surface.  Every  care  should  be  taken 
during  loading  or  storing  to  prevent  breaking  or  crushing  of  the  coal,  and 
on  no  account  must  a large  accumulation  of  small  coal  be  allowed.  These 
precautions,  if  properly  carried  out,  would  amply  suffice  to  entirely  do 
away  with  spontaneous  ignition  in  stored  coal  on  land.” 

When  the  coal  pile  has  ignited,  the  best  way  to  extinguish  the  fire  is  to 
remove  the  coal,  spread  it  out,  and  then  use  water  on  the  burned  part.  The 
incandescent  portion  is  invariably  in  the  interior,  and  when  the  fire  has 
gained  any  headway  usually  forms  a crust  that  effectually  prevents  the 
water  from  acting  efficiently. 


MODIFICATIONS  OF  ROOM-AN D-PI LLAR  METHODS. 

Some  modifications  of  the  room-and-pillar  plan  shown  in  Fig.  1 can 
usually  be  applied  to  seams  whose  dip  does  not  exceed  3°.  When  the  pitch 
is  greater,  rooms  are  often  turned  off  toward  the  rise  only,  and  the  cross- 
entries driven  correspondingly  closer  together.  When  the  pitch  is  from 
5°  to  10°,  the  cars  may  still  be  taken  to  the  face  if  the  rooms  are  driven 
across  the  pitch,  thus  making  an  oblique  angle  with  an  entry  or  gangway, 
the  rooms  being  known  as  room  breasts. 

Buggy  Breasts.— For  inclinations  between  10°  and  18°,  that  is,  after  mule 
haulage  becomes  impossible  and  until  the  coal  will  slide  in  chutes,  buggies 
are  often  used.  Fig.  8 shows  a buggy  breast  in  plan  and  section.  Coal  is 
loaded  into  a small  car  or  buggy  c,  which  runs  to  the  lower  end  of  the  breast 
and  there  delivers  the  coal  upon  a platform  l , from  which  it  is  loaded  into 
the  mine  car.  The  refuse  from  the  seam  is  used  in  building  up  the  track, 
and  if  there  is  not  sufficient  refuse  for  this,  a timber  trestle  is  used. 

Another  form  of  buggy  breast  is  shown  in  Fig.  7.  Here  the  coal  is 
dumped  directly  into  the  mine  car  from  the  buggy.  If  the  breast  pitches 
less  than  6°,  the  buggy  can  be  pushed  to  the  face  by  hand,  but  in  rooms  of 
a greater  pitch,  a windlass  is  permanently  fastened  to  timbers  at  the  bottom 
of  the  breast,  while  the  pulleys  at  the  face  are  temporarily  attached  to  the 
props  by  chains,  so  that  they  can  be  advanced  as  the  face  advances.  The 
rope  used  is  from  £ in.  to  f in.  in  diameter,  and  any  form  of  ordinary 
horizontal  windlass  can  be  used.  With  the  windlass  properly  geared,  one 
man  can  easily  haul  a buggy  to  the  face  of  a breast  in  a few  minutes  time. 
The  buggy  runs  upon  20-lb.  T rails  spiked  with  2£"  X 1"  spikes  upon  2"  X 4" 


292 


METHODS  OF  WORKING . 


hemlock  studding  sawed  into  lengths  of  14  ft.  This  system  has  been 
thoroughly  tested  by  the  Delaware  & Hudson  Canal  Co.,  Scranton,  Pa., 
and  has  proved  a very  successful  and  economical  one.  _ _ 

Chute  Breasts.— Seams  pitching  more  than  15°  are  usually  worked  by 
chutes,  or  self-acting  inclines.  When  the  pitch  is  between  15°  and  30°,  sheet 
iron  is  laid  to  furnish  a good  sliding  surface  for  the  coal.  On  inclinations 
of  less  than  18°  to  20°,  it  is  usually  necessary  to  push  the  coal  down  the 
chute  Sheet  iron  is  not  required  on  pitches  above  30°.  It  must  be  remem- 
bered that  these  pitches  are  only  fair  averages,  as  much  depends  on  the 
character  of  the  coal.  Anthracite  slides  more  easily  than  bituminous.  _ To 
secure  the  best  returns  from  a coal  seam,  the  slope  or  shaft  should  be  driven 
to  the  basin,  and  the  lowest  gangways  or  levels  first  driven  to  the  property 
limits,  and  the  coal  then  worked  retreating  toward  the  slope  or  shaft. 
Practice  is,  however,  usually  contrary  to  this,  and  the  upper  levels  or  gang- 
wavs  are  turned  off  first,  and  working  places  opened  out  as  rapidly  as  the 
gangway  is  driven.  Fig.  9 shows  a method  of  grouping  rooms  that  may  be 


Fig.  7. 


used  where  the  pitch  is  from  8°  to  20°,  the  straight  heading  being  driven  on 
the  strike  and  the  other  headings  at  such  angles  as  will  give  a good  grade 
for  haulage  purposes. 

The  pillar-and-stall  system  is  a modification  of  the  room-and-pillar,  to 
which  it  is  similar  in  ali  respects  excepting  in  the  relative  size  of  the  pillars 
and  breasts.  The  stalls  are  usually  opened  narrow  and  widened  inside, 
according  to  conditions  of  roof,  floor,  coal,  depth,  etc.,  being  from  4 to  6 yd. 
in  the  single-stall  method,  with  the  pillars  about  the  same  width.  Fig.  10, 
A and  B , shows  single  and  double  stalls.  This  system  is  adapted  to  weak  roof 
and  floor,  or  strong  roof  and  soft  bottom,  to  a fragile  coal,  or  wherever 
ample  support  is  required,  and  is  particularly  useful  in  deep  seams  with 


CONNELLS  VILLE  METHOD . 


293 


great  roof  pressure.  Double  stalls  are  often  driven  from  12  to  15  yd.  wide, 
with  an  intervening  pillar  of  sometimes  30  yd.  A „ 

The  following  are  a few  of  the  applications  of  the  pillar-and-stall  method 
of  working  as  they  are  carried  out  in  some  of  the  leading  coal  fields  of 
America  i 

Connellsville  Region  (if.  L.  Auchmuty)  .—Fig.  11  shows  the  common  method 
used  in  the  Connellsville,  Pa.,  region.  The  average  dip  is  about  50.  The 
face  and  butt  headings  are  driven,  respectively,  at  right  angles  to  each 
other  on  the  face  and  the  butt  of  the  coal.  The  face  headings  leave 


the  main  butts  about  1,000  ft.  apart,  while  from  these  face  headings,  and 
400  ft.  apart,  secondary  butts  are  driven,  and  again  from  these  butts  on 

the  face  of  the  coal  the 
rooms  or  wide  work- 
ings are  excavated  to  a 
length  of  300  ft.,  this 
having  proved  the  most 
convenient  length  for 
economical  working. 
Koom  pillars  have  a 
thickness  of  30  to  40 
ft.,  while  the  rooms  are 
12  ft.  in  width  and  are 
spaced  42  to  52  ft. 
between  centers,  de- 
pending on  depth  o 
strata  over  the  coal. 
The  headings  are  8 ft. 
wide,  and  in  all  main 
butts  and  faces  the  dis- 
tance between  centers 
Fig.  9.  of  parallel  headings  is 

60  ft.,  leaving  a solid 

rib  of  52  ft.  A solid  rib  of  60  ft.  is  also  left  on  the  side  of  each  main 
heading.  The  average  thickness  of  cover  at  the  Leith  mine,  which 


294 


METHODS  OF  WORKING. 


is  here  described  and  which  may  be  considered  as  a type  of  the  region, 
is  250  ft.,  the  overlying  measures  being  alternated  layers  of  soft  shale 
’ & and  coal  for  4 ft.  The  bottom  is 

an  18"  layer  of  hard  fireclay 
and  slate.  These  floor  and  roof 
materials  are  soft,  and  are  easily 
disintegrated  by  air  and  water. 
At  some  mines,  cover  will  Teach 
as  much  as  700  ft.,  and  the  dip  of 
5 £ (as  at  Leith)  is  much  heavier 
at  some  points  on  eastern  out- 
crop, and  will  run  as  high  as  12<, 
flattening  off  as  the  synclinal  line 
of  the  basin  is  reached,  until  it  is 
almost  level.  In  some  localities, 
the  material  below  coal  is  hard 
limestone,  requiring  blasting  to 
remove  it,  and  at  other  places 
the  roof  slates  are  much  more 
solid  than  at  Leith,  and  not  read- 
ily disintegrated.  The  method 
of  drawing  ribs  is  one  of  the  beauties  of  the  system,  since  it  is i harder  to  do 
successfully  in  a soft  coal  like  the  Connellsville  coal  than  in  hard  coal.  The 


Fig.  10. 


Fig.  1L 


CLEARFIELD  METHOD. 


295 


coal  nself  is  firm.  When  necessary  to  protect  the  top  or  bottom,  4 to  6 in.  of 
coal  are  left  covering  the  soft  material. 

The  method  as  given  above  is  often  applied  to  a whole  series  of  butts 
(4  or  5)  at  once  instead  of  to  butt  by  butt,  as  shown  in  Fig.  11.  In  this  case, 
work  is  started  at  the  upper  end  of  the  uppermost  butt  and  progresses,  as 
shown  in  Fig.  11;  but,  after  cutting  across  the  butt  heading  from  which  the 
rooms  were  driven,  the  butt  heading  itself  and  the  upper  rooms  from  the 
second  butt,  or  that  just  before,  are  likewise  drawn  back  by  continuous 
slices  being  removed  from  the  rooms  of  the  upper  butt,  and  on  across  the 
next  lower  butt,  etc.,  all  on  an  angle  to  the  butts,  and  so  continued  as  the 
operations  progress,  until  another  butt  is  reached,  etc.,  thus  gradually 
making  a longer  and  longer  line  of  fracture,  which  is  only  limited  by  the 
number  of  butts  it  is  desired  to  include  at  one  time  in  the  section  thus 
mined.  This  works  very  nicely  and  makes  long  even  lines  of  fracture,  the 
steps  of  the  face  of  the  workings  (in  the  rib  drawing)  being  about  30  ft. 
ahead  of  one  another. 

Pittsburg  Region  {H.  L.  Auchmuty) .—The  coal  is  worked  in  much  the  same 
way  as  in  the  Connellsville  region,  except  that  a different  system  of  drawing 
ribs  is  used.  The  coal  is  worked  on  the  room-and-pillar  system,  with  double 
entries,  with  cut-throughs  between  for  air,  and  on  face  and  butt,  entries  are 
about  9 ft.  wide,  and  the  rooms  21  ft.  wide  and  about  250  ft.  long;  narrow  (or 
neck)  part  of  room,  21  ft.  long  by  9 ft.  wide;  room  pillars,  15  to  20  ft.  wide, 
depending  on  depth  of  strata  over  the  coal,  which  is  from  a few  feet  to 
several  hundred  feet.  The  mining  is  done  largely  by  machines  of  various 
types.  Coal  is  hard,  of  course,  and,  in  many  places,  the  roof  immediately 
over  the  coal  is  also  quite  hard.  There  are  about  4 ft.  of  alternate  layers  of 
hard  slate  and  coal  above  the  coal  seam.  Rooms  are  mined  from  lower  end 
of  butt  as  fast  as  butt  is  driven,  the  ribs  being  drawn  as  mining  progresses. 
As  the  coal  is  harder  than  in  the  Connellsville  region,  thickness  of  coal 
pillar  between  parallel  entries  is  somewhat  less. 

Clearfield  Region  ( G . F.  Duck).— The  butt  and  face  are  not  strongly  marked 
in  the  B or  Miller  seam,  the  one  chiefly  worked  in  this  region.  Where 
possible,  these  cleavages  are  followed  in  laying  out  the  workings,  but  the 
rule  is  to  drive  to  the  greatest  rise  or  dip  and  run  headings  at  right  angles  to 
the  right  and  left,  regardless  of  anything  else.  The  main  dip  or  rise  heading 
is  usually  driven  straight,  and  is  raised  out  of  swamps  or  cut  down  through 
rolls— very  common  here— unless  they  are  too  pronounced,  when  the  head- 
ing is  curved  around  them.  The  same  is  true  of  room  headings,  except  that 
they  are  more  usually  crooked,  not  being  graded  except  over  very  minor 
disturbances. 

As  the  B seam  rarely  runs  over  4 ft.  in  thickness,  and  is  worked  as  low  as 
2 ft.  8 in.  in  the  haulage  headings,  the  roof  is  taken  down  to  give  5 ft.  to 
5 ft.  2 in.  above  the  rail,  or  5 ft.  8 in.  to  5 ft.  10  in.  in  the  clear.  Where  the 
resulting  rock  is  taken  outside,  the  headings  are  driven  10  ft.  wide  with 

24  ft.  of  pillar,  roof  taken  down  in  haulage  heading  but  not  in  air-course. 
Where  the  rock  is  gobbed  underground,  the  haulage  heading  is  18  to  24  ft. 
wide,  air-course  10  ft.,  pillar  24  ft.,  and  roof  taken  down  in  haulage  heading 
only.  The  thinner  the  coal,  the  wider  the  heading.  It  is  more  economical 
to  haul  the  rock  to  daylight.  The  bottom  generally  consists  of  3 ft.  to  5 ft.  of 
hard  fireclay,  frequently  carrying  sulphur  balls. 

In  numerous  places,  the  sand  rock  is  immediately  over  the  coal,  but  in 
most  cases  there  is  from  3 to  5 ft.  of  slate  before  the  sand  rock  is  reached. 
Room  headings  are  driven  280  ft.  apart,  haul  rock  to  daylight,  heading  10  ft. 
wide  with  24  ft.  pillar  to  10  ft.  air-course,  in  which  roof  is  left  up.  A 15  ft.  to 

25  ft.  chain  pillar  is  left  between  air-course  and  faces  of  rooms  from  the  lower 
heading,  every  fourth  to  eighth  of  which  is  driven  through  to  the  air-course 
to  shorten  the  travel  of  the  air.  The  rooms  are  therefore  180  to  200  ft. 
long,  and  the  men  push  the  cars  to  the  face,  an  important  economical  item 
in  this  thin  coal. 

Rooms  are  21  ft.  wide  with  a 15  ft.  pillar,  and  a 15  ft.  chain  pillar  is  left 
between  the  first  room  on  any  room  heading  and  the  main  heading,  and 
roof  is  not  taken  down  in  rooms.  Main-heading  track  is  usually  30-lb.  iron, 
room  heading,  12  lb.,  and  2"  X *"  strap  iron  set  on  edge  is  used  in  the  rooms 
in  low  coal.  Mine  cars  hold  from  600  to  800  lb.  in  low  seams,  and  1,500  to 
2,000  lb.  in  the  so-called  thick  seams,  i.  e.,  3 ft.  8 in.  to  4 ft.  thick. 

Reynoldsville  Region.— The  measures  are  very  regular,  and  the  method 
employed  the  typical  one  shown  in  Fig.  1.  The  average  thickness  of  the 
principal  seam  is  6£  ft.  and  the  pitch  is  3°  to  4°.  The  coal  is  hard  and  firm, 

\ 


296 


METHODS  OF  WORKING. 


and  contains  no  gas;  the  cover  is  light,  and  on  top  of  the  coal  there  are 
3 or  4 ft  of  bony  coal;  the  bottom  is  fireclay.  Drift  openings  and  the  double- 
entry system  are  used.  Both  main  and  cross-entries  are  10  it.  wide,  with  a 
94-ft  pillar  between.  The  cross-entries  are  600  ft.  apart,  and  a 24  ft,  chain 
pillar  is  left  along  the  main  headings.  The  rooms  are  about  24  it.  wide 
and  open  inbye,  the  necks  being  9 ft.  wide  and  18  ft.  long.  The  pillars  are 

from  18  to  30  ft.  thick.  . 

West  Virginia  ( James  W.  Paul).—  The  general  plan  of  working  the  Pitts- 
burg coal  in  the  northern  part  of  West  Virginia  is  as  follows.  The  coal 
measures  vary  from  7 to  8 ft.  in  thickness,  and  have  a covering  varying 
from  50  to  500  ft.  The  coal  does  not  dip  at  any  place  over  5$.  In  most  places  the 
coal  is  practicallv  level,  or  has  just  sufficient  dip  to  afford  drainage.  The  usual 
method  of  exploitation  is  to  advance  two  parallel  headings,  30  ft.  apart  on  the 
face  of  the  coal.  At  intervals  of  500  to  600  ft.,  cross-headings  are  turned  to  right 
and  left,  and  from  these  headings  rooms  are  turned  off.  These  cross-headings 
are  driven  in  pairs  about  20  or  30  ft,  apart.  Between  the  main  headings  and 


the  first  room  is  left  a block  of  coal  about  100  ft.,  and  on  the  cross-headings 
there  is  often  left  a barrier  pillar  of  100  ft.  after  every  tenth  room. 

The  headings  are  driven  from  8 to  12  ft.  wide,  and  the  rooms  are  made 
24  ft.  wide  and  250  to  300  ft.  long.  A pillar  is  left  between  the  rooms 
about  15  to  20  ft.  wide.  These  pillars  are  withdrawn  as  soon  as  the  panel 
of  rooms  has  been  finished.  The  rooms  are  driven  in  from  the  entry  about 
10  ft.  wide  for  a distance  of  20  ft.,  and  then  the  room  is  increased  m width  on 
one  side.  The  track  usually  follows  near  the  rib  of  the  room.  Cross-cuts 
on  the  main  and  cross-headings  are  made  every  75  to  100  ft.,  and  m rooms 
about  every  100  ft.  for  ventilation.  . . . ~ ^ 

The  double-heading  svstem  of  mining  and  ventilation  is  m vogue.  Over- 
casts are  largelv  used,  but  a great  many  doors  are  used  in  some  of  the 
mines.  Rooms' are  worked  in  both  directions.  This  is  the  general 
practice  when  the  grades  are  slight.  When  the  coal  dips  over  1#,  the 
rooms  are  driven  in  one  direction  only.  In  this  case,  the  rooms  are 
made  longer,  as  much  as  350  ft.  It  is  the  custom  then  to  Break  about 
every  third  room  into  the  cross-heading  above  (a  practice  ill  advised). 
The  floor  of  this  bed  of  coal,  being  composed  of  shale  and  fireclay,  often 


ALABAMA  METHODS. 


297 


heaves,  especially  when  it  is  made  wet.  Some  trouble  is  at  times  experi- 
enced by  having  the  floor  heave  by  reason  of  the  pillars  being  too  small  for 
the  weight  they  support.  . . 

The  dimensions  of  rooms  and  pillars  given  are  for  a mine  (with 
covering  300  to  500  ft.  thick)  having  a fairly  good  and  strong  roof.  Where 
roof,  bottom,  and  thickness  of  cover  change,  these  dimensions  are  altered  to 
suit  the  requirements.  The  main-heading  pillars  may  be  reduced  to  30  or 
40  ft.;  the  rooms  may  he  made  15  ft.  wide  with  12  ft.  pillars,  and  no  harrier 
pillars  mav  be  left  on  the  cross-headings. 

The  foregoing  plan  is  very  much  followed  in  other  parts  of  the  State;  at 
least  an  attempt  is  made  to  do  so,  but  local  disturbances  often  require 
changes  in  the  plan.  This  plan  is  followed  on  some  parts  of  New  River, 
and  also  in  the  Flat  Top  field. 

Alabama  Methods  (J.  E.  Strong).— Fig.  12  shows  the  common  methods  used 
in  working  the  Alabama  coals.  The  seams  now  working  vary  from  2 to 
6 ft.  thick,  and  they  pitch  from  2°  to  40°.  Where  the  seams  are  thin,  the 
coal  is  hard,  and  pillars  of  about  20  to  30  ft.  are  used  to  support  the  roof. 


Fig.  13. 


The  thick  seams  are  soft  and  easily  broken,  and  much  larger  pillars  are  left. 
The  character  of  bottom  and  top  varies;  fireclay  bottom  and  slate  roof  are 
usually  found  with  the  thick  seams,  and  hard  bottom  and  sandstone  rqof 
with  the  thin,  seams.  The  general  plan  of  laying  out  the  mine  is  to  drive 
the  slope  straight  with  the  pitch  of  the  seam;  this  is  usually  on  the  butts  of 
the  coal.  A single-track  slope  is  8 ft.  wide,  and  a double-track  slope  16  ft. 
Cross-headings  are  driven  or  turned  from  the  slope  water  level  every 
300  ft.;  air-courses  are  driven  parallel  on  either  side  of  the  slope.  Where 
an  8 ft.  slope  is  driven,  30  ft.  of  pillar  are  left  between  the  slope  and  airway, 
and  for  a 16  ft.  slope,  30  ft.  of  pillar.  The  size  of  pillar,  however,  depends 
largely  on  the  character  of  the  roof  and  thickness  and  strength  of  coal.  On 
the  lower  side  of  the  headings,  pillars  from  20  to  60  ft.  are  left  on  the 
entry  before  turning  the  first  room.  The  rooms  are  worked  across  the  pitch 
on  an  angle  of  about  5°  on  the  rail,  Fig.  12,  A,  when  the  coal  does  not 
pitch  greater  than  20°;  where  the  pitch  is  greater,  chutes  are  worked  and 
the  rooms  are  driven  straight  up  the  pitch  (Fig.  12,  B).  In  a few  cases, 
where  the  pitch  is  not  greater  than  15°,  double  rooms  are  worked  with  two 
roadways  in  each  room  (Fig.  12,  C).  A rope  with  two  pulleys  is  used,  and 
each  track  keeps  the  rib  side  of  the  room,  the  loaded  car  pulling  up  the 
empty  on  the  opposite  side  of  the  room;  distance  between  room  centers, 
about  42  ft.  Where  single  rooms  are  worked,  the  room  is  driven  narrow 
(8  ft.  wide)  for  21  ft.,  when  connections  are  made  with  the  room  outside  of 
it;  the  room  is  then  widened  out  to  about  25  ft.,  sloping  gradually  until  this 
width  is  at  tained;  pillars  of  from  10  to  20  ft.  thick  are  left  between  the 
rooms,  and  cross-cuts  fdr  ventilation  are  made  about  every  50  ft.;  every  third 
or  fourth  room  is  driven  through  to  the  entry  above;  pillars  are  then  drawn 
back  to  the  entry  stumps  or  pillars.  The  average  cover  over  the  coal  now 
working  is  from  100  to  600  ft.  Air-courses  usually  have  an  area  of  30  ft., 
and  sufficient  coal  is  taken  out  to  give  this  area,  the  roof  and  bottom  being  left. 

George’s  Creek  District,  Md.— Fig.  13  shows  the  method  used  in  the  George’s 
Creek  field,  Maryland.  The  coal  shows  no  indication  of  cleats,  and  the 
butts  and  headings  can  be  driven  in  any  direction.  The  main  heading  is 
driven  to  secure  a light  grade  for  hauling  toward  the  mouth.  Cross- 
headings making  an  angle  of  35°  to  40°  are  usually  driven  directly  to  the 


298 


METHODS  OF  WORKING. 


rise,  and  of  the  dimensions  shown.  Pillars  are  drawn  as  soon  as  the  rooms 
are  completed,  being  attacked  on  the  ends  and  from  the  rooms  on  either 
side,  the  coal  being  shoveled  to  the  mine  car  on  a track  in  the  room.  Very- 
wide  pillars  are  split.  No  effort  is  made  to  hold  up  the  overlying  strata,  and 
the  entire  bed  is  removed  as  rapidly  as  possible.  An  extraction  of  85$  of  the 
bed  is  considered  good  work.  A section  of  the  seam  is  as  follows:  Roof 
coal,  10  in.;  coal,  7 ft.;  slate,  i in.;  coal,  10  in.;  slate,  1 in.;  coal,  10  in.;  fireclay; 
slate.  The  top  bench  is  bony  and  frequently  left  in  place  to  prevent 


disintegration  of  the  roof  by  the  air.  Above  this  coal  is  from  8 to  10  ft.  of 
“rashings,”  consisting  of  alternating  thin  beds  of  coal  and  shale,  that  is  very 
brittle,  and  requires  considerable  timber  to  keep  it  in  place.— (“  Mines  and 
Minerals,”  Vol.  19,  page  422.) 

Blossburg  Coal  Region,  Pa.— Coal  is  generally  mined  from  drifts,  but  in  a 
few  cases  by  slopes.  Fig.  14  shows  the  general  method  adopted;  the  breasts 
are  run  at  right  angles  to  the  slips;  the  breast  pillars  are  split  by  a center 
heading  and  taken  out  as  soon  as  the  breasts  are  finished.  The  gangway 
pillars  are  taken  out  retreating  from  the  crop  or  boundaries  of  the  property. 


Fig.  15. 

The  general  average  of  the  coal  seams  is  not  over  31  ft.,  accompanied  by 
fireclay  and  some  iron  ore.  The  dip  of  the  veins  is  about  3$. — (‘‘Mines  and 
Minerals,”  Vol.  19,  page  126.) 

Indiana  Coal  Mining.— Fig.  15  shows  the  double-entry  room-and-pillar 
method  as  used  in  Indiana.  The  entries  are  generally  6 ft.  high,  8 ft.  broad, 


IOWA  METHOD. 


299 


the  minimum  height  required  by  law  being  4 ft.  6 in.  The  rooms  are  from 
21  to  40  ft.  in  width.  The  mines  are  generally  shallow.  The  rooms  m Fig.  15 
are  shown  as  widened  on  both  ribs,  but  a more  usual  method  in  this  locality 
is  to  widen  the  room  on  the  inbye  rib,  leaving  one  straight  rib  for  the  protec- 
tion of  the  road  in  the  room.— (“  Mines  and  Minerals,”  Yol.  20,  page  202.) 

Iowa  Coal  Mining.— The  coal  lies  at  a depth  of  200  ft.  below  the  surface,  and 
is  geologically  similar  to  that  of  the  Missouri  and  Illinois  fields.  It  lies  in 
lenticular  basinsextending  northwest  and  southeast  and  outcropping  in  the 
larger  river  beds.  The  seams  are  practically  level,  non-gaseous,  and  gen- 
erally underlaid  by  fireclay  and  overlaid  by  a succession  of  shales,  sand- 
stones, and  limestones,  which  are  generally  of  a yielding  nature,  giving  a 
strong,  good  roof  for  mining.  There  are  three  distinct  seams,  the  lower  one, 
which  varies  from  4 to  7 ft.  in  thickness,  being  the  only  one  worked.  The 
coal  is  a hard,  brittle,  bituminous  coal  that  shoots  with  difficulty,  but  is 
excellent  for  steam  and  domestic  uses.  About  Centerville,  the  coal  has  a 
distinct  cleat,  but  elsewhere  in  the  State  this  is  lacking. 

The  entry  pillars  along  the  main  roads  are  6 to  8 yd.  thick,  for  the 
cross-entries  5 to  6 yd.,  and  for  the  rooms  3 to  5 yd.  Room  pillars  are 
drawn  in  when  approaching  a cross-cut.  Both  room-and-pillar  and  longwall 
methods  are  in  use,  with  modifications  of  each.  In  the  ro9m-and-pillar 
system,  the  double-entry  system  is  almost  invariably  used  in  the  larger 
mines.  Rooms  are  driven  off  each  entry  of  each  pair  of  cross-entries  at 
distances  of  30  to  40  ft.,  center  to  center;  the  rooms  are  8 to  10  yd.  m width, 
and  pillars  3 to  4 yd.  The  rooms  are  narrow  for  a distance  of  3 yd.,  and  then 
widened  inbye  at  an  angle  of  45°  to  their  full  width.  They  vary  from  50  to 
100  yd.  in  length,  and  the  road  is  carried  along  the  straight  rib. 

When  double  rooms  are  driven,  the  mouths  of  the  rooms  are  40  to  50  ft. 
apart,  and  they  are  driven  narrow  from  the  entry  a distance  of  4 or  5 yd. 


Fia  16. 


A cross-cut  is  then  made  connecting  them,  and  a breast  16  yd.  wide  is  driven 
up  50  to  60  yd.  The  pillar  between  each  pair  of  rooms  is  12  to  15  yd. 

In  pillar-and-stall  work,  the  stalls  are  usually  turned  off  narrow  and 
widened  inside,  the  pillar  varying  from  5 to  8 yd.  The  stalls  are  30  to  40  yd. 
in  length,  and  the  pillars  are  drawn  back.  When  the  stalls  are  driven  m 
pairs,  the  pillar  8 to  10  yd.  in  width  is  carried  between  them. 

Longwall. — The  main  haulage  road  runs  in  each  direction  from  the  foot  of 
the  shaft,  and  on  both  sides  of  this  diagonal  roads  are  turned  at  an  angle  of 
45°,  or  parallel  to  the  main  haulageway.  These  are  spaced  10  yd.  apart  and 
driven  50  to  60  yd.,  when  they  are  cut  off  by  another  diagonal  road.  Panel 
breasts  are  used  where  the  conditions  are  such  as  to  induce  a squeeze. 
Rooms  are  turned  narrow  off  entries  and  are  arranged  in  sets  of  6 to  12 
rooms,  with  a pillar  10  to  20  yd.  wide  between  the  sets  of  rooms.  When  the 
rooms  have  progressed  a short  distance  from  the  entry,  they  are  connected 
by  cross-cuts,  and  the  longwall  face  is  carried  forward  from  this  point. 
Packs  are  built  and  the  roof  allowed  to  settle,  as  in  longwall.  The  wide 
pillars  are  taken  out  after  the  roof  has  settled. 


300 


METHODS  OF  WORKING. 


Ventilation:— The  system  of  ventilating  the  workings  usually  employed  is 
that  of  conducting  the  air  to  the  inside  workings  by  means  of  an  air-course 
forming  the  back  entry  of  each  haulage  road.  From  this  point  it  is  carried 
along  the  face  of  the  rooms,  through  the  breakthroughs  or  cross-cuts  in  the 
room  pillars,  returning  thence  to  the  haulage  road,  which  is  usually  made 
the  return  airway.  When,  however,  the  mine  is  ventilated  by  means  of  a 
furnace  or  an  exhaust  fan,  the  intake  airway  is  usually  made  the  haulage 
road,  in  order  to  avoid  doors  at  the  shaft  bottom. 

The  Tesla,  California,  method  is  shown  in  Fig.  16.  The  coal  seam  averages 
7 ft,  of  clear  coal,  and  pitches  60°.  This  system  was  adopted  m a portion  of 
the  mine  to  get  coal  rapidly:  for,  at  this  point,  a short-grained,  slate  cap 
rock  came  in  over  the  coal,  making  it  difficult  to  keep  props  in  place.  The 
floor  is  a close  blue  slate  and  has  a decided  heaving  tendency.  The  roof  is 
an  excellent  sandstone.  There  is  a small  but  troublesome  amount  of  gas. 
Two  double  chutes  are  driven  up  the  pitch  at  a distance  of  36  ft.  apart,  con- 
nected every  40  ft.  by  cross-cuts.  One  side  of  each  chute  is  used  for  a coal 
chute  and  the  other  for  a manway  and  air-course.  At  a distance  of  12  yd. 
apart  small  gangways  are  driven  parallel  with  the  main  mine  gangways. 
These  are  continued  from  each  chute  a distance  of  300  ft.,  if  the  conditions 
warrant  it.  The  top  line  is  then  attacked  from  the  back  end  and  the  coal  is 
worked  on  the  cleavage  planes;  the  breast,  or  room,  therefore  consists  of 
a 12-yd.  face,  including  the  drift  or  gangway  through  which  the  coal  is 
carried  to  the  chutes;  a rib  of  coal  (2  or  3 ft.)  is  left  between  the  breasts  to 
keep  the  rock  from  falling  on  the  breast  below.  Thus  in  each  breast  the 


Fig.  17. 


miners  have  a working  face  of  about  15  or  16  yd.,  and  as  the  coal  is  directed 
to  the  car  by  a light  chute,  moved  along  as  the  face  advances,  the  coal  is 
delivered  into  the  cars  at  small  cost,  and  but  little  loss  results  from  the 
falling  coal,  as  a minimum  of  handling  is  thus  obtained.  Immediately 
above  each  gangway,  and  starting  from  these  main  chutes,  an  angle  chute  is 
driven  at  about  45°,  connecting  with  the  breast  gangway  above  it,  and  into 
these  chutes  the  coal  from  that  breast  is  delivered,  runs  into  the  mam  chute, 
and  from  it  is  loaded  into  the  mine  cars  in  the  main  gangway.  These  angle 
chutes  serve  as  a means  of  keeping  the  main  chute  full,  and  at  the  same 
time  giving  each  breast  an  opportunity  to  send  out  coal  continuously. 
Thev  also  serve  the  purposes  primarily  intended,  of  saving  the  coal  from 
breakage,  by  giving  it  a more  gradual  descent  into  the  full  chute,  me 
breast  gangways  are  driven  5 ft.  wide.  No  timbers  are  needed  in  these 
gangways,  as  they  are  driven  iu  the  coal,  except  ou  the  foot-waU  or  floor 


TESLA  METHOD. 


301 


side,  which,  as  before  stated,  is  a firm  sandstone.  It  is  found  safest  to  leave  a 
rib  of  coal  on  the  top  of  the  breast  2 or  3 ft.  thick,  until  the  working-  face  has 
passed  on  12  or  15  ft.,  when  this  rib  is  cut  out  and  thus  all  the  coal  extracted, 
the  roof  caving  behind  and  filling  in  the  opening.  As  cross-cuts  are  driven 
every  36  ft.,  ventilation  is  kept  along  the  working  faces,  and  a safe  and 
effectual  means  of  securing  all  the  coal  in  the  seam  is  thus  attained. 

Fig.  17  shows  another  system  used  in  No.  7 vein  at  the  same  place.  The 
seam  averages  7 ft.  of  coal.  The  roof  is  shelly  and  breaks  quickly,  hence 
the  coal  must  be  mined  rapidly. 

In  this  system  the  gangway  chutes  are  driven  at  right  angles  with  the 
strike  of  the  seam,  40  ft.  up  the  pitch;  a cross-cut  5 ft.  X 6 ft.  is  then  driven 


Fig.  18. 

parallel  with  the  gangway.  From  this  cross-cut,  chutes  are  driven  at  same 
distance  apart  as  the  gangway  chutes  (30  ft.),  at  an  angle  of  35°,  and  cross- 
cuts are  driven  every  40  ft.  between  chutes,  for  ventilation.  After  a panel 
of  five  or  more  chutes  is  driven  up  the  required  distance,  work  is  com- 
menced on  the  upper  outside  pillar  and  the  pillars  on  that  line  are  drawn 
and  the  next  line  is  attacked,  and  this  is  continued  until  the  panel  or  block 
is  worked  down  to  the  cross-cut  over  the  gangway.  About  every  80  ft.  in 
this  level  it  is  found  advantageous  to  build  a row  of  cogs  parallel  with  the 
strike  of  the  seam  as  the  pillars  are  drawn.  This  serves  to  save  the  crushing 
of  the  pillars,  and  prevents  any  accidents  from  falls  of  rock.  But  few 
timbers  are  required  by  this  system.— (“Mines  and  Minerals, ” Yol.  19, 
page  145.) 


302 


METHODS  OF  WORKING. 


New  Castle  Colorado,  Method.— The  following  method  as  described  by  Mr. 
R M Hosea  * Chief  Engineer  of  the  Colorado  Fuel  and  Iron  Co.,  is  used 
at  New  Castle  Colo  for  highly  inclined  bituminous  seams.  The  coals  mined 
are  only  feirly  hard,  contain  considerable  gas,  and  make  much  waste  in 
mining  Fig-  18  shows  the  method  used  for  extracting  the  Wheeler  or 
thicker*  veinto  its  ful  1 width  of  45  ft.,  and  the  E seam  18  ft.  thick,  excepting 
that  left  for  pillars.  Rooms  and  pillars  are  laid  out  under  each  other  m 
the  two  seams  whenever  practicable.  Entries  are  along  the  foot-wall,  30  it. 
un  the  pitch  is  an  air-course.  Rooms  and  breasts  are  laid  out  as  shown 
in  B and  C Fig.  18.  In  the  Wheeler  vein,  the  manways  go  through  the 
entrv  pillars  to  the  air-course  and  thence  along  the  ribs  each  side  of 
the  room  one  manway  to  the  main  entry  serving  for  two  double  rooms.  A 
lower  bench  of  6 ft.  is  first  mined  the  full  length  of  the  rooms,  120  ft.,  side 
man  wavs  being  protected  by  vertical  or  leaning  props,  bordered  with  3 
planks  outside  and  the  chute  or  battery  is  then  put  in.  At  the  top  the  rooms 
arrconnected  by  cross-cuts,  and,  occasionally,  intermediate  cross-cuts  are 
reauired  The  room  is  kept  full  of  loose  coal,  only  sufficient  being  drawn  to 
keen  the’ working  floor  at  the  proper  height  for  the  mining.  When  driven 
to  the  limit  and^ with  cross-cuts  connected,  the  coal  is  all  dra\vn  out  at 
the  chutes  which  have  receptacles  for  rock  and  waste  at  their  sides,  to  be 
picked  out  by  the  loaders.  The  next  operation  is  to  dnve  across  the  seam  at 


Fig.  19. 


the  air-course  until  the  hanging  wall  is  reached,  manways,  called  back  wan- 
t 4“  be°ng  mrnteined  as  before.  A triangular  section  of  coal  is  mined  off, 
as  shown  in  A,  Fig.  18,  and  the  room  filled  with  loose  coal.  The  full  thick 
ness  of  the  seam  is  now  taken  off*,  shots  being  first  placed  at  S S,  coa| 
drawn  out  at  the  bottom  as  required.  Section  D,  Fig.  18,  shows  a method  of 
robbing  a pillar.  In  doing  this,  the  manways  are  moved  back  into  the 
uillar  each  side  10  ft.  or  so,  by  mining  on  the  lower  bench  as  before,  and 
E0ies  are  drilled  into  the  roof  with  long  drills,  which  bring  down  as  much  of 
^eo^erhanging1^^  as  can  be  reached.-(“ Mines  and  Minerals,1  Yol.  17, 

page  377.)  

MODIFICATIONS  OF  LONGWALL  METHOD. 

Fig  19  shows  a good  arrangement  of  the  main  and  temporary  haulage- 
wavs  in  a fiat  seam  The  chief  object  in  any  plan  of  longwall  workings  is  to 
w!  the  permanent  roadways  the  arteries  of  the  system,  providing  the  most 
toect  route^rom11  aU°  sections  of  the  mine  to  the  shaft.  The  temporary 


LONG  WALL  METHOD . 


303 


roads  or  working  places  are  only  maintained  for  a distance  of  60  to  100  yd., 
until  cut  off  by  subroads  branching  at  regular  intervals  from  the  main 
roads.  In  the  figure,  full  heavy  lines  indicate  the  permanent  haulageways, 

except  only  the  main 
intake  airway  (12  ft. 
wide),  running  west 
from  the  downcast  shaft 
D , and  the  main  return 
air-course  (12  ft.  wide) 
leading  from  the  face  on 
the  east  side  to  the  man- 
way around  the  upcast  U, 
which  is  the  hoisting- 
shaft.  The  full  light 
lines  indicate  the  diag- 
onal subroads,  driven  to 
cut  off  the  working 

S laces,  shown  by  the 
otted  lines.  The  stables 
are  located  as  shown  in 
the  shaft  pillar,  between 
the  two  shafts,  where 
they  will  not  contami- 
nate the  air  going  into 
the  mine,  but  will  receive 
air  fresh  from  the  down- 
cast and  discharge  it  at 
once  into  the  upcast  cur- 
rent. This  position  also 
affords  ready  access  from 
either  shaft  in  case  of 
accident,  and  for  the 
handling  of  feed  and 
refuse.  The  pumps  may 
be  located  in  any  con- 
venient position  at  the 
foot  of  the  upcast.  The 
shaft  bottoms  are  driven 
14  ft.  wide  nearly  through 
the  shaft  pillar,  and  are 


rA  __ 


[Three', ! Sp/iff''  '• 

L1/7& 

Fig.  20. 


Wor/rec/.  Oaf 

MB 


continued  10  ft.  wide  north 
and  south  through  the  gob. 
The  width  of  all  other  roads 
and  subroads  is  made  8 ft.  The 
Fig.  21.  extra  width  of  the  straight 
road  through  the  hoisting  shaft 
is  to  provide  for  the  future  need,  when  the 
size  of  the  workings  will  demand  that  the 
mine  be  ventilated  in  four  sections  or  splits;  and  these  two  roads  will  then 
each  form  the  return  of  two  sections.  This  will  be  accomplished  by  over- 
casting the  main  road  forming  the  shaft  bottom,  and  carrying  half  the  cur- 
rent by  this  means  to  the  east  face,  where  it  is  again  divided.  The  same 
thing  is  done  on  the  west  side.  The  divided  currents,  after  traversing  the 
faces  of  their  own  respective  sections,  unite  and  return  to  the  hoisting  shaft 
by  the  main  haulage  road. 

When  the  roof  is  very  solid,  the  gob  roads  turn  off  the  entries  at  45°,  and 


304 


METHODS  OF  WORKING. 


maybe  a considerable  distance  apart,  so  that  the  tracks  can  be  turned  in 
along  the  working  face  and  the  mine  cars  loaded  at  the  face.  Whenthe 
roof  is  tender,  making  it  impossible  to  maintain  sufficient  room  for  the  mine 
cars  to  pass  along  the  face,  gob  roads  are  turned  off  near  together,  and  the 
mine  cars  run  to  the  road  heads,  to  which  points  the  coal  is  shoveled  or 
hauled  in  buckets.  When  the  working  face  has  reached  such  a distance 
from  the  bottom  of  the  shaft  that  it  becomes  impossible  to  work  rapidly 
enough  to  avoid  the  destructive  weighting  action  of  the  roof,  the  mining 
must  be  divided  into  panels  or  sections,  the  working  face  of  each  of  which 
can  be  advanced  at  the  proper  rate.  . . . ,,  , 

Figs  20  and  21  show  a plan  and  section,  respectively,  of  two  methods 
largely*  used  in  Europe  for  working  thick  pitching,  contiguous  seams  of 
hard  long-grained  coal.  From  the  foot  of  the  shafts,  levels  are  driven  on 
the  strike,  and  jig  roads  turned  off  these  in  the  top  seam  at  right  angles 
up  the  pitch.  The  working  faces  are  advanced  in  the  same  horizontal 
plane,  the  lower  one  being  always  ahead.  The  coal  from  the  two  lower 
seams  is  run  through  horizontal  passages  to  the  upper  seam,  where  it  is 
lowered  to  the  levels  below  by  means  of  jigs  or  gravity  planes  The  slates 
between  the  seams  and  the  refuse  obtained  in  mining  are  used  to  fill  m as 
the  faces  advance.  This  gobbing  must  be  done  quite  thoroughly,  m order  to 
prevent  excessive  settling  of  the  roof  and  consequent  crushing  of  the  coal  at 
the  faces.  Where  spontaneous  combustion  is  liable  to  occur,  it  is  not 
advisable  to  use  this  method,  but  rather  that  shown  in  the  lower  portion  of 
the  figures.  Slopes,  or  inclined  planes,  are  driven  down  the  pitch  from  the 
levels  to  the  basin,  or,  if  possible,  to  the  boundary  line,  where  the  working 
faces  are  formed  by  driving  levels  to  the  right  and  left  of  the  ends  of  the 
slopes.  The  working  faces  are  here  also  kept  in  a horizontal  plane  with 
the  lower  one  farthest  up  the  pitch.  The  coal  from  the  two  upper  seams  is 
taken  through  tunnels  or  flats  to  the  slopes  in  the  lower  seam,  and  hoisted  to 
the  shaft  bottom.  Here  all  the  inclined  planes  or  other  passages  are  mthe 
solid  coal,  and  the  worked-out  places  are  left  behind.  A very  small  amount 
of  coal  is  left  in  the  mine  when  worked  from  the  basin  upwards,  and  the 
effects  of  squeezes  are  not  felt  to  any  great  extent,  as  the  weight  of  the  roof 
is  thrown  on  the  gob.  Where  there  is  not  sufficient  refuse  material  to  fill  in 
with,  it  is  taken  into  the  mine  from  the  surface,  or  from  another  adjacent 
mine  having  an  extra  amount  of  stowing  material.  . _ 

It  is  not  necessary  that  the  slopes  be  sunk  to  the  boundary  line,  m which 
case  the  main-slope  pillars  should  be  large  and  left  in  so  that  the  dip 
workings , as  they  are  called,  can  be  continued  downwards  when  desired. 
In  this  way,  the  first  cost  of  opening  up  is  greatly  reduced.  The  ventila- 
tion of  these  workings  is  quite  simple,  the  intake  being  split  at  the  ends  of  the 
main  entries,  or  slopes,  and  the  air  forced  along  the  different  working  faces 
to  the  right  and  left,  and  thence  to  the  upcast  by  way  of  the  main-return 
airways.  If  at  all  possible,  it  is  advisable  to  provide  an  outlet  near  the 
faces  of  the  rise  workings  that  are  advancing  upwards,  because  the  lighter 
gases  cannot  be  forced  down-hill  with  satisfaction  unless  an  excessive 
velocity  of  the  air-current  be  maintained.  These  systems  are  well  adapted 
to  deep  or  shallow  mines,  and  to  give  maximum  outputs  for  minimum 
development,  provided  the  work  is  carried  on  quickly  and  steadily. 

Overhand-Stoping  Method.— Where  several  thick  and  heavily  pitching 
seams,  in  which  considerable  firedamp  is  given  off  and  the  roof  falls 
freely,  are  to  be  worked,  a shaft  is  sometimes  sunk  m the  adjacent  strata, 
and  at  certain  distances  horizontal  tunnels  are  driven  to  the  coal  seams. 
From  these  tunnels,  levels  or  haulage  roads  are  driven  m each  seam  to 
the  right  and  left,  provided  the  seams  are  not  so  close  together  as  to  make 
it  more  profitable  to  use  rock  chutes  or  tunnels,  through  which  the  coal 
is  run  from  one  seam  into  the  other.  At  certain  intervals,  depending  on  the 
length  of  the  lifts  horizontally,  pairs  of  headings,  usually  called  dtps,  are 
driven  up  the  pitch  until  they  intersect  the  levels  and  tunnels  above. 
Headings  are  turned  off  these  dips  to  the  right  and  left,  parallel  to  the  mam 
levels  or  haulage  roads,  and  when  they  meet  or  have  reached  their  limit 
horizontally  they  are  holed,  or  cut  through,  by  cross-cuts  driven  on  the 
pitch.  The  working  faces  thus  formed  are  then  carried  back,  as  shown  in 
Fig.  22.  Skips  are  taken  off  the  face  and  the  roof  allowed  to  cave  in  after 
each  operation  and  fill  up  the  gob  behind.  The  order  of  working  is  such 
that  the  top  faces  are  worked  in  advance  of  the  lower  ones.  The  cars, 
which  are  taken  to  the  working  faces,  are  handled  in  the  dips  by  balance 
carriages,  or  back  balances , as  they  are  termed  in  some  localities,.  I he 


ANTHRACITE  MINING. 


305 


barney,  or  balance,  runs  on  a narrow  track  in  the  middle  of  the  track  for  the 
carriage  on  which  the  car  is  placed.  The  barney  will  raise  the  carnage  with 
the  empty  car  on  it,  and  the  carriage  and  loaded  car  will  hoist  the  barnew 
These  gravity  planes  are  only  made  one-half  the  length  of  the  dips,  or  about 
150  ft.,  in  order  that  greater  safety  may  be  secured  and  shorter  ropes  used. 
One  is  placed  in  the  lower  half  of  one  of  the  pairs  of  dip  headings,  and 
another  in  the  upper  half  of  the  other,  thus  necessitating  that  the  cars  be 
changed  from  one  gravity  plane  to  the  other  midway  along  the  dips.  This 
is  done  by  taking  the  car  off  one  carriage  and  pushing  it  through  a break- 
through or  cross-cut  to  the  other.  Fig.  22  shows  the  method  of  working  these 
lifts  in  some  parts  of  England  and  Belgium  where  the  seams  are  gaseous,  and 
some  of  them  quite  thick.  The  face  is  stepped  more  or  less  deeply,  depend- 
ing on  the  pitch,  in  order  to  protect  ea,ch  miner  from  the  falling  coal  of  his 
neighbor.  The  men  reach  the  higher  portion  of  the  working  face  through 
timbered  manways.  The  coal  is  generally  run  down  chutes  to  the  cars 
below,  but  in  some  places  it  is  run  to  the  end  of  the  gangway  below  by 
means  of  inclined  chutes,  or  spouts,  laid  on  the  gob.  The  essential  feature 
for  the  successful  operation  of  this  system  is  the  close  and  careful  stowing  of 
the  gob  between  walls.  In  Belgium,  cord  wood  and  brush  wood  are  very 
largely  used  for  gobbing  material  or  stowing  between  the  regular  timbers. 
All  the  coal,  except  very  thin  vertical  pillars,  is  taken  out.  Where  there  is 


Fig.  22. 


much  firedamp,  the  miners  simply  nick  the  coal  and  leave  it  stand  over 
night  during  which  time  the  gas  either  forces  it  off  the  solid  or  so  loosensit 
that  the  miner  can  easily  take  it  off  with  a pick.  (See  also  Highly  Incline 
Mineral  Deposits.)  , 

METHODS  OF  MINING  ANTHRACITE. 

A perfectly  flat  seam  of  anthracite  is  seldom  found  in  America,  and  even 
where  a portion  of  the  seam  maybe  found  lying  comparati^ 
sudden  changes  in  dip  must  be  expected  that  a system  adapted  to  working 
on  a pitch  is  almost  universally  used.  A breast  may  start  on  a How _ pitch  au d 
the  pitch  may  increase  gradually  until  it  beeves  vertical,  or  Pj? 
may  be  the  case.  The  cleat  is  usually  lacking  m anthracite  and  the  direc- 
tion  of  driving  the  breasts  is  determined  largely  by  the  pitch  and  by  haulage 

COIFor^hches  up  to  30°,  the  methods  shown  in  Figs.  1,7, 8, 9, 10, 12,  and  13  are, 
in  general,  applicable,  with  certain  changes  due  to  local  considerations. 
There  is  considerable  difference  in  the  methods  of  opening  rooms  m anthra- 
cite and  bituminous  mines,  owing  to  variations  in  thecharac^ 
coals  and  to  the  fact  that  anthracite  will  slide  on  chutes  of  1^so1^1"^tla°T5 
than  bituminous  coal.  Where  the  pitch  does  not  exceed  4Jthewoingm 
turned  off  at  right  angles  to  the  gangway.  In  moderately  thick . & oal  i seams, 
pitching  between  4°  and  18°,  the  rooms  are  generally  driven 
forming  room  breasts,  thus  securing  a grade  that  permits  the  haulage  of  the 
cars  to  the  face. 


306 


METHODS  OF  WORKING. 


There  are  two  methods  of  mining  thick  coal  in  breasts  when  nearly  flat. 
(1)  The  breasts  are  opened  out  and  driven  to  the  limit  in  the  lower  bench  of 
coal,  and  the  top  benches  are  blown  down  afterwards,  beginning  at  the  face 
and  working  back.  (2)  When  the  roof  is  good  and  there  is  no  danger  of  its 
falling  and  closing  up  the  workings,  the  upper  benches  may  be  worked  in 
the  opposite  direction,  beginning  at  the  gangway  and  driving  towards  the 
limit  of  the  lift,  or  the  working  of  the  upper  bench  may  follow  up  that  of  the 
lower  bench.  When  the  seam  is  less  than  12  ft.,  the  top  is  supported  by 
props;  in  thicker  seams,  the  expense  is  so  great  for  propping  that  but  little 
attempt  is  made  to  support  the  roof.  In  the  thicker  anthracite  seams 
(notably  the  Mammoth),  the  coal  in  the  breasts  is  so  worked  as  to  make  an 
arch  of  the  upper  benches  of  coal,  which  acts  as  a temporary  support  for  the 
roof,  the  coal  in  the  arch  being  extracted  when  the  pillars  are  robbed. 

When  the  inclination  of  anthracite  seams  is  less  than  30°,  the  breasts  may 
be  opened  with  one  chute  in  the  center,  which  ends  in  a platform  projecting 
into  the  gangway,  off  which  the  coal  can  be  readily  loaded  into  the  mine 
car.  When  this  method  is  employed,  the  refuse  is  thrown  to  either  side  of 
the  chute.  If  the  pillars  are  to  be  robbed  by  skipping  or  slabbing  one  rib 
only,  it  is  well  to  keep  most  of  the  refuse  on  one  side.  Sometimes,  when  the 
top  is  good,  and  the  breasts  are  driven  wide,  two  chutes  are  used,  but  the 
cost  of  making  the  second  chute  is  considerable  and  is  therefore  not 
advisable  unless  necessitated  by  the  method  of  ventilation  employed. 

Col.  Brown’s  Method.— Fig.  23  shows  a panel  system  devised  by  Col.  D.  P. 
Brown,  of  Lost  Creek,  Pa.,  wiiich  gives  good  results  in  thick  seams  pitching 
from  15°  to  45°,  where  the  top  is  brittle,  the  coal  free,  and  the  mine  gaseous. 
Rooms  or  breasts  are  turned  off  the  gangway  in  pairs,  at  intervals  of  about 


* Fig.  23. 

60  yd.  The  breasts  are  about  8 yd.  wide,  and  the  pillar  between  about  5 yd. 
wide,  which  is  drawn  back  as  soon  as  the  breasts  reach  the  airway  near  the 
level  above.  In  the  middle  of  each  large  pillar  between  the  several  pairs  ot 
breasts,  chutes  about  4 yd.  wide  are  driven  from  the  gangway  up  to  the 
airway  above.  These  are  provided  with  a traveling  way  on  one  side,  giving 
the  miners  free  access  to  the  workings.  Small  Headings  are  driven  in  the 
bottom  bench  of  coal,  at  right  angles  to  these  chutes,  and  about  10  or  20  yd. 
apart.  These  headings  are  continued  on  either  side  of  the  chutes  until  they 
intersect  the  breasts.  When  the  chute  and  headings  are  finished,  the  work 
of  getting  the  coal  in  the  panel  is  begun  by  going  to  the  end  of  the  upper- 
most heading  and  widening  it  out  on  the  rise  side  until  the  airway  above  is 
reached  and  a working  face  oblique  to  the  heading  is  formed.  This  face  is 
then  drawn  back  to  the  chute  in  the  middle  of  the  panel.  After  the  work- 
ing face  in  the  uppermost  section  has  been  drawn  back  some  10  or  12  yd., 
work  in  the  next  section  below  is  begun,  and  so  on  down  to  the  gangway, 
working  the  various  sections  in  the  descending  order.  Both  sides  of  the 
pillar  are  worked  similarly  and  at  the  same  time  toward  the  chute. 

Small  cars,  or  buggies,  are  used  to  convey  the  coal  from  the  working  faces 
along  the  headings  to  the  chute,  where  it  is  run  down  to  the  gangway  below 
and  loaded  into  the  regular  mine  cars.  This  system  affords  a great  degree  of 
safety  to  the  workmen,  because  whenever  any  signs  of  a fall  of  roof  or  coal 
occur,  the  men  can  reach  the  heading  in  a very  few  seconds  and  be 
perfectly  safe.  A great  deal  of  narrow  work  must  be  done  before  any  great 


anthracite  mining. 


307 


Quantity  of  coal  can  be  produced.  The  breasts  are  driven  in  pairs  and  at 
intervals,  to  get  a fair  quantity  of  coal  while  the  narrow  work  is  being  done, 
and  they  are  not  an  essential  part  of  th,e  system  It  is  claimed  that  the 
facility  and  cheapness  with  which  the  coal  can  be  mined,  ^ 

cleaned  in  the  mine  more  than  counterbalance  the  extra  expense  for  the 

nalB a tte ry°Work i n g.  — Fig.  24  shows  a method  of  opening  a breast  by  two 
chutes  c/c,  when  there  is  a great  amount  of  refuse,  or  when  a great  amount 


Fig.  24. 


25. 

are 


of  £?as  is  given  off.  The  chutes  are  extended  up  along  the  rib  to  mthm 
fewfeet  If  the  working  face,  either  by  planking  carried  ^upright  posts,  or 
by  building  a jugular  manway,  as  shown  inthe  sections  (a)  and  (5),  Fig. 
These  chutes,  built  of  jugulars  or  inclined  props  and  faced  by  2 plank, 
made  as  nearly  air-tight  as  possible,  to 
carry  the  air  from  the  heading  a to  the 
working  face.  Fig.  24  shows  a breast 
on  a pitch  too  steep  to  enable  the  miner  to 
keep  up  to  the  face.  In  seams  of  less  than 
35°  the  platform  / shown  near  the  face  ot 
the  breast  is  unnecessary,  and  in  seams 
thicker  than  12  ft.  it  cannot  be  built; 
hence,  this  method  of  working  is  applica- 
ble (1)  to  beds  pitching  more  than  35°, 
and  (2)  to  thin  seams. 

The  coal  is  separated  from  the  refuse 
on  the  platform  /,  and  is  run  down  the 
manway  chutes  and  loaded  into  the  cars 
from  a platform  projecting  into  the  gang- 
way g.  The  refuse  is  thrown  in  the  middle 
of  the  breast  behind  the  platform.  A cer- 
tain amount  of  coal  is  kept  on  the  plat- 
form to  deaden  the  blow  from  the  falling 
coal.  The  chutes  are  timbered  when  the 
character  of  the  coal  requires  it.  This 
plan  can  also  be  employed  in  thick  seams 

refuse’ tcf fin\  InT center^/ the  breast  so  that  the  miner  can  work  without  the 

PlaFig.I25  (a)  is  a section  through  p,p  when  jugulars  a,  a areusedtoform  the 
manways  b,  b along  the  sides  of  the  breast;  and  (5)  is  a section  through  the 


308 


METHODS  OF  WORKING. 


same  line  when  upright  posts  a,  a are  used  to  support  the  plank  in  forming 
the  manways  b,  b.  The  refuse  in  these  eases  only  partially  fills  the  gob. 

In  working  very  thick  seams  op  heavy  dips,  where  there  is  not  enough 
refuse  to  fill  the  middle  of  the  breast,  the  miner  has  nothing  to  stand  on,  the 


l 


Plan  along  ts.  Fig.  27.  Section  on  pq. 

platform  being  impracticable;  therefore,  it  is  necessary  to  leave  the  loose 
coal  in  the  breast.  Loose  coal  occupies  from  50 $ to  90$  more  space  than  coal 
in  the  solid.  This  surplus  is  drawn  out  through  a central  chute.  If  the  roof 


ANTHRACITE  MINING. 


309 


is  poor,  the  movement  of  the  coal  will  not  in  this  way  cause  it  to  fall  ano 
mix  with  the  coal;  and  if  the  floor  is  soft,  the  jugulars,  which  are  stepped 
into  the  floor,  are  not  so  liable  to  be  unseated,  closing  the  manway  and 
blocking  the  ventilation.  The  surplus  is  sometimes  sent  down  the  manways, 
leaving  the  loose  coal  in  the  center  of  the  breast  undisturbed,  until  the  limit 
is  reached. 

Single-Chute  Battery.— To  prevent  the  coal  from  running  out  through  the 
chutes,  the  opening  into  the  breast  is  closed  by  a battery  constructed  by 
laying  heavy  logs  across  the  openings,  as  shown  at  b,  Fig.  26,  or  else  built  on 
props,  as  shown  at  b , Fig.  27;  a hole  is  left  in  the  center,  or  at  one  side  of  the 
battery,  through  which  the  coal  may  be  drawn.  The  battery  closes  all  the 
openings  into  the  breast,  except  the  space  occupied  by  the  jugular  manways, 
and  is  made  air-tight,  or  as  nearly  so  as  possible,  by  a covering  of  plank. 

Fig.  26  is  a plan  and  section  of  a breast  opened  up  by  a single  chute.  The 
plan  A is  taken  on  the  line  m n shown  on  the  section  B , which  section  is 
taken  on  the  line / 1 shown  on  the  plan  A.  The  pitch  is  great  and  the  seam 
is  so  thick  that  the  breast  must  be  kept  full  of  loose  coal  for  the  men  to  work 
upon,  the  surplus  being  drawn  off  at  the  battery  b and  run  into  the  car 
standing  on  the  gangway  g through  the  chute  c.  A manway  w is  made 
along  each  side  of  the  breast,  for 
the  purpose  of  ventilation  and 
affording  a passage  for  the  men 
to  reach  the  working  face.  The 
heading  a is  used  for  an  air- 
course  between  breasts.  The 
main  airway  h is  driven  over 
the  gangway  g , where  it  will  be 
well  protected. 

By  drawing  the  surplus  coal 
through  a central  chute,-  the 
manways  are  not  injured  so 
much  as  when  it  is  drawn  off 
through  side  chutes,  as  the  coal 
will  move  principally  along  the 
middle  of  the  breast.  When  the 
breast  is  worked  up  to  its  limit, 
all  the  loose  coal  is  run  out  of 
the  breast  and  the  drawing  back 
of  the  pillars  is  commenced, 
unless  for  some  purpose  they 
are  allowed  to  stand  for  a time. 

Double-Chute  Battery.— Fig.  27 
shows  a plan  and  section  of 
double-chute  breasts  used  in 
very  thick  seams  having  a heavy 
dip.  The  breasts  are  entered  by 
two  main  coal  chutes  c,  c,  each 
of  which  is  provided  with  a battery  6,  through  which  the  coal  is  drawn. 
A manway  chute  rri  is  driven  up  through  the  middle  of  the  pillar  for  a few 
yards  and  is  then  branched  in  both  directions  until  each  branch  (slant 
chute)  intersects  the  foot  of  a breast  near  the  battery  b,  as  shown.  The  jugu- 
lar manways  n,  n are  started  at  this  point  and  continued  up  each  side 
of  the  breast.  The  main  airway  h is  driven  in  the  solid  through  the 
stump  A above  the  gangway.  By  driving  the  main  gangway  g against  the 
roof,  as  shown,  the  pitch  of  the  chute  is  lessened,  and  the  loading  chute  c 
is  more  readily  controlled. 

When  the  main  gangway  is  not  driven  against  the  roof,  a gate  is  placed 
in  the  chute  below  the  check-battery,  which  enables  the  loader  to  properly 
handle  the  coal.  Coal  in  excess  of  the  amount  necessary  to  keep  the  miner 
up  to  the  face  may  be  drawn  through  the  main  battery,  or  sent  down  the 
manway  chute,  from  which  it  is  loaded  through  an  air-tight  check-battery. 

The  main  chutes  are  usually  8 or  9 ft.  wide,  but  sometimes  only  for  the 
first  6 or  8 ft.;  above  this  they  are  driven  about  6 ft.  square.  The  manway 
and  slant  chutes  are  also  about  6 ft.  square. 

When  the  seam  is  not  thick  enough  to  carry  the  return  airway  h (Fig,  27) 
over  the  gangway,  the  chutes  are  driven  up  in  the  same  manner  as  in 
Fig.  27,  for  a distance  of  about  30  ft.,  where  they  intersect  the  airway.  The 
breast  is  opened  out  just  above  the  airway,  a battery  being  built  in  the  airway 


Fig.  28. 


310 


METHODS  OF  WORKING. 


immediately  above  each  chute.  A manway  is  driven  from  the  gangway 
up  through  the  middle  of  the  stump  until  it  intersects  the  airway,  and  a 
trap  door  is  placed  at  this  point  to  confine  the  air.  This  manway  is  made 
about  4 ft.  X 6 ft.,  or  smaller.  . . . 

Fig.  28  shows  a less  complicated  plan  than  Fig.  27.  The  main  chutes  n,  n 
are  driven  up  to  the  heading  c,  from  which  the  breast  is  opened  out;  a log 

battery  is  built  at  the  top 


Fig.  29. 


of  each  chute  at  the  points 
marked  a,  a.  The  chutes 
are  used  for  drawing  the 
battery  coal,  and  for  re- 
ceiving the  manway  coal, 
and  are  also  used  for  trav- 
eling ways.  A check-bat- 
tery b is  placed  in  the  chute 
to  prevent  the  air-current 
from  taking  a short  cut 
from  the  gangway  through 
the  chute  to  the  breast  air- 
ways. This  check-battery 
is  of  great  assistance  to  the 
loader  when  the  chute  has 
a very  steep  pitch,  as  he 
can  readily  control  the  flow 
of  coal  through  the  draw- 
hole. 

All  these  methods  are 
open  to  the  objection  that 
in  case  of  any  accident  to 
the  breast  manway,  by 
which  the  flow  of  air, 


shown  by  the  arrows,  is  obstructed,  there  is  no  means  of  isolating  the  breast 
in  which  the  accident 
occurs,  and  the  venti- 
lation of  all  the  breasts 
beyond  it  is  entirely 
stopped.  To  overcome 
this,  sometimes  the  pil- 
lar A,  shown  in  left- 
hand  breast,  Fig.  28,  is 
left  in  each  breast  to 
protect  the  airway. 

Rock-Chute  Mining. 

Fig.  29  shows  a section 
of  two  seams,  sepa- 
rated by  a few  yards 
of  rock.  Chutes  from 
4i  to  7 ft.  high  and  7 to 
12  ft.  wide  are  driven 
in  the  rock  from  the 
gangway  or  level  g to 
the  level  l in  the  seam 
above,  at  such  an 
angle  that  the  coal 
will  gravitate  from  the 
upper  seam  into  the 
gangway  g.  The  work- 
ing, otherwise,  is  sim- 
ilar to  that  previously 
described. 

Rock-chute  mining 
contemplates  the  fol- 
lowing sequence  of 
operation; 

1.  The  opening  of 
all  gangways  and  air- 
ways in  the  lower  seam, 
lying  a few  feet  above  it. 


Fig.  30. 


to  develop  coal  as  yet  untouched  in  a thick  seam 


ANTHRACITE  MINING. 


311 


2.  Developing  the  thick  bed  by  a regular  series  of  rock  chutes  driven 
from  the  gangway  below;  workings  being  opened  out  from  chutes  as  in 
ordinary  pillar-and-breast  working — the  panel  system  or  some  other  plan 
may  be  found  better  than  pillar-and-breast  workings 

3 Driving  the  breasts  to  the  limit  of  the  lift  and  robbing  out  the  pillars 
from  a group  of  breasts  as  soon  as  possible,  even  if  a localized  crush  is  induced. 

4 After  one  group  of  breasts  is  taken  out  and  the  roof  has  settled,  open- 
ing a second  series  of  chutes  for  the  recovery  of  coal  from  any  large  pillars 
that  were  not  taken  out  when  the  crush  closed  the  workings. 

5.  While  the  work  of  recovering  the  pillar  coal  is  in  progress,  a second 
group  of  breasts  may  be  worked,  and  the  process  continued  until  all  the 
area  to  be  worked  from  that  gangway  has  been  exhausted.  The  same 
process  is  employed  in  opening  lower  lifts.  , , 

6 When  all  the  upper  bed  of  coal  has  been  exhausted,  the  lower  seam 
may  be  worked  by  the  ordinary  method.  Workings  in  this  seam  may  be 


Fig.  31. 


carried  on  simultaneously  with  the  upper  bed,  but  to  avoid  the  possibility 
of  a squeeze  destroying  these  workings,  very  large  pillars  must  be  left. 
After  exhausting  the  upper  seam,  these  pillars  may  be  advantageously 
worked  by  opening  one  or  two  breasts  in  the  center  of  each,  and  when  these 
are  worked  to  the  upper  limit,  attacking  the  thin  rib  on  each  side,  com- 
mencing at  the  top  and  drawing  back.  . , 

When  the  roof  of  the  lower  bed  is  good,  the  cost  of  timbering  and  keeping 
open  the  gangways  and  airways  will  be  considerably  less  than  if  these  were 
driven  in  the  upper  seam,  and  this  difference,  in  some  cases,  may  be  suf- 
ficient to  pay  for  driving  all  the  rock  chutes.  . 

There  are  three  undetermined  points  in  this  connection,  viz.:  (1)  The 


312 


METHODS  OF  WORKING. 


maximum  distance  between  the  two  beds,  or  the  length  of  rock  chute  that 
can  be  driven  with  satisfactory  financial  results.  (2)  The  maximum  dip  on 
which  such  working  can  be  successfully  opened.  (3)  The  maximum  thick- 
ness of  the  upper  and  also  of  the  lower  seam,  which  wTill  yield  results  war- 
ranting the  additional  outlay  w'hen  rock  chutes  are  of  considerable  length. 

Fig.  30  show's  how  one  or  more  seams  are  worked  by  connecting  them  by 
a “stone  drift,”  or  “tunnel,”  driven  horizontally  across  the  measures, 
through  w hich  the  coal  from  the  adjacent  seams  is  taken  to  the  haulage- 
way leading  to  the  landing  at  the  foot  of  the  slope  or  shaft.  Tunnels  are 
sometimes  driven  horizontally  through  the  measures  from  the  surface,  so  as 
to  cut  one  or  more  seams  above  water  level. 

The  lowrer  seam  of  coal  is  wrorked  from  a gangw  ay  or  level  l,  connected 
by  a tunnel,  or  stone  drift  t,  to  the  level  or  gangway  g,  in  the  thick 
seam,  The  stone  drift  may  be  extended  right  and  left  to  open  seams  above 
and  below'  the  thick  seam*  This  tunnel,  or  stone  drift,  is  never  driven  under 
a breast  in  the  upper  seam,  but  directly  under  the  middle  of  the  pillar. 

In  the  upper  and  thicker  seam,  when  the  coal  is  very  hard,  a breast  5 is 
worked  to  the  limit  and  the  loose  coal  nearly  all  run  out  through  the  chute  s 
into  the  gangw  ay  g.  The  “ monkey  gangway  ” m is  driven  near  the  top  as  a 
return  airway,  and  is  connected  to  the  upper  end  of  the  chute  s by  a level 
heading  n,  and  to  the  main  gangw  ay  g by  a heading  v.  These  headings  are 
driven  for  the  purpose  of  ventilation  and  to  provide  access  to  the  battery  in 
case  the  chute  s should  be  closed.  In  the  lower  seam,  the  breast  is  still  being 
w orked  upwards  in  the  ordinary  way. 

The  J.  L.  Williams  method  of  working  anthracite,  Fig.  31,  has  been  applied 
successfully  by  the  originator  at  the  Richards  Mine,  Mt.  Carmel,  Pa.;  and  by 
it  90£  of  the  available  coal  is  said  to  have  been  obtained.  The  method  is  a pil- 
lar-and-stall  method  with  the  folio wTing  distinguishing  points:  (a)  Timbering 
the  gob  with  props  set  not  more  than  6 ft.  apart,  to  keep  up  the  roof  during 
the  extraction  of  the  pillars.  (6)  Making  holes  from  the  crop,  for  the 
delivery  of  timber  into  the  workings,  (c)  Removing  the  pillars  in  shorter 
lifts  than  is  possible  w hen  the  roof  is  supported  with  culm  pillars.  ( d ) Keep- 
ing the  gob  open  with  timber  for  dumping  the  fallen  rock,  that  would  have 
to  be  sent  to  the  surface  if  the  breasts  were  flushed. 

Both  the  floor  and  the  roof  of  the  mine  were  weak,  so  that  it  w'as  not 
possible  to  make  either  the  breasts  or  the  pillars  wide.  In  some  cases,  the 
floor  consisted  of  3 ft.  of  clod,  and  to  prevent  its  lifting  and  sliding,  every 
alternate  pronwas  put  through  the  clod  and  its  foot  set  in  the  slate  beneath, 
while  the  other  props  were  set  on  pieces  of  2"  plank  2 ft.  in  length  to  keep 
down  the  bottom.  A small  gangway  X is  driven  to  take  out  the  chain  pillar, 
and  Y is  a small  gangw  ay  for  taking  in  timber. 

Running  of  Coal.— In  large  seams,  when  the  coal  is  soft  and  shelly  91*  slip- 
pery and  lies  at  an  angle  of  more  than  50°,  and  generates  large  quantities  of 
firedamp  a danger  to  be  guarded  against  is  the  sudden  liberation  of  gas 
should  a breast  run;  that  is,  should  the  coal  at  the  face  loosen  and  run  out 
bv  its  own  gravity,  only  stopping  w'hen  it  chokes  or  fills  up  the  open  space 
below  To  meet  these  conditions,  the  air-course  maybe  driven  above  the 
gangway  and  used  as  a return,  the  fan  being  attached  as  an  exhaust,  and 
the  working  breasts  ventilated  in  pairs.  The  inside  manway  of  one  of  a pair 
of  breasts  is  connected  with  the  gangway  for  the  intake,  and  the  outside 
manwav  of  the  other  breast  with  the  return  airway,  giving  each  pair  of 
breasts  a separate  split  of  the  current.  In  collieries  where  this  system  of 
working  is  folio wTed,  the  coal  is  soft.  A newT  breast  is  worked  up  a few  ^ ards, 
but  as  soon  as  it  is  opened  out,  the  coal  runs  freely  and  the  manways  are 
pushed  up  on  each  side  as  rapidly  as  possible,  to  keep  up  with  the  face.  Two 
miners  one  on  either  side,  sometimes  finish  a breast  without  being  able  to 
cross  to  each  other.  The  work  is  done  exclusively  with  safety  lamps,  and 
when  a breast  “runs”  the  gas  is  liberated  in  such  quantities  that  it 
frequently  fills  breasts  from  the  top  to  the  airway  before  the  men  can  get 
down  the'manwav  on  the  return  side.  When  the  gas  reaches  the  cross-hole, 
it  passes  into  the ‘return  airway  without  reaching  any  part  where  men  are 
working.  Should  a run  of  coal  block  a breast  by  closing  the  manway,  it 
affects  the  current  of  one  pair  of  breasts  alone.  As  the  gangway  is  the 
intake,  leakage  at  the  batteries  passes  into  the  breasts,  as  the  cross-holes  are 
above  their  level  and  the  gas  is  thus  kept  above  the  starter  when  at  the 
draw-hole.  The  gangway,  chutes,  and  airway  are  supplied  by  w-ooden 
pipes,  wrhich  connect  with  a door  behind  the  inside  chute.  If  a breast  runs 
up  to  the  surface,  it  does  not  affect  the  return  airway,  as  it  is  in  the  solid,. 


ANTHRACITE  MINING . 


313 


Among  the  disadvantages  urged  against  this  system  of  working  are  the 

f<)1  ItTncfeases  the  friction,  as  the  air  must  pass  in  the  airway  all  the  distance 
from  the  breast  to  the  fan,  the  area  of  the  airway  being  small  in  comparison 

t0  ilis  t^faces  of  the  breasts  are  so  much  higher  than  the  return  airway, 
the  lighter  gas  must  be  forced  down  into  the  return  against  the  buoyant 
power  of  its  smaller  specific-  gravity. 

The  reduction  of  friction  obtained  by  splitting  is  neutralized  by  each  split 
running  up  one  small  manway  and  down  another;  the  advantage  of  running 
through  several  pillar  headings  and  thus  securing  a shorter  course  being 
lost.  This  can  be  partly  obviated  by  ventilating  the  breasts  in  groups,  but 
the  dangers  avoided  in  splitting  are  increased. 

Blackdamp,  which  accumulates  in  the  empty  or  partly  empty  breasts, 
works  its  way  down  and  mixes  with  the  intake  current,  as  there  is  no  return 
current  in  the  breast  strong  enough  to  carry  it  away,  the  return  being  closed 
in  the  airway.  . ^ , 

All  things  considered,  when  the  seam  is  soft  and  has  a pitch  of  40°  and 
upwards,  and  emits  large  quantities  of  gas  in  sudden  outbursts,  as  in  running 
breasts,  this  system  is  the  best  that  can  be  adopted. 

When  the  Coal  Is  Hard  and  Gas  Is  Not  Freely  Evolved.— The  reverse  of  the 
svstem  just  described  is  followed  at  some  collieries  where  the  coal  is  hard 
and  but  little  gas  is  encountered.  The  airway  is  driven  over  the  gangway 
or  against  the  top,  the  fan  being  used  to  force  the  air  inward  to  the  end  of 
the  airway.  The  air  is  distributed  as  it  returns,  being  held  up  at  intervals 
by  distributing  doors  placed  along  the  gangway. 

Among  the  advantages  claimed  for  this  plan  are  the  following:  ■ 

As  the  pressure  is  outward,  it  forces  smoke  and  gas  out  at  any  openings 
that  may  exist  from  crop-hole  falls  or  other  causes. 

The  warm  air  from  the  interior  of  the  mine  returning  up  the  hoisting 
slope  or  shaft  prevents  it  from  freezing. 

As  the  current  is  carried  from  the  fan  to  the  end  of  each  lift  without  pass- 
ing through  working  places,  the  opening  of  doors  as  cars  are  passing,  etc. 
does  not  interfere  with  the  current.  . 

If  a locomotive  is  used,  the  smoke  and  gases  generated  by  it  are  carried 
away  from  the  men  toward  the  bottom.  Locomotives  are  generally  used 
only  from  the  main  turnout  to  the  bottom. 

An  objection  to  this  svstem  is  that  the  gangway,  as  the  return,  is  apt  to  be 
smoky.  Starters  and  loaders  are  forced  to  work  in  more  or  less  smoke,  and 
even  the  mules  work  to  disadvantage,  while  if  gas  is  given  off,  it  is  passed 
out  over  the  lights  of  those  working  in  the  gangway. 

However,  in  places  where  there  is  but  little  gas,  and  airways  of  large  area 
can  be  driven,  this  plan  works  very  satisfactorily,  and  some  of  the  best  ven- 
tilated collieries  are  worked  upon  it.  . 

An  objection  advanced  by  some  against  forcing  fans  is  that  they  increase 
the  pressure,  thus  damming  the  gas  back  in  the  strata.  In  case  the  speed  of 
the  fan  is  slacked  off,  the  accumulated  gas  may  respond  to  the  lessened  pres- 
sure and  spring  out  in  large  volumes  from  its  pent-up  state.  This  argument, 
however,  works  both  wavs.  An  exhaust  fan  running  at  a given  speed  is 
taking  off  pressure,  and  if  anything  occurs  to  block  the  intake,  the  pressure 
is  diminished,  and  the  gas  responds  to  the  decrease  on  the  same  principle. 

Hints  for  the  Smaller  Seams  When  They  Are  Small  and  Lie  From  Horizontal  to 
About  10°. — ' Two  gangways  may  be  driven,  the  lower  or  main  gangway  being 
the  intake.  Branch  gangways  should  then  be  driven  diagonally  or  at  a slant, 
with  a panel  or  group  of  working  places  on  each  slant  gangway.  Large 
headings  should  connect  the  panels.  In  this  system,  the  air  is  carried 
directly  to  the  face  of  the  gangway  and  up  into  the  breasts,  returning  back 
through  the  working  places.  The  intake  and  return  are  separated  by  a solid 
pillar,  the  only  openings  being  the  slant  gangways  on  which  are  the  panels. 

The  advantages  of  this  plan  are  several: 

The  main  gangway  is  solid,  with  the  exception  of  the  small  cross-holes 
connecting  with  the  gangway  above;  these  furnish  air  to  the  gangway  and 
are  small  and  easily  kept  tight.  These  stoppings*  should  be  built  of  brick, 
and  made  strong  enough  to  withstand  concussion. 

A full  trip  of  wagons  can  be  loaded  and  coupled  in  each  panel  or  section 
without  interfering  with,  or  detaining  the  traffic  on,  the  main  road;  one  trip 
can  be  loaded  while  another  is  run  out  to  the  main  gangway  for  transpor- 
tation to  the  bottom. 


314 


METHODS  OF  WORKING. 


The  only  break  in  the  intake  current  is  when  a trip  of  cars  is  taken  out 
from,  or  returns  to,  a panel  or  section;  this  can  be  partially  provided  against 
by  double  doors,  set  far  enough  apart  to  permit  one  to  close  after  the  trip 
before  the  other  is  opened.  This  distance  can  be  secured  by  opening  the 
first  three  breasts  on  a back  switch  above  the  road  through  the  gangway 
pillar,  or  by  running  each  branch  over  the  other  far  enough  to  obtain  the 
distance  for  the  double  doors. 

If  it  is  not  desired  to  carry  the  whole  volume  of  air  to  the  end  of  the  air- 
way, a split  can  be  made  at  each  branch  road.  These  will  act  as  unequal 
splits  in  reducing  friction,  and,  although  not  theoretically  correct,  are  prefer- 
able to  dragging  the  whole  current  the  full  length  of  the  workings. 

The  objections  urged  to  this  plan  are  that  it  involves  too  much  expense 
in  the  large  amount  of  narrow  work  at  high  prices  necessary  to  open  out  a 
colliery,  that  it  necessitates  a double  track  the  whole  length  of  the  lift,  and 
that  the  grade  ascends  into  each  panel  or  section.  But  the  latter  criticism 
falls,  because  the  loss  of  power  hauling  the  empty  wagons  up  a slight  grade 
is  more  than  made  up  by  the  loaded  wagons  running  down  while  the  mules 
are  away  putting  a trip  into  another  panel  or  section. 

For  a large  colliery  this  is  without  doubt  the  best  and  cheapest  system. 

When  the  Seam  is  Small  and  Lies  at  an  Angle  of  More  Than  10°.— In  small  seams 
lying  at  an  angle  of  more  than  10°,  and  too  small  to  permit  an  airway  over 
the  chutes,  it  is  more  difficult  to  maintain  ventilation.  If  air  holes  are  put 
through  every  few  breasts,  and  a fresh  start  obtained  by  closing  the  back 
holes,  or  if  an  opening  can  be  gotten  through  to  the  last  lift  as  often  as 
the  current  becomes  weak,  an  adequate  amount  of  air  can  be  maintained, 
because  the  lift  worked  can  be  used  as  the  intake,  and  the  abandoned  lift 
above  as  the  return.  To  ventilate  fresh  ground,  the  filling  of  the  chutes 
with  coal  will  have  to  be  depended  on,  or  a brattice  must  be  carried  along 
the  gangway.  This  can  be  done  for  a limited  distance  only,  as  a brattice 
leaks  too  much  air.  As  a rule,  collieries  worked  on  this  plan  are  run  along 
until  the  smoke  accumulates  and  the  ventilation  becomes  poor;  then  a new 
hole  is  run  through  and  the  brattice  removed  and  used  as  before  for  the 
next  section.  This  operation  is  repeated  until  the  lift  is  worked  out.  Some- 
times, to  make  the  chutes  tight,  canvas  covers  are  put  on  the  draw'  holes, 
but  as  they  are  usually  left  to  the  loaders  to  adjust,  they  are  often  very 
imperfectly  applied.  Then,  as  the  coal  is  frequently  very  large,  the  air  will 
leak  through  the  batteries. 

This  plan  works  very  satisfactorily  if  the  openings  are  made  at  short 
intervals,  say  as  frequent  as  every  fifth  breast,  but  the  distance  is  usually 
much  greater  to  save  expense.  As  the  power  of  the  current  decreases  as  the 
distance  between  the  air  holes  is  increased,  good  ventilation  is  entirely  a 
question  of  how  often  a cut-off  is  obtained. 

An  effective  ventilation  could  be  maintained  in  a small  seam  at  a heavy 
angle  by  working  with  short  lifts,  say  two  lifts  of  50  yd.  instead  of  one  of 
100  yd.,  as  at  present.  The  gangways  should  be  frequently  connected,  and 
one  used  as  an  intake  and  the  other  as  a return.  This  would  necessitate 
driving  two  gangways  where  one  is  now  made  to  do,  but  the  additional 
expense  would  be  made  up  in  the  greater  proportion  of  coal  won. 


FLUSHING  CF  CULM. 

From  15 $ to  20$  of  the  coal  taken  out  of  an  anthracite  mine,  according 
to  the  methods  used  in  the  past,  became  so  fine  in  the  course  of  preparation 
through  the  breaker  that  it  could  not  be  used  or  sold,  and  had  to  be  piled 
away  as  refuse.  Recently,  the  coarser  portions  of  these  culm  piles  have 
been  screened  out  and  sold  for  use  as  steam  sizes,  while  the  finer  part, 
together  with  the  fine  material  from  the  breaker,  has  been  carried  back  into 
the  mines  with  water  to  fill  the  abandoned  portions  of  the  underground 
workings. 

This  culm  is  carried  through  a system  of  conveyors  to  the  hopper,  usually 
an  old  oil  barrel,  and  the  stream  of  water  is  conducted  into  the  same  hopper 
by  a 3"  pipe.  The  culm  is  then  carried  by  the  water  through  a pipe  from 
4 to  6 in.  in  diameter,  which  passes  into  the  mine  through  the  shaft,  bore 
hole,  or  other  opening,  thence  alo-ng  the  gangways  to  the  chambers  through 
the  cross-cuts,  and  to  the  point  where  it  is  desired  to  deposit  the  culm.  The 
bottoms  or  outlets  of  the  chambers  to  be  filled  are  closed  by  board  partitions 
fitted  closely,  or  by  walls  of  slate  or  mine  rubbish.  The  culm,  as  it  issues 


CULM  FLUSHING. 


315 


from  the  end  of  the  pipe,  takes  a very  flat  slope,  and  it  is  carried  a long  dis- 
tance by  the  water,  which  ultimately  filters  through  the  deposited  culm  to 
the  lower  portion  of  the  mine,  to  be  pumped  to  the  surface.  When  the 
chamber  is  filled  to  the  roof,  the  pipe  is  withdrawn  and  extended  to  the 
next  place  to  be  filled,  and  so  on.  Wrought-iron  pipe  is  said  to  be  the  best, 
and  the  life  of  the  pipe  depends  on  the  nature  of  the  water  used  and  the 
material  treated.  With  fresh  water  and  small  culm  from  the  buckwheat 
screen,  it  lasts  18  months;  when  carrying  culm  from  the  bank,  ranging  from 
dust  to  pea'coal  and  some  chestnut,  9 months;  and  when  mixed  with  ashes, 
6 months.  The  smaller  the  material  the  better. 

The  amount  of  water  used  depends  on  the  distance  to  which  the  culm  is 
carried  and  the  slope  of  the  pipe.  , i 

From  li  to  If  lb.  of  water  is  required  to  flush  1 lb.  of  culm  to  level  and 
down-hill  places;  3 to  6 lb.  of  water  to  1 lb.  of  culm  to  flush  up-hill  for  heights 
varying  from  10  to  100  ft.  above  the  level  of  the  shaft  bottom.  Any  ele- 
vation of  the  pipe  very  materially  increases  the  amount  of  water  necessary. 
Mr  James  B.  Davis,  superintendent  of  the  Dodson  and  Black  Diamond 
mines,  has  ascertained  by  experiment  that  1 cu.  ft.  of  anthracite  coal  ground 
to  culm  can  be  flushed  into  a space  of  nearly  1£  cu.  ft.,  and  it  is  therefore 
impossible  to  compress  the  culm  more  than  one-third.  In  addition  to  acting 
as  a filling  and  a support,  to  prevent  squeezes  and  crushing,  flushing  has 
been  advantageously  used  for  fighting  and  sealing  off  mine  fires.  No 
instance  has  been  recorded  where  spontaneous  combustion  has  taken  place 


in  the  flushed  culm. 

The  Dodson  culm*  plant,  which  was  a pioneer,  cost  $7,473.42,  with  the 
capacity  of  flushing  119  tons  per  day,  while  the  Black  Diamond  culm  plant 
is  capable  of  flushing  287  tons  per  day  and  cost  $6,280.12,  but  plants  can 
probably  be  put  up  much  more  cheaply  than  this. 

The  saving  from  the  flushing  of  culm  over  depositing  it  on  the  surface 
varies  for  the  ordinary  anthracite  colliery  from  $5  to  $15  per  day.  The 
average  cost  of  putting  in  stoppings  in  a 9'  vein  is  given  by  Mr.  Davis  as 
$9.50,  including  material. 

To  remove  the  pillars  after  the  intervening  breasts  have  been  filled  with 
culm,  the  face  of  the  pillar  along  the  gangway  is  attacked,  and  a road  driven 
up  through  the  pillar,  splitting  it  (z,  Fig.  32).  This  road  may  be  the  full 
width  of  the  pillar,  but  in  general  it  is  necessary  to  leave  a narrow  stump  of 
coal  on  either  side  to  keep  up  the  fine  flushed  material  in  the  adjoining 
breasts.  The  thickness  of  this  supporting  coal 
depends  entirely  on  the  condition  of  the 
flushed  material  behind  it.  If  that  is  fine, 
it  will  set  firmly  and  form  a compact  mass 
that  will  not  run.  In  such  a case,  the  pillar 
may  be  entirely  taken  out,  leaving  a vertical 
wall  of  solidly  packed  flushed  culm.  When 
the  flushed  material  is  of  a size  larger  than 
buckwheat,  it  will  not  set  compactly,  but  will 
run  when  it  is  opened  up,  and  when  such 
material  fills  the  adjoining  breasts,  the  thin 
pillar  of  coal  must  be  left  to  keep  back  the 
culm.  Timbers  are  placed  flush  up  against 
the  culm  or  the  coal  stumps,  as  the  case  may 
be,  and  if  there  is  a tendency  for  the  culm 
to  run,  lagging  is  placed  behind  the  timbers. 

In  some  cases,  as  much  as  700  ft.  of  timber 
have  been  used  per  100  ft.  of  pillar  taken 
out.  As  the  pillar  is  removed,  the  top  settles 
until  it  finally  rests  upon  the  flushed  culm, 
and  as  the  weight  from  the  top  and  the  pres- 
sure from  the  sides  comes  upon  these  props, 
they  are  broken,  while  the  coal  that  has  been 
left  will  also  be  crushed.  At  the  Black  Dia- 
mond colliery,  the  props  used  are  16  ft.  long, 

and  at  this  colliery  the  top  settles  about  4 ft.  if  the  flushed  material  is 
packed  tightly  before  the  roof  pressure  comes  on  it.  After  this  settling, 
new  props  12  ft.  in  length  are  put  in  close  up  against  the  culm  and  the 
broken  stump  of  the  original  pillar,  and  they  serve  to  keep  the  road  open 
up  to  the  working  face. 


Fig.  32. 


316 


MINING  MINERAL  DEPOSITS. 


METHODS  OF  MINING  MINERAL  DEPOSITS. 

Much  of  what  has  already  been  given  under  the  heading  of  Coal  Mining 
applies  equally  to  the  mining  of  mineral  deposits.  It  will  therefore  not  be 
repeated  under  this  heading,  and  the  only  methods  here  given  will  be  those 
that  have  not  already  been  covered. 

Highly  inclined  deposits  are  mined  out  as  follows:  Horizontal  passages 
called  drifts , levels , or  galleries  are  driven  through  the  ore  at  regular  intervals, 
and  connected  by  openings  at  right  angles  to  the  levels,  which,  in  the  case 
of  perpendicular  or  highly  inclined  deposits,  are  called  winzes  or  raises, 
according  as  they  are  sunk  from  above  or  raised  from  below.  These  parallel 
openings  divide  the  ore  body  into  a series  of  rectangles,  thus  serving  to  test 
its  value.  (See  also  Overhand-Stoping  Method,  page  304.) 

Levels. — The  distance  between  the  individual  levels  depends  on  the 
material  being  mined.  They  are  placed  nearer  together  in  high-grade  ore 
than  in  low-grade  material.  The  width  of  the  vein  also  has  considerable 
influence  on  the  distance  between  the  levels.  In  veins  where  it  is  necessary 
to  break  into  walls  to  afford  working  room  in  the  levels,  they  are  usually 
placed  as  far  apart  as  is  consistent  with  the  economical  handling  of  the 
material  in  chutes  and  convenient  access  to  the  working  faces  of  the  stopes. 
The  distance  between  the  levels  varies  from  60  to  100  ft.,  and  should  be 
measured  on  the  dip  and  not  perpendicularly. 

Winzes  or  Raises.— The  distance  between  the  raises  or  winzes  varies  from 
30  to  250  ft.,  depending  largely  on  the  character  of  the  material  and  the 


method  of  getting  it  into  the  chutes  or  winzes.  Where  the  material  at  the 
working  faces  is  shoveled  or  thrown  directly  into  the  chutes,  they  are  often 
placed  as  close  as  30  ft.,  while  if  the  material  is  carried  from  the  working 
face  to  the  chute  or  winze  in  a wheelbarrow,  the  chutes  may  be  much 
farther  apart. 

Stoping.— For  narrow  deposits,  there  are  two  general  styles  of  stoping  in 
regular  use,  called,  respectively,  underhand  and  overhand  stoping.  There  are 
several  minor  divisions  under  each. 

Underhand  stoping  may  be  conveniently  divided  into  underhand  regular 
and  underhand  Cornish. 

The  regular  method  of  underhand  stoping  is  illustrated  in  (a),  Fig.  33,  and 
may  be  described  as  follows:  The  miner  selects  a place  in  any  given  level 
or  on  the  surface  of  the  ore  deposit  from  which  to  commence  stoping.  A 
cut  6 or  7 ft.  in  depth  and  from  6 to  8 ft.  in  length  is  made.  This  forms  the 
first,  or  No.  1,  bench  in  the  stope.  After  this,  he  continues  the  work  in  each 
direction,  supporting  the  track,  if  any  exists  above,  upon  stulls  or  timbering. 
After  this  No.  1 bench  has  proceeded  a sufficient  distance,  he  starts  a similar 
cut  in  the  bottom  of  it,  which  forms  No.  2 bench,  and  is  driven  in 
both  directions  as  before.  At  first  the  ore  can  be  shoveled  to  the  level 
above,  but  after  considerable  depth  has  been  attained,  it  will  be  necessary 
to  provide  a winze,  as  shown  at  /,  through  which  the  ore  from  the  lower 
benches  can  be  hoisted.  Stulls  covered  with  lagging  are  placed  across  the 
stope  behind  each  bench  as  platforms,  to  support  the  waste  material.  Under- 
hand stoping  by  the  Cornish  system  is  illustrated  in  (6),  Fig.  33,  and  differs 
from  the  system  just  described  only  in  that  the  level  below  has  to  be  driven 
first,  and  a winze  sunk  to  it.  a is  the  lower  level,  b the  winze,  and  c the 
upper  level.  The  work  is  then  carried  on  in  successive  benches,  as  described. 


OVERHAND  STORING. 


317 


The  advantages  of  the  Cornish  method  are  that  any  water  that  collects 
in  the  stope  flows  to  the  lower  level  and  does  not  have  to  be  taken  care  ot  in 
each  individual  stope.  Also,  the  ore  can  be  tumbled  down  through  the  raise 
to  the  lower  level,  thus  avoiding  the  extra  hoisting  with  a windlass, 
or  small  hoist. 

The  advantages  that  apply  to  any  system  of  underhand  stoping  are  as 
follows:  The  ore  can  be  extracted  at  once;  while  the  stope  is  new,  the  miner 
is  protected  from  the  roof  by  stulls  and  stagings;  the  loss  of  fine  and  valuable 
mineral  is  reduced,  owing  to  the  opportunity  for  sorting  afforded  during  the 
handling  of  the  broken  ore. 

The  disadvantages  are  as  follows:  The  manner  in  which  the  ore  must  be 
handled  is  expensive;  an  individual  pumping  plant  will  be  necessary  in  each 
stope  of  a wet  mine  with  the  regular  system;  should  the  mine  be  abandoned 
for  any  length  of  time,  the  stulls  become  loose  and  allow  the  rock  stowed 
upon  them  to  fall  on  the  face  of  the  ore,  rendering  the  mine  unsafe,  and 
burying  the  ore  so  as  to  require  a large  expenditure  of  time  and  money  to 
reopen  the  workings;  in  a wet  stope,  the  water  flows  down  over  the  working 
faces,  interfering  with  the  workmen  and  forcing  them  to  stand  continually 


in  water.  . , _ _ 

Overhand  Stoping.— In  this  system  of  stoping,  the  ore  is  broken  down  from 
above  as  the  work  progresses.  Work  is  usually  started  from  the  bottom  of  a 
raise,  as  B,  Fig.  34.  After  the  lower  level  A has  been  driven,  the  miner 
stands  on  top  of  the  lagging  over  the  caps  and  works  out  a slice  C 5 or  6 ft. 
high,  this  being  followed  by  succeeding  slices,  as  D and  E.  Chutes  are 
timbered  or  cribbed  at  intervals,  through  which  the  material  may  be  thrown 
down  and  any  waste  packed  in  the  space  between  the  chutes,  as  at  F.  In 
cases  where  the  entire  deposit  is  of  value,  a portion  of  the  broken  ore  is 
allowed  to  accumulate  as  a platform  upon  which  the  men  stand  while 


Fig.  34. 


working,  only  enough  being  sent  through  the  chutes  to  provide  working 
room.  After  overhand  stoping  is  started,  the  work  may  be  carried  on  by 
means  of  breast  holes,  as  shown  at  E.  The  force  of  gravity  assists  in  break- 
ing the  rock,  and  reduces  the  powder  necessary  for  blasting. 

Where  rich  ore  is  broken,  platforms  of  planks,  or  sheets  of  canvas  or  bull 
hide  covered  with  plank,  may  be  placed  over  the  filling  to  receive  the  broken 
ore,  thus  preventing  the  loss  of  fine  and  valuable  material  in  the  filling. 
One  argument  which  is  usually  presented  against  overhand  stoping  is  that 
the  roof  is  not  secured  by  timbering,  but  this  is  offset  by  the  fact  that  the 
workmen  are  always  close  to  the  roof  and  thus  examine  its  condition  and 
break  off  any  dangerous  portions  or  give  them  such  support  as  may  be 
needed  with  temporary  timbers. 

Overhand  stoping  may  be  carried  on  in  a number  of  modified  forms,  all  of 
which  involve  the  principle  of  breaking  down  the  material  in  such  a manner 
that  thq  work  is  aided  by  gravitation.  Sometimes,  where  practically  the 
entire  deposit  is  removed,  temporary  platforms  supported  on  stulls  are  con- 
structed close  to  the  working  face  for  the  workmen. 

The  advantages  of  overhand  stoping  are  that  no  hoisting  or  pumping  is 
required  in  the  block  of  ore  being  worked,  as  with  underhand  stoping  with- 
out a winze;  water  gives  no  trouble  in  the  stopes;  less  timbering  is  required 
than  in  the  underhand  stoping,  because  no  platforms  are  required  to  store 
waste,  and  the  timbering  in  working  stagings  is  usually  recovered;  where 
the  mine  is  abandoned  for  a time,  the  working  face  is  usually  left  in  better 


318 


MINING  MINERAL  DEPOSITS. 


shape  with  overhand  than  with  underhand  stoping.  In  the  overhand  system, 
gravity  assists  in  the  breaking  of  the  ore. 

The  disadvantages  are  that  the  miner  is  forced  to  work  under  an  unsup- 
ported roof,  though  the  fact  that  he  is  close  to  it  enables  him  to  examine  it 
and  take  care  of  any  dangerous  portions.  There  may  be  greater  loss  of  the 
fine  and  valuable  material  that  becomes  mixed  with  the  waste  than  in 
underhand  stoping,  though  this  may  be  largely  prevented  by  the  use  of 
boards  or  canvas. 

Flat  or  Slightly  Inclined  Deposits.— Where  flat  or  slightly  inclined  ore  bodies 
are  being  worked,  the  working  drifts  (corresponding  to  levels  in  steeper 
deposits)  are  driven  comparatively  close  together  (about  30  ft.  apart)  and 
the  material  between  them  removed  in  successive  steps,  as  in  underhand  or 
overhand  stoping,  the  space  behind  the  miner  being  packed  with  waste  mate- 
rial to  support  the  roof,  or  the  roof  being  supported  by  timbering  until  the  ore 
is  removed.  Sometimes  pillars  of  ore  have  to  be  left  to  aid  in  the  support 
of  the  roof,  and  when  this  is  the  case,  the  miners  try  to  leave  the  pillars 
where  the  ore  is  low  grade.  When  a deposit  of  ore  is  of  uniform  value 
throughout,  and  the  roof  of  a somewhat  flexible  character,  it  may  be  let 
down  without  much,  if  any,  stowing,  as  in  the  longwall  system  of  coal 
mining.  In  other  cases,  the  material  is  removed  like  square  work  or  by  pillars 
and  rooms,  the  pillars  in  either  case  being  robbed  as  closely  as  possible 
before  leaving  the  workings. 


LARGE  DEPOSITS  OVER  8 FEET  THICK. 


With  a deposit  much  over  8 ft.  in 


Fig.  35. 

The  advantages  are  that  it 


thickness,  it  is  impossible  to  keep  the 
walls  in  place  by  stulls  or  single  sticks 
of  timber.  Large  masses  of  mineral 
frequently  contain  very  valuable  ma- 
terial, and  engineers  have  developed 
a number  of  methods  for  the  removal 
of  their  valuable  contents.  The 
method  depends  largely  on  the  value 
per  ton  of  the  material  being  removed, 
and  local  conditions  as  to  the  cost  of 
labor,  timber,  filling  material,  char- 
acter of  wall  rock,  etc.  The  methods 
used  for  these  deposits  are  square  work , 
filling , caving , and  square-set  timbering 
systems. 

Square  work,  also  called  the  cham - 
ber-and-pillar  system , is  illustrated  in 
Fig.  35.  Galleries  are  driven  through 
the  ore  as  shown,  the  deeper  galleries 
being  smaller  than  the  upper  ones, 
the  object  being  to  leave  larger  pillars 
for  the  support  of  the  material  above 
the  workings.  Galleries  are  then 
driven  at  right  angles  to  these,  to  leave 
square  pillars,  as  shown.  When  this 
system  is  applied  to  a bed  that  is  only 
30  or  40  ft.  thick,  from  three-fourths  to 
eight-ninths  of  all  the  material  in  the 
deposit  can  be  removed,  the  remainder 
being  left  as  pillars;  but  where  it  be- 
comes necessary  to  leave  floors  be- 
tween the  succeeding  levels,  as  shown 
in  (5),  Fig.  35,  scarcely  one-half  of  the 
deposit  can  be  removed,  even  when  it 
is  of  such  a firm  nature  that  the  gal- 
leries can  be  driven  considerably 
wider  than  the  thickness  of  the  pil- 
lars. This  system  of  mining  is  applied 
to  the  removal  of  salt,  gypsum,  build- 
ing stone,  and  various  low-grade  ores, 
and  is  very  similar  to  the  room-and- 
pillar  system  (see  page  280).  # 

;s  no  timbering,  and  that,  owing  to  the 


MINING  THICK  DEPOSITS. 


319 


Fig.  36.  Fig.  37. 

depending  principally  on  the  cost  of  the  stowing  material  compared  with 
the  value  per  ton  of  the  deposit  being  removed.  In  this  process,  the  filling 
* material  should  be  composed  entirely  of  large  pieces,  so  that  it  can  be 
packed  closely. 

Transverse  Rooming  With  Filling.— In  other  cases,  a filling  system  is  used 
in  which  rooms  or  chambers  are  driven  across  the  deposit  and  then  con- 
tinued upwards  by  overhand  stoping,  the  ore  being  thrown  to  a lower  level 
through  a chute  cribbed  up  as  the  work  progresses,  and  the  excavated 
space  filled  up  with  broken  rock  brought  down  through  a chute  from  above, 
as  showm  in  Fig.  36.  After  the  rooms  are  worked  out  between  two  levels, 
the  pillars  are  removed  in  the  same  manner. 

Longitudinal  Back  Stoping  With  Filling.— In  this  case,  the  deposit  is  worked  as 
a series  of  overhand  stopes,  Fig.  37,  the  space  below  the  workmen  being  filled 
with  broken  rock  a brought  down  through  raises  b from  above,  the  ore  being 
thrown  to  a level  c,  which  has  been  timbered  through  the  filling  material  on 


larger  size  of  the  chambers,  the  material  can  be  removed  at  a low  cost  per 
ton.  The  disadvantages  are  that  a large  portion  of  the  deposit  has  to  be  left 
untouched,  and  that  where  the  formation  being  mined  is  at  all  soft,  it  is  not 
safe  to  work  these  large  chambers. 

Filling  Methods.— Sometimes  a filling  of  worthless  material  is  substituted 
for  the  worked-out  ore.  This  system  may  be  carried  on  by  any  one  of  a 
number  of  different  plans. 

Slicing  Method. — In  some  cases,  comparatively  small  drifts  or  chambers 
(from  6 ft.  X 6 ft.  to  10  ft.  X 10  ft.)  are  driven  through  the  ore  across  the 
deposit,  and  then  tightly  packed  with  broken  rock,  after  which  other  drifts 
or  chambers  are  driven  beside  the  first  ones  and  also  packed  or  filled.  This 

Srocess  is  continued  until  a slice  has  been  removed  from  under  the  entire 
eposit.  The  process  is  then  repeated  on  top  of  the  filling,  taking  out  suc- 
cessive chambers  and  filling  them,  until  another  slice  has  been  removed. 
This  method  has  been  used  in  the  copper  mines  of  Spain,  and  has  also  been 
tried  at  some  mines  in  the  United  States  with  varying  degrees  of  success, 


320 


MIKING  MINERAL  DEPOSITS. 


the  first  or  lower  floor  of  the  stope.  This  method  has  been  very  successfully 
applied  to  some  of  the  large  iron  mines  of  the  Lake  Superior  region  of  the 
United  States.  . 

The  tilling  material  used  in  any  one  of  the  various  filling  methods  may  be 
obtained  at  the  surface,  may  be  partially  or  wholly  obtained  from  the  waste 
rock  associated  with  the  vein  material  and  from  drifts  or  passages  that  have 
to  be  driven  in  barren  ground,  or  it  may  be  obtained  by  driving  drifts  into 
the  hanging  wall,  and  opening  chambers  there,  from  which  the  waste  may 
be  obtained.  (See  also  Flushing  of  Culm,  page  314.) 

Caving  Methods.— The  longwall  method  of  mining  coal  is  really  a caving 
system,  but  where  this  system  is  applied  to  the  mining  of  large  masses,  it 
becomes  necessary  to  introduce  some  special  features.  There  are  two 
general  systems  in  use,  caving  a back  of  ore  and  caving  the  gob  or  waste  only. 

Caving  a Back  of  Ore. — In  this  system,  drifts  or  levels  are  run  through  the 
ore  a few  feet  below  the  top  of  the  deposit,  as  though  the  material  above  were 
to  be  removed  by  overhand  stoping,  but  in  place  of  breaking  the  material 
down,  it  is  allowed  to  cave  by  gravity.  When  a back  of  ore  is  thick  (20  ft. 
or  more),  the  entire  stope  is  sometimes  allowed  to  cave  full  and  then  the 
broken  ore  removed  by  driving  heavily  timbered  drifts  through  to  the 
farther  side  and  drawing  the  crushed  material  into  the  face  of  the  drift. 

When  the  overlying  worthless  material  appears,  op- 
erations are  continued  by  removing  the  last  set  in 
the  drift  and  drawing  the  ore  Horn  nearer  the  shaft. 
This  method  is  continued  until  practically  all  the 
broken  ore  has  been  removed.  Where  the  back  of 
the  ore  is  comparatively  thin  (less  than  20  ft.),  the 
caving  is  usually  accomplished  at  the  face  of  the 
drift  only,  the  drift  being  driven  a short  distance 
beyond  the  timbering  without  support.  The  ore 
above  this  unsupported  portion  will  cave  in  and  can 
be  removed.  When  the  waste  rock  and  old  timber 
from  above  appear,  the  operator  retreats,  removing 
one  set  of  timber  from  the  drift,  caving  and  remov- 
ing the  ore  over  it.  In  this 
manner,  operations  are  contin- 
ued until  all  the  ore  over  the 
drift  or  stope  has  been  caved, 
when  another  drift  or  stope  is 
driven  beside  the  first  and  the 
ore  over  it  caved.  In  this 
method,  blasting  has  to  be  re- 
sorted to  only  in  driving  the 
drifts,  from  one-half  to  three- 
fourths  of  the  ore  being  obtained 
without  the  use  of  powder. 

The  advantages  of  this  system 
are  that  little  blasting  is  re- 
quired; practically  the  entire 
deposit  is  recovered;  the  mining 
cost  per  ton  is  very  low. 

The  disadvantages  are  that 
the  ore  is  liable  to  become 
mixed  with  more  or  less  dirt,  which  caves  down  with  it;  only  one  level  of  the 
Sine  can  be  operated  at  a time,  and  the  surface  of  the  ground  is  allowed  to 
cave  into  the  openings,  thus  rendering  it  unfit  for  ordinary  surface  uses. 

Caving  the  Waste  Only.— In  this  system,  Fig.  38,  drifts  A and  galleries  B 
are  drivin  through  the  top  of  the  ore  body  immediately  under  the  waste 
rock.  After  one  of  these  drifts  or  galleries  is  completed,  the  floor  is  covered 
with  a lagging  of  plank  or  poles,  and  the  waste  material  allowed  to  cav  eon 
to  this  platform.  Subsequently,  other  drifts  are  driven  beside  the  first  one, 
the  floor  covered  with  lagging,  and  the  waste  allowed  to  cave.  This  Process 
is  continued  until  a slice  has  been  removed  over  the  entire  surface  of  the 
ore  deposit  when  more  drifts  are  driven  lower  down  and  another  slice 
removed  After  the  first  slice  has  been  removed,  the  broken  ot  waste  mate- 
rial is  supported  on  the  lagginglaid  on  the  floors  of  the  first  d rifts,  and  hence 
the  miners  have  only  to  support  this  lagging  m order  to  supigrt  the  waste. 
The  caving  of  any  individual  drift  crushes  the  ore  on  either  side  to  a con- 
siderable extent,  thus  materially  reducing  the  blasting  expense. 


Fig.  38. 


IRREGULAR  DEPOSITS. 


321 


The  advantages  of  this  system  are  that  the  entire  deposit  is  recovered*, 
little  blasting  is  required;  the  ore  obtained  is  clean;  the  mining  expense  is 
comparatively  low  per  ton.  , „ . _ , . „ 

The  disadvantages  are  that  only  one  level  of  a mine  can  be  producing  at  a 
time;  the  surface  is  allowed  to  cave,  thus  rendering  it  unfit  for  surface  uses. 


SQUARE-SET  SYSTEM. 


Frequently,  large  masses  of  material  are  encountered,  which  it  is  neces- 
sary to  remove,  and  at  the  same  time  support  the  surrounding  material. 
At  times,  it  is  not  desirable  to  fill  the 
stope  while  the  ore  is  being  removed, 
and,  at  the  samq  time,  it  is  impossible 
to  support  the  walls  by  single  sticks 
or  stulls.  To  overcome  these  diffi- 
culties, the  square-set  system  has  been 
evolved,  which  consists  in  the  sup- 
porting of  the  walls  by  means  of  a 
series  of  square  frames,  from  6 to  9 ft. 
square,  which  are  placed  in  position 
as  fast  as  the  ore  is  removed.  The  use 
of  these  frames  reduces  the  length  of 
the  individual  sticks,  and  so  produces 
a firm  structure.  The  timbers  may 
be  square-sawed  material  or  round 
logs.  If  the  walls  are  soft,  the  sides 
and  top  may  require  lagging,  and  if 
the  floor  is  soft  or  composed  of  ore, 
sills  will  be  necessary  under  the  posts. 

The  mining  ;s  carried  on  by  overhand- 
stoping  system,  removing  one  block  at 
a time  and  replacing  it  with  the  square 
set.  Fig.  39  represents  a stope,  the 
walls  and  roof  of  which  are  supported 
by  square  sets  that  are  lagged  from  the  outside, 
sets  are  made  from  round  timber. 


Fig.  39. 

In  this  case,  the  square 


IRREGULAR  DEPOSITS. 


Covoting  or  Gophering.— Bodies  of  valuable  material  frequently  occur  that 
cannot  be  mined  by  any  regular  system.  These  are  recovered  by  simply 
following  the  ore  throughout  its  irregularities  and  removing  it  with  the  use 
of  as  little  supporting  timber  or  other  material  as  possible.  Owing  to  the 
crooked  and  irregular  passages  that  occur  in  such  mines,  the  work  has  been 
called  coyoting , or  gophering.  Sometimes  regular  levels  are  driven  at  stated 
intervals,  and  the  coyoting,  or  gophering  carried  on  from  them  Many  of 
the  small  gold  and  silver  mines  of  the  West,  the  mines  of  Mexico  and  South 
America,  and  the  Missouri  lead  and  zinc  deposits  are  worked  by  this  system, 
the  object  being  to  remove  as  much  of  the  ore  as  possible  without  the  use  of 

timbering  or  the  driving  of  unnecessary  passages.  . 

Probably  one  of  the  best  examples  of  working  irregular  deposits  is  the 
mining  practice  in  the  Joplin  zinc  district,  Missouri.  The  deposits  of  zinc 
blende  are  irregularly  distributed  through  a limestone  rock,  and  the  mining 
is  carried  on  in  a very  crude  and  irregular  fashion. 

After  an  ore  bodv  has  been  found  by  drilling,  a shaft  5 ft.  X 5 jt.  to  6 it  X 
9 ft.  in  the  clear  is  sunk  by  the  contractor,  the  price  being  $4  per  foot  for  soft 
and  $9  per  foot  for  hard  ground  for  the  first  50  to  80  ft.,  the  contractor  doing 
all  the  work  in  sinking  and  timbering.  Through  the  soft  ground,  the  shaft  is 
timbered  by  4"  round  poles  or  by  2"  X 4"  or  2"  X 6"  timbers  laid  flatwise, 
skin  to  skin.  The  mines  are  divided  into  four  kinds.  (1)  Very  hard  mines 
that  require  all  the  ore  to  be  drilled  with  air  drills  and  blasted  out,  and 
require  no  timbering.  (2)  Mines  that  are  hard  but  have  open  crevices 
between  the  strata  where  a hand  drill  can  be  driven  and  a charge  of  dyna- 
mite lodged  and  exploded,  throwing  down  a large  amount  of  dirt  and  so 
iarring  the  surrounding  ground  that  it  may  be  easily  cut  down  with  the 
miner’s  pick.  This  kind  of  ground  needs  no  timber.  (3)  Mines  that  are 
moderately  soft  and  where  the  miner  can  place  a blast  anywhere  by  driving 


822 


COSTS  OF  MINING  ANTHRACITE, 


a spud,  throwing  down  a large  amount  of  ore.  The  drifts  are  carried 
10  ft.  X 12  ft.  in  the  clear,  and  are  cut  ahead  from  6 to  10  ft.  before  putting 
in  the  sets  of  timber  and  laggings  to  hold  the  roof.  (4)  Mines  that  are  very 
soft  and  where  a drift  cannot  be  carried  over  8 ft.  X 10  ft.  in  size,  where  the 
getting  of  the  ore  is  all  performed  by  pick  and  shovel,  and  where  it  is  neces- 
sary to  timber  close  and  drive  spiling  overhead  as  well  as  along  the  sides 
and  to  resort  to  mud -sills  in  the  floor  of  the  drift. 

When  the  shaft  reaches  the  ore  and  the  drift  is  extended  for  some  dis- 
tance to  prove  the  ore  bodv,  underhand  stoping  is  used  and  15'  holes 
are  drilled  bv  hand  in  the  bottom.  A charge  of  50  lb.  of  40*  dynamite  lifts  a 
stope  10  ft.  X 10  ft.  The  cost  of  75  tons  of  ore,  hoisting  it  and  dumping  it  on 
the  mill  platform  during  a shift  of  9 hours  in  the  two  classes  of  hard  mines 
mentioned,  is,  according  to  Mr.  E.  Hedburg,  as  follows: 


1 ground  boss  - 

2 miners  at  §2.00 

2 miners  at  §1.75 

2 shovelers  at  §1.75 

1 hoister 

1 engineer,  who  also  sharpens  picks  and  drills 

1 engineer  

Dynamite  - 

Fuel 

Oil  and  supplies 

Superintendent  - 

Total  - 


§ 2.50 

4.00 
3.50 

3.50 
1.75 
2.25 

1.50 

6.00 

2.50 

2.50 

3.50 
$33.40 


Or  44.5  cents  per  ton  of  rough  ore;  this  includes  pumping  the  mine. 

In  verv  soft  ground,  a drift  8 ft.  to  10  ft.  high  is  driven,  a spiling  put  in 
the  top  and  sides.  When  one  level  is  worked  out,  the  whole  drift  is  then 
caved  from  the  surface  and  allowed  to  settle  down  on  the  floor  of  timbers. 
The  cost  of  mining  in  soft  ground  is  about  the  same  as  in  hard  ore,  as  the 
saving  of  labor  and  dynamite  is  expended  in  timber  and  time.  A typical 
primitive  mining  plant  in  this  region,  which  has  a shaft  150  ft.  deep,  with 
pump,  hoisting  engines,  and  boilers,  and  including  hand  jigs,  screens,  and 
tools,  costs  from  §2,000  to  §3,000;  more  modern  plants  are  however  now 
being  erected,  costing  §8.000  to  §10,000. 


SPECIAL  METHODS. 

Frozen  Ground.— When  the  material  of  placer  deposits  is  frozen,  as  in 
Alaska  and  Siberia,  it  is  mined  by  building  a fire  on  the  surface,  which 
thaws  the  earth  to  a depth  of  from  1 ft.  to  14  in.  The  embers  are  then 
scraped  awav  and  the  thawed  material  removed.  By  repeating  this 
operation,  a shaft  can  be  sunk,  and  then,  by  building  a fire  against  one  side, 
a drift  can  be  started  and  continued  by  thawing  the  face.  1 ft.  at  a time. 
It  has  been  found  that  1 ft.  of  timber  piled  against  the  face  of  a drift  will 
thaw  to  a depth  of  about  1 ft.  The  latest  practice  thaws  the  frozen  grounc 
by  means  of  a steam  jet  instead  of  by  fire.  The  openings  have  to  be  securely 
but  not  heavily,  timbered. 

Leaching  Methods.— Salt,  copper,  and  sulphur  have  been  mined  by  leaching 
methods.  In  the  case  of  salt,  a hole  is  drilled  into  the  salt  formation,  water 
allowed  to  flow  down  and  dissolve  the  salt,  and  is  then  pumped  out  as  a con- 
centrated brine.  For  excavating  upward  in  salt,  a jet  of  water  is  made  to 
play  upon  the  roof  of  the  level  to  be  raised,  and  the  resulting  brine  is  carried 
off  'in  launders.  „ _ 

When  old  workings  containing  the  sulphides  of  copper  are  left  exposed 
to  the  action  of  air  and  to  percolating  waters,  part  of  the  copper  is  converted 
into  soluble  sulphate.  Water  pumped  from  such  mines  may  be  a profitable 
source  of  the  metal,  for  bv  passing  it  over  iron  bars  or  scrap  iron  the  copper 
will  be  separated  and  deposited  as  cement  copper  in  the  bottom  of  the 
vessel  containing  the  iron.  . 

In  the  case  of  sulphur,  superheated  steam  is  forced  down  to  melt  the 
sulphur,  which  is  then  pumped  out. 


LEHIGH  REGION. 


323 


COSTS  QF  MINING  ANTHRACITE. 

The  following  costs  include  only  labor  and  supplies,  and  do  not  include, 
in  general,  improvements,  royalties,  taxes,  and  other  similar  fixed  charges 
that  are  independent  of  the  method  of  mining. 


LEHIGH  REGION  (PENNA.). 


The  costs  for  the  Lehigh  region,  though  based  on  the  results  of  a single 
company,  are  believed  to  be  very  fairly  representative  of  the  entire  region. 
They  are  the  mean  costs  of  two  collieries  where  about  2,000  men  were 
employed  inside  and  outside,  and  apply  to  the  year  1897,  when  the  con- 
dition at  all  anthracite  mines  was  very  unfavorable  to  economical  working, 
as  the  mines  were  then  working  on  very  short  time. 

The  tonnage  at  these  collieries  for  the  year  was  as  follows: 


January,  29,775.04 
February,  30,872.97 
March,  42,827.04 

April,  38,553.08 


May,  34,090.02 
June,  35,761.89 
July,  44,409.13 
August,  37,500.97 


September,  27,406.94 1 
October,  56,710.04  ! Total, 
November,  48,177.94  [ 463,672.08. 

December,  37,587.02  J 


The  following  tables  show  the  distribution  of  this  output  by  sizes  during 
the  year,  and  the  costs  per  ton  itemized  under  the  several  headings  given: 


Percentages  of  Different  Sizes. 


Month. 

Lump. 

Broken. 

Egg. 

Stove. 

Chestnut. 

Pea. 

January 

10.56 

23.59 

18.27 

18.69 

14.21 

14.68 

February  

12.34 

22.54 

18.11 

17.98 

14.50 

14.53 

March 

11.85 

19.26 

18.81 

19.69 

13.18 

17.21 

April  

12.81 

19.21 

18.35 

19.48 

11.14 

19.01 

May 

13.81 

19.11 

18.35 

19.01 

11.32 

18.40 

June 

15.29 

18.60 

17.73 

19.08 

11.23 

18.07 

July 

14.26 

19.89 

17.41 

18.30 

11.25 

18.89 

August  

13.56 

20.26 

18.10 

17.72 

11.49 

18.87 

September 

12.31 

20.41 

18.27 

18.28 

11.61 

19.12 

October 

12.21 

18.01 

19.15 

18.89 

12.28 

19.46 

November 

11.40 

18.53 

19.78 

19.79 

12.01 

18.49 

December 

10.78 

19.56 

20.09 

20.32 

12.07 

17.18 

Year 

12.58 

19.71 

18.59 

18.99 

12.15 

17.98 

Costs  of  Mining  and  Preparation. 


Month. 

Outside. 

Inside. 

Total 

Cost. 

Credits. 

Net  Cost 

Labor. 

Supplies. 

Total. 

Labor. 

Supplies. 

Total. 

January... 

.300 

.109 

.409 

.951 

.196 

1.147 

1.595 

.100 

1.495 

February.. 

.297 

.085 

.382 

.909 

.190 

1.099 

1.519 

.063 

1.456 

March 

.243 

.047 

.290 

.844 

.151 

.995 

1.311 

.088 

1.223 

April  

.242 

.071 

.313 

.822 

.137 

.959 

1.303 

.075 

1.228 

May 

.251 

.100 

.351 

.852 

.166 

1.018 

1.397 

.103 

1.294 

June 

.300 

.079 

.379 

.500 

.203 

.703 

1.576 

.103 

1.473 

July 

.240 

.063 

.303 

.487 

.162 

.649 

1.485 

.084 

1.401 

August  .... 

.248 

.095 

.343 

.709 

.182 

.891 

1.579 

.085 

1.494 

September 

.278 

.096 

.374 

.682 

.158 

.840 

1.588 

.054 

1.534 

October.... 

.228 

.093 

.321 

.721 

.129 

.850 

1.580 

.072 

1.508 

N ovember 

.247 

.093 

.340 

.806 

.210 

1.016 

1.846 

.091 

1.755 

December. 

.290 

.061 

.351 

.833 

.220 

1.053 

1.883 

.090 

1.793 

Year  

.271 

.092 

.363 

1.109 

.162 

1.271 

1.634 

.088 

1.546 

324 


COSTS  OF  MINING  ANTHRACITE. 


Cost  per  Ton  of  Supplies  Used  Inside. 


Distribution. 

Jan. 

Feb. 

Mar. 

Apr. 

May. 1 

Jun. 

JuJ. 

Oils 

.010 

.011 

.007 

.010 

.007 

.009 

.006 

Powder 

.033 

.030 

.031 

.026 

.030 

.032 

.029 

Lumber 

.007 

.025 

.011 

.004 

.002 

.008 

.007 

Props 

Feed  

.040 

.027 

.021 

.015 

.022 

.027 

.019 

.039 

.018 

.019 

.017 

.023 

.022 

.022 

Mules  killed,  etc 

.010 

.005 

.014 

.019 

.013 

.009 

.015 

T rails,  frogs,  etc. 

Wire  ropes  

.005 

.012 

.018 

.007 

.016 

.009 

.018 

.010 

.025 

.010 

.013 

General  supplies  , — - 

.019 

.021 

.014 

.009 

.018 

.021 

.013 

Total  general  supplies 

.166 

.167 

.140 

.109 

.133 

.163 

.134 

Pumping  machinery  

Hoisting  machinery  

Ventilating  machinery 

Boilers  

.009 

.005 

.004 

.012 

.016 

.023 

.004 

Mine  cars 

Engines 

.021 

.018 

.007 

.016 

.017 

.,017 

.024 

Total  repairs  

.030 

.023 

.011 

.028 

.033 

.040 

.028 

Total  cost  inside  ' 

.196 

.190 

.151 

.137 

.166 

.203 

.162 

Credits  

.100 

.063 

.088 

.075 

.103 

.103 

.084 

Net  cost  inside - 

.096 

.127 

.063 

.062 

.063 

.100 

.078 

Cost  per  Ton  of  Supplies  Used  Outside. 


Distribution. 

Jan. 

Feb. 

Mar. 

Apr. 

May. 

Jun. 

Jul= 

QJ]g  

.010 

.008 

.007 

.006 

.009 

.009 

.008 

T.nmhpr  

.022 

.025 

.003 

.016 

.015 

.005 

.012 

Feed  - 

.008 

.004 

.005 

.004 

.005 

.005 

.006 

Mules  killed,  etc 

T rails,  frogs,  etc 

.001 

.003 

.004 

.005 

.002 

Wire  ropes  

General  supplies  

.020 

.021 

.015 

.008 

.040 

.016 

.019 

Total  general  supplies 

.060 

.058 

.031 

I .037 

.073 

.040 

.047 

Pumping  machinery  

Hoisting  machinery 

.001 

.008 

.002 

.001 

! .001 

.003 

.008 

.001 

Ventilating  machinery 

.028 

.012 

.008 

.014 

.017 

.003 

.008 

Breaker  machinery 

.011 

Boilers  

.006 

.005 

.002 

| .013 

.001 

.011 

.005 

RroalrPT  

.006 

.008 

.005 

| .006 

.005 

.006 

.002 

Tracks  and  sidings  

Miscellaneous 

1 

.001 

rVt\tnl  wnnirs  

.049 

.027 

.016 

.034 

.027 

.039 

.016 

I Uttlo  1 G 1 O ----- 

Total  cost  dutside 



1 .109 

.085 

.047 

1 .071 

.100 

.079 

.063 

Net  cost  outside 

.109 

.085 

1 

.047 

! .071 

.100 

.079 

.063 

In  the  two  tables  above  and  the  one  following,  the  figures  were  available 
for  seven  months  of  the  year  only,  but  an  average  for  these  months  gives  a 
fair  average  for  the  year. 


WYOMING  REGION. 


32S 


Itemized  Cost  of  Outside  Labor. 


Occupations. 

Jan. 

Feb. 

March. 

April* 

May. 

June. 

July. 

Foreman  and  assistants 

.013 

.012 

.007 

.006 

.006 

.006 

.003 

Clerks,  shipper  and  supply 

.004 

.004 

.003 

.003 

.002 

.002 

.002 

Hoisting  engineers 

.009 

.022 

.018 

.021 

.019 

.026 

.021 

Pump  and  fan  engineers 

.003 

.003 

.003 

.002 

.003 

.003 

Locomotive  engineers  and  helpers 

.014 

.014 

.011 

.009 

.011 

.013 

.011 

Firemen  and  ashmen 

.078 

.071 

.056 

.060 

.063 

.069 

.057 

Stablemen 

.005 

.005 

.003 

.003 

.004 

.005 

.003 

Watchmen 

.007 

.006 

.004 

.005 

.006 

.006 

.004 

Total  miscellaneous 

.133 

.137 

.105 

.109 

.114 

.130 

.101 

Topmen  and  footmen 

.004 

.004 

.002 

.003 

.003 

.004 

.003 

Top  drivers  and  oilers 

.007 

.007 

.006 

.006 

.007 

.008 

.007 

Dumpmen 

.002 

.003 

.002 

.002 

.002 

.003 

.002 

Platform  and  docking  boss 

.014 

.013 

.013 

.012 

.012 

.012 

.012 

Chute  bosses 

.006 

.006 

.005 

.006 

.005 

.004 

.006 

SI  are  pickers 

.059 

.063 

.058 

.053 

.048 

.056 

.057 

Car  loaders 

.007 

.007 

.007 

.006 

.006 

.008 

.008 

Breaker  engineer 

.003 

.003 

.002 

.002 

.002 

.001 

.002 

Dirt  and  plane  engineer 

.007 

.001 

.001 

.001 

.001 

.001 

.001 

Rock  and  dirt  men 

.007 

.009 

.009 

.006 

.004 

.005 

.005 

General  laborers 

.012 

.013 

.009 

.011 

.020 

.022 

.012 

Total  breaker 

.128 

.129 

.114 

.108 

.110 

.124 

.115 

Pumping  machinery 

.001 

.001 

Hoisting  machinery 

.010 

.005 

.005 

.005 

.006 

.009 

.005 

Ventilating  machinery 

.003 

Breaker  machinery 

.005 

.004 

.004 

.006 

.003 

.002 

.002 

Boilers 

.004 

.004 

.001 

.005 

.002 

Breakers 

.007 

.009 

.007 

.005 

.011 

.019 

.006 

Tracks  and  sidings 

.008 

.007 

.007 

.009 

.007 

.008 

.007 

Miscellaneous 

.004 

.001 

.002 

Total  repairs 

.039 

.031 

.024 

.025 

.027 

.046 

.024 

Total  cost  outside  labor 

.300 

.297 

.243 

.242 

.251 

.300 

.240 

WYOMING  REGION  (PENNA.). 

The  following  tables  of  costs  for  the  Wyoming  region  give  mean  results 
from  a number  of  different  collieries  which  are  quite  widely  separated 
in  location  and  at  which  the  conditions  of  working  are  so  different  that 
the  mean  results  given  are  thought  to  represent  average  results  for  the 
entire  region.  They  also  apply,  approximately,  to  the  Lackawanna  Valley, 
where  the  general  conditions  are  the  same,  although  the  seams  are  much 
nearer  the  surface  than  in  the  Wyoming  region,  and  the  amount  of  gas 
present  in  the  coal  is  much  less.  These  same  figures  are  probably  also  fairly 
representative  of  the  Schuylkill  and  Shamokin  fields. 

The  collieries  for  which  the  following  figures  are  averages  are  all  operated 
through  shafts,  varying  in  depth  from  350  to  1,100  ft.,  and  many  of  the  mines 
are  extremely  gaseous.  The  number  includes  several  entirely  new  and 
modern  surface  and  underground  plants,  and  the  others,  though  not  new, 
have  been  overhauled  and  modernized  as  much  as  possible.  At  these 
collieries  10,000  men  were  employed  during  the  year  1895,  for  which  the 
data  are  given,  and  during  the  same  year  the  output  was  1,862,144  tons, 
distributed  during  the  year  as  follows: 


Month. 

Ton- 

nage. 

Days 

Worked. 

Month. 

Ton- 

nage. 

Days 

Worked. 

Month. 

Ton- 

nage. 

Days 

Worked. 

January. 

107,952 

7.94 

May 

179,752 

12.84 

September 

161,213 

11.52 

February 

98,109 

7.37 

June 

164,062 

11.92 

October.... 

198,161 

13.90 

March.... 

141,991 

9.95 

July 

145,445 

10.59 

November 

228,433 

17.15 

April  .... 

136,375 

9.69 

August .. 

177,241 

12.96 

December 

123,406 

8.87 

326 


COSTS  OF  MINING  ANTHRACITE. 


Percentages  of  Different  Sizes. 


Month. 

Lump. 

Steamer. 

Broken. 

Egg. 

Stove. 

Chestnut. 

Pea. 

January  

8.21 

.02 

17.53 

20.31 

21.46 

18.04 

14.43 

February 

8.29 

.12 

17.75 

20.41 

20.85 

17.44  I 

15.14 

March  

6.20 

.55 

17.64 

20.04 

20.65 

18.00 

16.92 

April 

7.01 

.38 

16.76 

20.17 

20.92 

18.12 

16.64 

May  

4.79 

.27 

18.63 

20.33 

21.42 

18.23 

16.33 

June  

3.29 

.21 

22.43 

19.72 

20.21 

18.57 

15.57 

July  

August 

September  

October 

7.84 

.42 

19.42 

19.54 

19.46 

18.58-  ! 

14.74 

5.05 

.57 

19.84 

20.69 

18.92 

18.62 

16.31 

4.25 

.27 

18.81 

21.98 

19.98 

19.32 

15.39 

4.72 

.01 

16.77 

22.00 

21.27 

19.88 

15.35 

November  

2.69 

.16 

15.56 

22.42 

22.66 

20.71 

15.80 

December 

4.40 

.57 

14.03 

22.62 

21.27 

21.41 

15.70 

Year  

5.23 

.29 

17.96 

20.95 

20.80 

• 19.03 

15.74 

Costs  of  Mining  and  Preparation  per  Ton. 


! 

Months. 

Outside. 

Inside. 

Total  Cost. 

Credits. 

Net  Cost. 

Labor. 

Supplies,  j 

Repairs. 

Total. 

Labor. 

Supplies. 

Repairs. 

Total. 

January  

.363 

.042 

.014 

.419 

.934 

.249 

.028 

1.211 

1.630 

.120 

1.510 

February 

.376 

.042 

.014 

.432 

.047 

.273 

.030 

1.250 

1.682 

.104 

1.578 

March  

.297 

.031 

.010 

.338 

.872 

.182 

.022 

1.076 

1.414 

.096 

1.318 

April 

.305 

.034 

.023 

.362 

.870 

.203 

.020 

1.093 

1.455 

.103 

1.352 

May  

.270 

.022 

.011 

.303 

.839 

.164 

.015 

1.018 

1.321 

.101 

1.220 

June 

.290 

.032 

.011 

.333 

.874 

.206 

.018 

1.098 

1.431 

.105 

1.326 

July  

.309 

.046 

.019 

.374 

.879 

.266 

.033 

1.178 

1.552 

.098 

1.454 

August 

.286 

.030 

.017 

.333 

.873 

.194 

.026 

1.093 

1.426 

.102 

1.324 

September  — 

.284 

.039 

.012 

.335 

.890 

.201 

.024 

1.115 

1 1.450 

.105 

1.345 

October  

.267 

.036 

.013 

.316 

.856 

.188 

.020 

1.064 

1.380 

.100 

i 1.280 

November .... 

.262 

.029 

.010 

j .301 

.860 

.214 

.018 

1.092 

1.393 

.104 

1.289 

December  .... 

.344 

.045 

.018 

! .407 

.954 

.307 

.028 

1.289 

1.696 

.120 

1.576 

Year 

.297 

.034 

.014 

| .345 

.881 

.214 

.023 

1.118 

1.463 

.104 

1.359 

Coal  Production  of  United  States. 


Year. 

Bituminous. 

Anthracite. 

Tons  of  2,000  Lb. 

Value. 

Tons  of  2,240  Lb. 

Value. 

1890 

1895 

1897 

1898 

1899 

111,302,322 

135,118.193 

147,609.985 

166,592,023 

193,321,987 

$110,420,801 

115,779,771 

119,567,224 

132,586,313 

167,935,304 

46,468,641 

57.999,937 

52,611,680 

53,382,644 

53,944,647 

$66,383,772 

82,019,272 

79,301,954 

75,414,537 

88,142,130 

PRICES  OF  COAL. 

The  table  on  page  327,  given  by  the  U.  S.  Geological  Survey  ,will  be  of  interest 
as  showing  the  fluctuations  in  the  average  prices  ruling  in  each  State  since  188t. 
Prior  to  that  vear.  the  statistics  were  not  collected  with  sufficient  accuracy  to 
make  a statement  of  average  prices  of  any  practical  value.  These  averages  are 
obtained  bv  dividing  the  total  value  by  the  total  product,  except  for  the  years 
1886, 1887,  and  1888,  when  the  item  of  colliery  consumption  was  not  considered 


Average  Prices  per  Short  Ton  for  Coal  at  the  Mines  Since  1886. 


PRICES  OF  COAL.  327 


1901. 

05  CO  O CO  O CO  rH  rH  05  ©1  lO  0©  rH  CO  CO  ©!©00©©la0©>©l©©©«0© 

OHOHCj  © © so  CO  ©J  05  05  t}J  ©J  TjH  T(H©l©lO5©©rHt''-©J00©QOCO 

rH  rH  ©4  rH  >—1  HHHHH  H H H Hr- In  ©4  rH  rH  rH  rH  rH 

1.04 

1.67 

1.18 

•0061 

N-^iOWNOHCOiOGOMCJOOCOHCO  t^©)©l©l">HI>Tt<CO<0©©rH© 

HHOHHOOO^CONOOHCjO  C0CC^ONOJH<O(N00  0500M 

HHCOHH^HHHHri  tHVh  rH  iHi—irHrHCO  H H H rH  rH 

1.04 

1.49 

1.14 

1899. 

05  1>  00  <N  © O iO  00  CO  T*KO  05  CO  05  O O © 00  rH  I>  <M  00  CO 

©rH©rH©©OOOOHJC^rHt^I>-CO<NiO  C0C0rH00Ol>C0i0<N©l>«0<N 

rH  rH  ©4  rH  rH  © HHH  rH  rH  rH  rH  rH  rH  CO  HH  rH  rH 

rO 

.87 

1.46 

1.01 

1898. 

iCC0C0iOHN0OH(N^OiO5<ONNN  © © rH  CO  © IH  t'-  © © 00  rH  CO 

t^©U0rH00u0lH0qc0rH©lHlH'^©lO  COC^rHOO©©l^©<NlOlH©(N 

© rHCirH  c4  HHH  HHH  rH  rH  rH  CO  H H rH  rH 

.80 

1.41 

£ 

1897. 

00©iCt^<MC0!NTtlTflC0a0O5©©a0©  OOT^OOOO©©rH(M©lH'HCOrH 

00©uOrHl^COl^OOCOr-irHt-l>:T}|©t^  COC0©l>©©00©rH©O5©©J 

© rH  ©1  rH  CO  rHrHrH  rH  rH  rH  rHrHrH  CO  rH  rH  rH  rH 

^ © <0 

.81 

1.51 

© 

© 

1896. 

©rH©<D©  © Ttl  © © 00  © <N  GO  1H  ©©©©©  rH  ©©©  GO  ©© 

05  rH  CO  rH  00G0r^rHrHt>-Q0CO©T^  ^LOOi>05I^GO©©;©©©CO 

© rH  ©4  r-i  HrHn  rHrHrH  rHrHrH  ©4  rHrH  ©4  rH 

HO  O 

.83 

.1.50 

1.02 

1895. 

©UOCO©CO  © rH  CO  ©©©  rH  © ©3  © ©©  1H  ©<0  <N  CO  00  rH  CO  © 00  CO 

05  ©j  CO  ©J  00  GO  05  ©}  ©4  00  GO  © rH  go  T^©©l>;C0t>O5  00  CO©rH©CO 

© rH©)rH  rHrHrH  rHrHrH  rHrHrH  CO  rHrH  ©l  rH 

.86 

1.41 

1.02 

1894. 

CO©JrH-^lO  © © © © CO  CO  t>»  !>•  fr  © tr  © ©1  CO  t"  |>.  ©J  © © CO  © rH 

05  ©1  CO  ©|  CO  <»O5©©|©3(»l^TtfrH©rH©|>.rHa5<»^O5C0'>HX>COI>;C0 
© rH  ©Q  rH  rHrHrH  rHrH©icOrHrHrH  CO  ©l  rH  ©4  rH 

.91 

1.52 

1.09 

CO 

05 

GO 

rH 

©rfrHTfOO  © © GO  © CO  © tr  © CO  ©^  © 00  00  00  ^ rH  1>  lO 

05  CO  CO  ©|  05  CO  © CO  ©}  GO  GO  ©J  05  © H 05  © GO  © ©1  hJH  GO  CO  I>  CO 

rH  ©4  rH  rH  rH  rH  rH  rHrHrH  t— 1 H rH  CO  rH©4rH  ©4  rH 

.96 

1.59 

1.14 

1892. 

r|« 

© ^ © ©}  © rH  00  rH  ©1  H ©J  05  © CO  © ©|Tf©r^©^HCO©l©©GO©rr 

rH©JHJ©05  05  © l>  CO  CO  05  GO  © ©}  CO  © 05  05  ©q  00  rH  CO  © GO  ©J  GO  ©] 

rH  rH©i^H  rHrHrHrH  rH  rH  ©5  rHrH  tJ*  rH  ©l  rH  ©4  rH 

.99 

1.57 

1.16 

1891. 

t"  © © t''-  © HCOHt^HCOH©CON  QOCO©^©tr  rH  ©©  CO  rH  © CO 

© rH  ©1  CO  © 05©!>©qc0  0500©©^©q  ©05TjH05©OqrHT^GOGOCOQO© 

H H ©j  H H HHHrH  rH  rH  ©4  rHrHrH  CO  t— 1 ©1  r-i  ©4  rH 

.99 

1.46 

1.13 

1890. 

C0O5©©TjH  CO  © ©J  rfH  © ©|  © as  ©J  © rf  © CO  © — 1 ^ © 

©©4©t1H©  0505GO©aC0  0500  05©Jrt<  CO  tr  TfJ  05  GO  GO  rH  © tr  !>.  |>.  00  t". 

rH  rH  ©4  rH  rH  V "rHrHrH  " ‘ rH  rH  ©4  rHrHrH  ‘©4  * rH  ©4  rH  ’©4  ’ rH 

.99 

1.43 

1.12 

1889. 

rH©J©rH©  X'-  ©J  © CO  GO  ©©  rH  © ©1  © COCO  rH  © © CO  ©1  ©J  © 

rH  Tf  CO  © © ©<©t>-COT^©QOI>.CO'rtl  t'r  rj<©  !>©1©©©COOO©I 

H rl  ©4rH  H rlnHH  rH  rH  ©4  rH  rH  rH  ©4  rH  ©4  rH 

w 

1.00 

1.44 

1.13 

1888. 

©©©©©  ©1  © GO  © © © © © rH  © © ©CO©©©©©©©©© 

rH©©©{©  rHTjJ  00  CO  © ©J  © © ©J  © © ©05©©rH©rH©©rH© 

HHT(i©iH  HhHHHH  rH  ©4  CO  CO  CO  CO  rH  ©4  ©4  rH  CO  rH  CO 

a 1.00 
a 1.95 

a 1.42 

1887. 

©GO©©©  ©HfrrHtl©©©©T^©  © ©00©©©©©^©©© 

CO©©©j©  ©COOOCOTHrH05©CO©  © ©GO©l©CO©©©©l©© 

rH  rH  CO  ©4  rH  rH  rH  rH  —5  rH  rH  * rH  rH  CO  CO  rH  "©4  " rH  ©j  ©j  '©4  ‘ CO 

W 

a 1.12 
a 2.01 

a 1.45 

1886. 

CO©©©©  rH©©©©©©0©©  © © © © © © © © © © rH  © 

Tf  © © CO  © rHrH©©}©XrH©©CO©  © © © © GO  rH  00  rH  © ©l  © © 

rH  rH  CO  ©<  l-H  HHHHHH  H H CO  CO  rH  ©4  rH  rH  ©4  rH  ©J  CO 

a 1.06 
a 1.95 

a 1.30 

State  or  Territory. 

Alabama 

Arkansas 

California  

Colorado 

Georgia 

Idaho 

Illinois 

Indiana 

Indian  Territory 

Iowa 

Kansas 

Kentucky  

Maryland 

Michigan 

Missouri  

Montana 

Nevada 

New  Mexico 

North  Carolina 

North  Dakota  

Ohio  

Oregon  

Pennsylvania  bituminous 

Tennessee  

Texas 

Utah  

Virginia  

Washington  

West  Virginia 

Wyoming 

Total  bituminous  

Pennsylvania  anthracite.... 

General  average 

a Exclusive  of  colliery  consumption,  b Includes  Alaska,  c Includes  Nebraska. 


328 


COST  OF  COKING  COAL. 


COST  OF  COKING  COAL 

The  cost  for  labor  alone  of  coking  coal  has  been  given  by  a number  of 
companies  in  the  Connellsville  district  as  61  cents  per  ton  of  coke  produced, 
or  40j  cents  per  ton  of  coal  coked,  exclusive  of  royalties,  taxes,  rents,  and 
such  fixed  charges. 

In  the  “American  Manufacturer”  for  July  27,  1899,  Mr.  F.  C.  Keighley 
gave  the  following  as  the  proportional  costs  of  the  several  items  of  mining 
and  coking  Connellsville  coal: 


Coke  Yard. 

Per 

Cent. 

Coke  Yard. 

Per 

Cent. 

Drawing 

70.01 

Shifting  cars 

1.28 

Leveling 

8.96 

Y"ard  bosses  

1.12 

Charging 

3.48 

Masons  on  repairs 

6.12 

Carters 

Bookkeeper  and  superin- 

2.48 

Forking 

Individual  cars  

1.60 

.52 

tendent,  £ of  total  for 

Sundry  

.51 

TYviTTA  q nn  vfi rn 

2.04 

1.20 

Yard  pumps 

.76 

III!  1 1 tv  allU  J Ql  vA  

Cleaning  tracks 

Total  - 

100.08 

Mine. 

Per 

Cent. 

Mine. 

Per 

Cent. 

Room  coal 

52.15 

Machinist  

.49 

Drivers - 

8.07 

Bookkeeping,  £ of  total  for 

TTpudin?  oorI  i 

11.15 

mine  and  yard..: 

.49 

Rope  haulage  

2.81 

Outside  labor  1 

2.03 

Roads  

3.03 

Stable  boss 

.96 

Mine  bosses  

1.31 

Teams 

.65 

Fire  boss 

1.44 

Blacksmith  

.98 

Timber 

2.83 

Carpenters 

f 1.01 

.43 

Lamp  cleaners 

.82 

irdpptib - 

Superintendence,  £ of  total 

Inside  pumps  

.59 

for  mine  and  yard 

.49 

Steam  pumps  

.55 

Cagers  

.66 

Surveys  

.41 

Runners  and  oilers  

.80 

Extra  men 

.51 

Engineers  

1.01 

Supplies - 

.92 

Vi  rPTTIPTI 

1.13 

Betterments  - 

1.05 

Dumpers 

1.25 

Total 

100.02 

The  mine  labor  is  67.20£  of  the  total  labor  cost,  and  the  coke-yard  labor  is 
32.804  of  the  total  labor  cost. 

The  cost  of  equipping  a coke  plant  and  opening  a mine  to  furnish  the 
coal  in  the  Connellsville  region  is  from  8500  to  $1,000  per  oven,  dependent  on 
the  kind  of  opening  for  the  mine  and  local  considerations.  8500  per  oven  is 
a fair  price  for  a plant  when  the  conditions  are  favorable  and  the  mine  is  a 
drift  mine,  and  81.000  is  a fair  price  for  a shaft  mine  about  300  ft.  deep, 
under  rather  unfavorable  conditions. 

Fulton  gives  the  cost  of  the  various  types  of  coke  ovens  as  follows: 

Not  saving  by-products:  Beehive,  8300;  Thomas,  8800;  McLanahan,  8800; 

Belgian,  81,000;  Cop  pee.  81.000;  Bernard,  81,000.  „ 

Saving  by-products:  Simon  Carves,  81.300;  Semet-Solvay.  $1,600;  Huessner, 
81,400;  G.  Seibel.  81.300;  Otto-Hoffman.  81.600;  Festner-Hoffinan,  81.500. 

The  usual  quantitv  of  coal  required  to  make  1 ton  of  coke  is  1.4  to  1.6  tons. 
The  lo<5s  in  loading  coke  at  the  ovens  and  again  unloading  it  at  the 
furnaces  or  steel  works  is  24  to  34.  During  the  winter  and  in  wet  seasons 
coke  takes  on  2d'  to  3*  of  moisture  in  transit  between  the  ovens  and  the 
furnaces. 


EXPLOSIVES. 


329 


EXPLOSIVES. 

The  characteristics  of  a good  blasting  explosive  are:  (1)  sufficient  stability 
and  strength;  (2)  difficulty  of  detonating  by  mechanical  shock;  (3)  handy 
form;  (4)  absence  of  injurious  effects  on  the  user. 

Explosives  are  divided  into  two  general  classes:  (1)  low  explosives  or 
^.irect-exploding  materials;  (2)  high  explosives  or  indirect-exploding  mate- 
rials that  require  a detonator. 

Low  Explosives.— Gunpowder  or  black  powder  is  the  type  of  this  group. 
Its  composition  varies,  depending  on  the  purpose  for  which  it  is  to  be  used, 
but  the  ingredients  commonly  used  in  its  manufacture  are  saltpeter,  sulphur, 
and  charcoal. 

The  following  table  gives  the  composition  of  blasting  powder  in  different 
countries: 

Composition  of  Blasting  Powder  ( Guttmann ). 


Ingredients. 

Great 

Britain. 

Germany. 

Austria- 

Hungary. 

France. 

Russia. 

Italy. 

United 

States. 

Saltpeter 

75 

66.0 

64 

62 

66.6 

70 

64 

Sulphur 

10 

12.5 

16 

20 

16.7 

18 

16 

Charcoal  

15 

21.5 

20 

18 

16.7 

12 

20 

High  Explosives.— These  are  a mixture  of  nitroglycerine  with  an  absorbing 
dope,  the  composition  of  which  is  such  that,  in  addition  to  thoroughly  and 
permanently  absorbing  the  nitroglycerine,  it  is  itself  a gas-producing  com- 
pound. Nitroglycerine  at  60°  F.  has  a specific  gravity  of  1.6.  It  is  odorless, 
nearly  or  quite  colorless,  has  a sweetish  burny  taste,  is  poisonous  even  in 
very  small  quantities,  and  is  insoluble  in  water.  All  nitroglycerine  com- 
pounds freeze  at  42°  F.,  and  explode  when  confined  at  360°  F.  It  takes  fire 
at  306°  F.,  and,  if  unconfined,  burns  harmlessly  unless  in  large  quantities,  so 
that  a part  of  it,  before  coming  in  contact  with  the  air,  becomes  heated  to 
the  exploding *point. 

Thawing  Dynamite. — All  frozen  cartridges  should  be  thawed,  as,  when 
frozen,  cartridges  are  very  hard  to  explode,  and  even  if  they  do  explode, 
the  results  are  not  nearly  as  satisfactory  as  when  properly  thawed.  When 
cartridges  are  frozen,  do  not  expose  to  a direct  heat,  but  thaw  by  one  of 
the  following  methods:  First,  place  the  number  of  cartridges  needed  for 

a day’s  work  on  shelves  in  a room  heated  by  steam  pipes  (not  live  steam) 
or  a stove.  Where  regular  blasting  is  done,  a small  house  can  be  built  for 
this  purpose,  fitted  with  a small  steam  radiator.  Exhaust  steam  through 
these  pipes  gives  all  heat  necessary.  Bank  your  house  around  with  earth, 
or,  preferably,  fresh*  manure.  Second,  use  two  water-tight  kettles,  one 
smaller  than  the  other,  put  cartridges  to  be  thawed  in  smaller  kettle,  and 
place  it  in  larger  kettle,  filling  space  between  the  kettles  with  hot  water  at, 
say,  130°  to  140°  F.,  or  so  that  it  can  be  borne  by  the  hand.  To  keep  water 
warm,  do  not  try  to  heat  it  in  the  kettle,  but  add  fresh  warm  water.  Cover 
kettles  to  retain  heat.  In  thawing  do  not  allow  the  temperature  to  get 
above  212°  F.  Third,  where  the  number  of  cartridges  to  be  thawed  is  small, 
they  may  be  placed  about  the  person  of  the  blaster  until  ready  for  use,  the 
heat  of  the  body  thawing  the  cartridges.  Keep  cartridges  away  from  all 
fires— this  applies  to  all  explosives.  Do  not  be  in  a hurry,  but  thaw  slowly. 
Do  not  thaw  before  an  open  fire.  Do  not  put  cartridges  in  an  oven,  on  a hot 
stove,  against  hot  iron  plates,  or  against  brick  casing  of  a boiler.  Do  not  put 
cartridges  in  hot  water,  or  expose  them  to  live  steam.  And  do  not  take  any 
kind  of  powder,  fuse,  or  caps  near  a blacksmith  shop. 

A large  number  of  high  explosives  are  made  that  vary  but  little  in  their 
composition,  the  main  difference  being  in  the  character  of  the  dope  and  in 
the  percentage  of  nitroglycerine.  The  trade  name  is  usually  determined 
by  the  percentage  of  nitroglycerine,  thus  10/«  dynamite  means  that  the  dyna- 
mite contains  10 Jo  of  nitroglycerine,  etc. 

Safety  explosives,  or  as  they  are  called  in  England,  -permitted  explosives,  are 
compounds  intended  for  use  in  gaseous  mines,  and  they  are  so  constituted 


330 


EXPLOSIVES. 


that  they  will  ignite  without  producing  the  extremely  high  temperature 
given  by  ordinary  explosives.  The  term  flameless  explosives  was  formerly 
used,  but  it  has  been  replaced  by  safety  explosives , as  the  absence  of  a flame 
is  not  now  necessary  to  a permitted  explosive. 

Common  Blasting  Explosives. 


Atlas. 


A 

B+ 

B 

C + 

c 

D+ 

D 

E + 
E 


<x> 

M <V 
<D  O 

ft  be 
CD  o 

Ph  H 


75 

60 

50 

45 

40 

33 

30 

27 

20 


Brands  Equivalent  in  Strength  to  Atlas. 


a> 

0 

o 

a 

3 

p. 

0> 

P4 


A 

B + 

B 

C + 

c 


No.  1 XX 
No.  1 
No.  2 SS 
No.  2 S 
No.  2 
No.  2 C 
No.  3 
No.  3B 
No.  4 B 


& 

£ 

(2 

1 

0 


No.  1 XX 
No.  1 
No.2SS 
No.  2S 
No.  2 


Old  No.  1 
No.  1 A 
New  No.  1 
No.  2 Extrs 
No.  2 
No.  2C 
No.  3 
XXX 

xxxx 


Giant  Gelatine. 

Hecla  Powder. 

9 

cD 

£ 

o 

Ph 

o3 

% 

No.  1 A 

No.  1 XX 

No.  1 

No.  1 XS 

No.  1 

No.  2 

i 

No.  IX 

No.  2 XX 
No.  2 X 

No.  3 C 

No.  1 

No.  2 

No.  2X 

No.  3 A 

No.  2 

No.  3 

No.  3 X 

No.  3B 

No.  3 

No.  4 

Drilling  -Adapt  the  size  and  depth  of  the  hole  to  the  work  to  be  accom- 
plished As  a rule  for  ordinary  rock  blasting,  the  distance  between  the  boles 
shouM  be  equa?to  from  one-half  to  the  total  depth  of  the  holes,  the  holes 
set  back  from  the  face  twice  as  far  for  dynamite  as  for  common  black 
powder  sav  a distance  equal  to  the  depths  of  the  holes  or  slightly  less,  and 
Cd  oSe-third  1 thl  lenlth  of  the  hole^  These  directions  are  only  general, 
and  do  not  apply  to  very  deep  holes.  dePe^ 

ness  of  the  rock,  also  on  size  of  drill  holes.  In  all  cases,  the  experience 

shafts,  experience  shows 

in  weak  rock.  All  the  holes  in  the  heading  or  shaft  should  have  the  same 

“iff  SSSSSS-t 

the  free  faces  formed  by  firing  the  previous  holes  , . 

l"°ho!e  should^ever'hS’e^ a^harge™  f Smore  than  12  in.  of  explosive  placed 
iu  it  Where  several  holes  are  fired  together,  this  rule  is  sometimes  slight  y 
deviated  from It  fs  usually  best  to  employ  a length  of  charge  between  these 
two  limits  as  for  instance,  about  10  times  the  diameter  of  the  hole* 

Chambering  orsquibbing  is  the  blasting  out  of  a cavity  at  the  bottom  of  a 
drill  hole  to  allow  of  a larger  charge  of  explosive  being  used.  . , 

Rniiino  a drill  hole  is  the  working  of  clay  into  any  cracks  op^hing  into 
a drill  "lofe  to  p?eveit  the  power  gof  the  "blast  being  scattered  through 

thecharCgrh.|k-The  charge  must  fit  and  fill  the  bot^m  of  bore  and  be  packed 
wise  with 


. -The  charge  must  fit  and  fill  the  bottom  of  bore  and  be  pacK< 
a'knife,  a^^^achH^S’oppe^ into^the^hole,Cstrikega  wooch 


h* 

len 


BLASTING. 


331 


rammer  on  it  with  sufficient  force  to  make  the  powder  completely  fill  the 
bottom  and  diameter  of  the  bore.  Where  water  is  not  present,  a more  per- 
fect loading  is  made  by  taking  powder  out  of  cartridge  and  dropping  it  in 
loosely,  ram  each  6 or  8 in.  of  the  charge,  using  the  paper  of  each  cartridge 
as  a wad,  to  take  down  any  powder  that  may  have  stuck  to  the  sides  of  the 
hole.  If  water  is  standing  in  the  hole,  do  not  break  the  paper  of  the  car- 
tridges and  avoid  ramming  more  than  enough  to  settle  the  charge  on  the 
bottom, using  cartridges  of  as  large  diameter  as  will  readily  run  into  the  bore. 

When  cartridges  are  used,  the  last  cartridge  placed  in  the  hole  should 
contain  an  electric  exploder,  or  cap  with  fuse  attached.  When  loose  powder 
is  used,  a piece  of  cartridge  2 or  3 in.  in  length,  with  exploder  or  cap  attached, 
should  be  pressed  firmly  on  top  of  charge.  Some  blasters  put  an  exploder  or 
cap  in  the  first  cartridge  put  in  the  hole,  placing  remainder  of  charge  on  top. 
The  charge  should  be  placed  in  a solid  part  of  the  material  to  be  broken.  If 
possible,  the  face  should  be  undercut  and  then  the  overhanging  material 
shot  down.  Best  results  are  obtained  when  the  bore  holes  cross  the  faces  or 
layers  of  the  material  at  right  angles.  The  charges  should  be  placed  so  as  to 
disturb  the  sides  and  roof  of  a tunnel  through  material  of  medium  hardness 
as  little  as  possible.  The  charge  at  the  bottom  of  the  tunnel  snould  be 
placed  from  6 to  12  in.  below  the  permanent  level. 

Amount  of  Charge. — No  invariable  rule  can  be  laid  down  as  to  the  diameter 
and  length  of  cartridges  to  be  used  under  any  and  all  circumstances,  nor  the 
amount  or  grade  of  powder  required  for  all  kinds  of  work.  Much  depends 
on  the  good  sense  and  judgment  of  the  persons  using  the  explosive. 
Guttmann,  in  his  well-known  handbook  on  blasting,  says:  “There  is  no  lack  of 
theories  for  tne  determination  of  blasting  charges,  ‘but  their  application 
depends  on  empirical  facts  determined  by  practical  work.  I therefore 
advise  that  the  calculation  of  charges  under  ordinary  conditions  be  neg- 
lected, and  recommend  watching  actual  operations  for  some  weeks,  asking 
for  explanation  from  the  most  expert  miners.  In  this  way  experience  will 
be  gotten  in  a short  time  that  will  enable  one  to  estimate  with  some  precision 
the  proper  charge  to  use  after  inspecting  the  spot  to  be  blasted." 

A good  rule  by  which  to  determine  the  weight  of  black  powder  to  use  in 
any  given  hole  in  bituminous  workings  is  the  following:  Find  the  distance 
in  feet  from  the  charge  out  in  the  line  of  least  resistance.  Multiply  the 
fourth  power  of  this  distance  by  ^ the  diameter  of  the  hole  in  inches,  and 
divide  this  product  by  the  thickness  of  the  seam  in  inches.  The  result  will 
be  the  weight  of  the  charge  in  pounds.  Thus,  for  a 2\rt  hole  in  a seam  of 
bituminous  coal  6 ft.  thick,  where  the  charge  is  placed  4£  ft.  deep  from  the 
face  of  the  coal,  or  cutting,  we  have  for  the  weight  of  charge  to  be  used, 


9 X 9 - 9 - 9 ^-4X2-5  5 71b 

2 X 2 X 2 X 2 X 6X  12  6 


Tamping.— -In  deep  holes,  water  makes  a good  tamping,  but  fine  sand, 
clay,  etc.  are  generally  used.  Fill  in  for  the  first  5 or  6 in.  carefully,  so  as 
not  to  displace  cap  and  primer;  then  with  a hardwood  rammer  pack  bal- 
ance of  material  as  solid  as  possible,  ramming  with  the  hand  alone,  and  not 
using  any  form  of  hammer.  Never  use  a metal  tamping  rod. 

Firing.— If  the  work  is  wet,  or  the  charge  used  under  water,  use  water- 
proof fuse,  and  protect  the  end  of  the  fuse  by  applying  bar  soap,  pitch,  or 
tallow  around  the  edge  of  the  cap.  Water  must  not  be  allowed  to  reach  the 
powder  in  the  fuse  or  the  fulminate  in  the  cap.  Exploding  by  electricity  is 
best  under  water  at  great  depth,  as  the  pressure  of  water  is  so  great  on  the 
fuse  that  it  is  forced  through  and  dampens  it  so  as  to  prevent  firing. 

Seam  Blasting.— If  a seam  is  found  in  the  rock,  remove  the  powder  from 
the  cartridges  and  push  it  into  the  seam  and  fire  a cap  beside  it.  This  will 
open  the  seam  so  that  a larger  quantity  of  explosive  can  be  used,  and  the 
rock  broken  without  drilling.  In  blasting  coal,  slate,  marble,  granite,  free- 
stone, or  any  other  material  that  it  is  desirable  to  obtain  in  large  blocks, 
cartridges  of  small  diameter  should  be  used  in  wide  bore  holes,  the  charge 
being  rolled  in  several  folds  of  paper,  to  prevent  its  touching  the  sides  of  the 
bore  holes.  The  intensity  of  action  and  the  crushing  effect  of  the  explosive 
are  thus  lessened. 

Firing  by  Detonation.— Nitroglycerine  explosives  always  require  detonation 
by  a cap  or  exploder  in  order  to  develop  their  full  force.  Fig.  1 illustrates 
the  method  of  attaching  such  an  exploder  to  the  end  of  a fuse  and  the  pla- 
cing of  it  in  the  cartridge.  The  exploders  are  loaded  with  fulminate  of  mer- 
cury and  are  slipped  over  the  end  of  the  fuse,  after  which  the  upper  end  is 


332 


EXPLOSIVES. 


crimped  tightly  against  the  end  of  the  fuse,  as  shown.  (Miners  sometimes 
bite  the  caps  on  to  the  fuse  w ith  their  teeth.  This  is  a very  dangerous  pro- 
ceeding and  should  never  be  allowed,  as,  with  strong  caps,  one  of  them 
exploding  in  a man’s  mouth  would  prove  fatal.)  In  placing  the  cap  or 


Fig.  1. 


Fig.  2. 


Fig.  3. 


exploder  into  the  dynamite  or  giant-powder  cartridge,  care  should  be  taken 
that  only  about  two-thirds  of  the  cap  be  embedded  in  the  material  of  the 
cartridge,  for  if  the  fuse  had  to  pass  through  a portion  of  the  material  before 


reaching  the  cap.  there  w ould  be  danger  of  its  igniting  the  material,  thus 
causing  deflagration  of  the  cartridge  in  place  of  detonation.  The  fumes 
given  off  by  high  explosives  are  much  w^orse  in  the  case  of  del 
cartridge. 


The  electric  exploder,  Fig.  2,  has  wires  A and  B , which  carry  the  current  to 
the  exploder.  D is  a cement  (usually  sulphur)  that  protects  the  explosive 
compound  C (usually  mercury  fulminate)  and  the  w^hole  is  contained  m a 
Conner  shell.  A small  platinum  wire  E is  heated  by  the  passage  of  a current 
^ and  ignites  the  explosive.  Fig.  3 

shows  the  method  of  placing  a cap 
or  an  electric  exploder  in  a cartridge 
of  powder. 

When  a number  of  holes  are  ex- 
ploded at  one  time,  the  electric 
exploders  are  connected  in  series,  as 
shown  in  Fig.  4,  for  a small  number 
of  holes,  and  as  in  Fig.  5 for  a larger 
number. 

The  battery  for  furnishing  the 
current  of  electricity  is  a magneto 
machine  that  is  worked  by  either  pulling  up  or  by  depressing  a handle  or 
rack  bar,  or  else  by  turning  a crank.  _ . , . . 

Directions  for  Blasting  by  Electricity.— Drill  the  number  of  holes  desired  to  be 


Fig.  4. 


fired  at  one  time;  depth  and  spacing  of  holes  depending  on  character  of 
rock  size  of  drill  holes,  etc.,  the  blaster,  of  course,  using  his  judgment  in  this 
matter  Load  the  hole  in  the  usual  manner,  fitting  one  cartridge  with  a fuse 


ARRANGEMENT  OF  DRILL  HOLES. 


333 


(electric  exploder)  instead  of  cap  and  fuse.  The  fuse  head  is  fitted  into 
the  bottom  end  of  the  cartridge,  or  into  the  middle  of  one  side  of  the 
cartridge,  where  a hole  has  been  punched  with  a pencil  or  small  sharp  stick 
to  receive  it;  push  the  powder  close  around  the  fuse  head.  The  fuse  can  then 
be  held  in  position  by  tying  a string  around  the  cartridge  and  the  fuse  wires, 
binding  the  wires  to  the  cartridge,  as  shown  in  Fig.  3.  A shows  head  of  fuse,  £ 
the  two  fuse  wires,  C string  used  to  tie  wires  to  cartridge.  Avoid  taking 
hitches  in  fuse  wires,  as  by  this  very  common  practice,  the  insulation  of 
the  wires  may  be  injured  and  the  current  of  electricity  may  pass  from  one 
wire  to  the  other,  without  passing  through  the  cap,  hazarding  a misfire. 

The  cartridge  containing  the  fuse  is  put  in  on  top  of  the  charge  by  some 
blasters;  by  others,  at  bottom  of  the  charge.  The  best  place  for  it  is  in  the 
center  of  the  charge,  having  part  of  the  charge  above  and  part  below  it. 
In  tamping  the  hole,  great  care  must  be  taken  not  to  cut  the  wires,  or  injure  the 
cotton  covering  of  fuse  wires,  or  to  pull  the  fuse  out  of  the  cartridge.  Allow 
at  least  8 in.  of  the  fuse  wire  to  project  above  the  hole,  to  make  connections. 

When  all  the  holes  to  be  fired  at  one  time  are  tamped,  separate  the  ends 
of  the  two  wires  in  each  hole,  and,  by  the  use  of  connecting  wire,  join  one 
wire  of  the  first  hole  with  one  of  the  second,  the  other  or  free  wire  of  the 
second  with  one  of  the  third,  and  so  on  to  the  last  hole,  leaving  a free  wire 
at  each  end  hole. 

All  connections  of  wires  should  be  made  by  twisting  together  the  bare 
and  clean  ends;  it  is  best  to  have  the  joined  parts  bright.  Scrape  off  the  cotton 


covering  at  the  ends  of  the  wires  to  be  connected,  say  for  2 in.,  then  rub  the 
wire  with  a small  hard  stone.  This  makes  a bright  fresh  wire.  Be  sure  that 
all  connections  are  clean,  bright,  and  well  twisted.  Do  not  hook  or  loop  wires 
in  making  connections.  Bare  joints  in  wire  should  never  be  allowed  to  touch 
the  ground,  particularly  so  if  the  ground  is  wet.  This  can  be  prevented  by 
putting  dry  stones  under  the  joints.  The  charges  having  all  been  connected, 
as  directed  above,  the  free  wire  of  the  first  hole  should  be  joined  to  one  of  the 
leading  wires,  and  the  free  wire  of  the  last  hole  to  the  other  of  the  two 
leading  wires.  The  leading  wires  should  be  long  enough  to  reach  a point  at 
a safe  distance  from  the  blast,  say  250  ft.  at  least.  All  being  ready,  and  not 
till  the  men  are  at  a safe  distance,  connect  the  leading  wires,  one  to  each  of 
the  projecting  screws  on  the  front  side  or  top  of  the  battery,  through  each 
of  which  a hole  is  bored  for  the  purpose,  and  bring  the  nuts  down  firmly  on 
the  wires.  Now,  to  fire,  take  hold  of  the  handle  for  the  purpose,  lift  the 
rack  bar  (or  square  rod,  toothed  on  one  side)  to  its  full  length,  and  press  it 
down,  for  the  first  inch  of  its  stroke  with  moderate  speed,  but  finishing  the 
stroke  with  all  force,  bringing  rack  bar  to  the  bottom  of  the  box  with  a solid 
thud,  and  the  blast  will  be  made.  Do  not  churn  rack  bar  up  and  down.  It 


334 


EXPLOSIVES. 


is  unnecessary  and  harmful  to  the  machine.  One  quick  stroke  of  the  rack 
bar  is  sufficient  to  make  the  blast.  Never  use  fuses  (exploders)  made  by 
different  manufacturers  in  the  same  blast.  Connecting  wire  should  be  of 


Fig.  8.  Fig.  9. 


same  size  as  the  fuse  wire;  leading  wire  should  be  at  least  twice  as  large. 
Covering  on  wire  should  not  “ strip  ” or  come  off  easily. 

The  power  of  an  explosive  cannot  be  exactly  calculated  from  the  quantity 
and  temperature  of  the  gas  resulting  from  its  detonation,  as  it  is  impossible 
to  determine  the  exact  composition  of  gas  at  the  moment  of  explosion  and 
during  the  subsequent  cooling  period.  Tables  that  give  the  relative  strength 


Fig.  10.  Fig.  11. 


of  explosives  are  apt  to  be  misleading,  as  so  much  depends  on  the  compo- 
sition of  the  explosive,  and  since  there  are  so  many  explosives  of  varying 
compositions  that  are  sold  under  the  same  name. 

Pressures  Developed  by  Explosives.— According  to  experiments  conducted 


ARRANGEMENT  OF  DRILL  HOLES. 


335 


by  Sarrau,  Vielle,  Nonle,  and  Abel,  the  following  approximate  maximum 
pressures,  in  tons  per  square  inch,  developed  by  various  explosives,  have 
been  arrived  at:  Mercury  fulminate,  193;  nitroglycerine,  86;  guncotton,  71; 
blasting  powder,  43.  _ , . 

Values  of  Explosives.— Taking  gunpowder  (containing  61#  saltpeter)  as  a 
standard,  and  calling  its  value  1,  the  following  are  the  comparative  values 


Fig.  12.  Fig.  13. 


of  the  other  explosives:  Dynamite,  containing  75#  nitroglycerine,  2.2;  blasting 
gelatine,  containing  92 # nitroglycerine,  3.2;  nitroglycerine,  3.3. 

The  arrangement  of  aril  I holes  for  driving  and  sinking  should  be  such  as  to 
permit  the  easy  handling  of  the  drills  and  also  to  minimize  the  number  of 
holes  and  the  weight  of  explosive.  Two  distinct  systems  are  m use:  (1)  the 
center  cut , by  which  a center  core  or  key  is  first  removed,  and  after  that 
concentric  layers  about  this  core;  (2)  the  square  cut , in  which  the  lines  of 


336 


MACHINE  MIXING. 


holes  are  parallel  to  the  sides  of  the  excavation,  the  rock  being  removed  in 
wedges  instead  of  in  concentric  circles. 

The  center-cut  method  is  shown  in  Figs.  6,  7,  8,  and  9,  Fig.  6 showing  the 
face  of  a heading,  Fig.  7 an  elevation  or  vertical  section,  and  Figs.  8 and  9 
plans.  The  numbers  of  the  holes  correspond  in  the  several  views.  The 
holes  are  supposed  to  be  drilled  by  rock  drills,  and  they  are  so  placed  that 
all  except  the  breaking-in  holes  have  an  equal  line  of  resistance.  The  num- 
ber of  holes  given  is  supposed  to  take  out  a clean  cut  of  the  whole  section 
abed  to  the  extent  of  3 ft.  6 in.  The  order  of  firing  the  holes  is:  (1)  break- 
ing-in shots  1,  2,  8 , and  4 simultaneously;  (2)  5,  6,  7,  8 ; (3)  9,  10,  11,  12; 
(4)  IS,  U,  15,  16;  (5)  17,  18,  19,  20. 

The  square-cut  arrangement  is  shown  in  Figs.  12  (face),  10,  11  (plans), 
and  13  (vertical  elevation).  The  entering  wedge,  Fig.  11,  is  best  removed  in 
two  stages:  First,  the  part  egh  by  the  shots  1,  2,  8,  and  4;  and  second,  part 
efh  by  shots  5,  6,  7,  and  8.  The  other  shots  are  then  fired:  (1)  9, 10, 11, 12: 
(2)  13,  lit,  15, 16;  (3)  17, 18, 19, 20,  each  volley  being  fired  either  simultaneously 
or  consecutively.  Where  there  is  a natural  parting  in  the  heading,  advan- 
tage is,  of  course,  taken  of  this- in  the  location  of  the  shots. 

Figs.  14  and  15  show  two  arrangements  of  drill  holes  used  in  sinking  the 
Parker  shaft  at  Franklin  Furnace,  N.  J.  The  size  of  the  shaft  was  10  ft.  X 
20  ft.  in  the  rock.  At  first,  only  6'  cuts  were  put  in,  but  these  were  gradually 
increased  until  IF  and  12'  cuts  were  pulled.  The  best  average  obtained  was 
66  ft.  of  shaft  from  6 consecutive  cuts. 


MACHINE  MINING. 


The  number  of  coal-mining  machines  in  use  has  increased  rapidly  within 
a very  short  time.  In  1896  there  were  1,446  in  use  in  the  United  States. 
During  1897  there  was  an  increase  of  542,  or  37.5$,  while  the  average  yearly 
gain  from  1891  to  1896  was  only  about  22$.  The  total  tonnage  won  by 
machines  in  20  States  in  1897  was  22,649,220  short  tons,  or  16.17$  of  the  total 
product  of  these  States,  and  15.3$  of  the  total  bituminous  product  of  the 
United  States.  A universal  mining  machine  has  not  yet  been  brought  out, 
and  one  of  the  principal  reasons  for  the  failure  of  mining  machines  in  a 
number  of  instances  has  been  the  attempt  to  use  a machine  under  condi- 
tions to  which  it  was  not  adapted.  When  a mining  machine  is  designed  and 
built  to  suit  the  conditions  under  which  it  is  to  be  operated,  it  is  safe  to  say 
that  there  are  but  few  mines  in  which  they  cannot  be  successfully  utilized. 
They  are  of  particular  advantage  where  there  is  a long  working  face  and 
where  the  coal  is  over  3 ft.  in  thickness.  Low  seams  require  more  under- 
cutting for  the  given  output  than  high  seams.  As  a rule  it  has  not  been 
found  economical  to  use  machines  in  seams  pitching  over  12°  to  15°,  though 
pick  machines  have  been  used  in  mines  having  an  inclination  of  23°,  the 
difliculty  being  not  so  much  in  the  cutting  as  in  moving  the  machine  from 
place  to  place. 

There  are  four  general  types  of  mining  machines  in  use;  pick  machines, 
chain-cutter  machines,  cutter-bar  machines,  and  longwall  machines.  The 
first  two  are  the  types  almost  universally  used  in  America.  Cutter-bar 
machines  have  almost  entirely  disappeared  from  use  excepting  one  type 
which  is  at  present  used  in  Iowa.  Longwall  mining  machines  have  not 
been  very  generally  adopted  in  America,  as  the  longwall  method  of  mining 
is  not  extensively  used. 

Both  compressed  air  and  electricity  are  used  for  operating  mining 
machines.  Pick  machines  driven  by  compressed  air  are  made  by  three 
separate  concerns.  Four  companies  make  electric  chain  machines  and  one  of 
these  four  is  also  making  a compressed-air  chain  machine.  One  makes  a 
longwall  machine,  and  one  has  brought  out  a pick  machine  for  electric 
power. 

Pick  machines  work  very  similarly  to  a rock  drill.  They  can  be  used 
wherever  mining  machines  are  applicable,  and  their  particular  advantage  is 
that  they  are  more  perfectly  under  the  control  of  the  operator,  who  can  cut 
around  pvrites  and  similar  obstructions  without  cutting  them  with  the 
machine.  ‘ This  renders  such  a machine  particularly  applicable  for  seams  of 


VENTILATION  OF  MINES. 


337 


coal  having  rolls  in  the  bottom  and  containing  pyrites  or  other  hard  impuri- 
ties. They  are  also  applicable  for  working  pillars  on  which  there  is  a 
saueeze,  as  they  are  light  and  can  be  easily  handled  and  readily  removed. 
q Chain-cutter  machines  consist  of  a. low  metal  bed  frame  upon  which  is 
mounted  a motor  that  rotates  a chain  to  which  suitable  cutting  teeth  are 
attached.  To  operate  chain  machines  to  the  best  advantage,  the  coal  should 
be  comparatively  free  from  pyrites.  They  also  require  more  room  than  pick 
machines,  and  a space  from  12  to  15  ft.  in  width  is  nece&sap,„aJonl=t^e^® 
to  work  them  to  advantage.  These  machines  have  proved  failures  m some 
mines  on  account  of  the  incessant  jarring  of  the  roof  by  the  re&r  Jack. 
Chain-cutter  machines  cannot  be  used  to  undercut  coal  when  a squeeze  is 
upon  it.  Coal  seams  that  are  comparatively  level  and  free  from  pyrites  and 
have  a comparatively  good  roof  can  undoubtedly  be  more  satisfactorily  and 
economically  cut  with  chain-cutter  machines  than  with  any  other  type. 

The  average  height  of  cut  is  to  5 in.,  and  at  this  height  the  chain- 
cutter  machines  makes  only  about  60/c  as  much  small  coal  as  a pick  machine. 
This  is  not  always  an  advantage,  as  it  does  not  always  allow  sufficient  height 
for  the  coal  to  fall  down  after  the  cut  is  made.  In  a 3£'  seam,  3 men  are 
required  to  handle  the  machine  to  advantage.  ..  , . _ . . „ 

Shearing  —All  the  pick  machines  can  be  converted  into  shearing  machines 
and  can  be  used  for  longwall  work  by  using  a longer  striking  arm  and  a 
longer  supply  hose.  The  chain  machines  are  used  to  do  shearing  work  by 
having  the  cutting  parts  turned  vertically.  . . ..  „ , 

Capacity.— The  average  producing  capacity  of  each  mining  machine  used 
in  the  United  States  was  11,398  tons  in  1891,  11,373  tons  m 1896,  and  11,393 
tons  in  1897.  So  much  depends  on  the  local  conditions  that  it  is  almost 
impossible  to  give  specific  data  of  rates  of  working  and  costs,  but  the 

following  are  fair  working  approximations. 

A good  pick  machine  will  undercut  450  sq.  ft.  m 10  hours,  while  an  ordi- 
nary miner  will  undercut  120  sq.  ft.  in  the  same  time.  In  a seam  varying  from 
41  to  6 ft  in  thickness,  the  machine  will  undercut  from  50  to  100  tons  of  coal 
in  10  hours.  The  cost  of  undercutting  under  these  conditions  has  been  giv en 
as  approximately  10  cents  per  ton.  Extraordinary  records  show  1,400  sq.  it. 
to  have  been  cut  in  9 hours  in  Western  Pennsylvania,  and  in  an  8'  seam, 

240  tons  have  been  undercut  in  a shift  of  10  hours. 

A good  chain  cutter  will  make  from  30  to  45  cuts,  44  m.  wide  and  6 it. 
deep  in  10  hours  under  moderately  fair  conditions,  while  m high  seams 
two  men  handling  the  same  machine  under  ordinary  conditions  can  make 
60  cuts  per  shift,  and  under  particularly  favorable  conditions,  80  to  120  cuts 
per  shift. 


VENTILATION  OF  MINES. 


This  subject  is  divided  naturally  into  (a)  gases  occurring  m workings, 
explosive  conditions,  quantity  of  air,  distribution  of  air,  and  (o)  ventilating 
methods  and  machinery.  

THE  ATMOSPHERE. 

Composition.— Air  consists  chiefly  of  oxygen  and  nitrogen,  with  small  and 
varying  amounts  of  carbonic-acid  gas,  ammonia  gas,  and  aqueous  vapor. 
These  gases  are  not  chemically  combined,  but  exist  in  a free  state  m umtorm 

proportion,  as  follows:  ■ ■ r ,,r  • 

* ^ By  Volume.  By  \\  eight. 


100.0 


100.0 


Wherever  air  is  found,  its  composition  is  practically  the  same. 

Weight  —The  weight  of  1 cu.  ft.  of  air  at  32°  F.  and  under  a barometric 
pressure  of  30  in.  is  .080975  lb.  Air  decreases  in  weight  per  cubic  foot  as  we 
ascend  in  the  atmosphere,  and  increases  as  we  descend  below  the  surface 
of  the  earth. 


338 


VENTILATION  OF  MINES. 


The  weight  of  1 cu.  ft.  of  dry  air  at  any  temperature  and  barometric 
pressure  is  found  by  means  of  the  formula 

1.3253  X B 
W 459  + t * 

in  which  w = weight  of  1 cu.  ft.  of  dry  air;  B = barometric  pressure 
(inches  of  mercury);  t = temperature  (degrees  F.). 

The  constant  1.3253  is  the  weight  in  pounds  avoirdupois  of  459  cu.  ft.  of 
dry  air  at  a temperature  of  1°  F.  and  1 in.  barometric  pressure. 

Example.— Find  the  weight  of  1 cu.  ft.  of  dry  air  at  a temperature  of 
60°  F.  and  a barometric  pressure  of  30  in. 


w 


1.3253  X 30 
“459  + 60 


= .07661b. 


Table  of  Weight  of  Dry  Air. 


Weight  of  1 cu.  ft.  of  dry  air  at  different  temperatures  and  barometric 

1 3253  X B 

pressures,  as  calculated  by  the  formula  w = + . 


Temperature. 
Degrees  F. 
t 

Weight  of  1 Cu.  Ft.  of  Dry  Air  (Lb.  Avoirdcpois). 

Barometer  (In.). 
B — 27. 

Barometer  (In.). 
B = 28. 

Barometer  (In.). 
B = 29. 

Barometer  (In.). 
B = 30. 

0 

.07796 

.08085 

.08373 

.08662 

5 

.07718 

.08002 

.08285 

.08569 

10 

.07631 

.07914 

.08196 

.08478 

15 

.07550 

.07830 

.08109 

.08388 

20 

.07470 

.07747 

.08023 

.08300 

25 

.07393 

.07667 

.07041 

.08215 

30 

.07318 

.07589 

.07860 

.08131 

32 

.07288 

.07558 

.07828 

.08098 

35 

.07244 

.07512 

.07780 

.08048 

40 

.07171 

.07435 

.07701 

.07967 

45 

.07099 

.07362 

.07625 

.07888 

50 

.07031 

.07291 

.07551 

.07811 

55 

.06961 

.07219 

.07477 

.07735 

60 

.06895 

.07150 

.07405 

.07660 

65 

.06828 

.07081 

.07324 

.07587 

70 

.06766 

.07016 

.07266 

.07516 

75 

.06701 

.06949 

.07197 

.07445 

80 

.06648 

.06884 

.07130 

.07376 

85 

.06576 

.06820 

.07064 

.07308 

90 

.06519 

.06760 

.07001 

.07242 

95 

.06490 

.06699 

.06938 

.07177 

100 

.06401 

.06638 

.06875 

.07112 

110 

.06288 

.06521 

.06754 

.06987 

120 

.06180 

.06409 

.06638 

.06867 

130 

.06075 

.06300 

.06525 

.06750 

140 

.05974 

.06195 

.06416 

.06637 

150 

.05874 

.06092 

.06310 

.06528 

160 

.05781 

.05995 

.06209 

.06423 

170 

. .05688 

.05899 

.06110 

.06321 

180 

.05601 

.05808 

.06015 

.06222 

190 

.05514 

.05718 

.05922 

.06126 

200 

.05430 

.05631 

.05832 

.06033 

220 

.05271 

.05466 

.05661 

.05856 

240 

.05119 

.05309 

.05498 

.05688 

260 

.04978 

.05162 

.05346 

.05530 

280 

.04840 

.05020 

.05200 

.05380 

300 

.04714 

.04888 

.05063 

.05238 

350 

.04423 

.04587 

.04751 

.04915 

400 

.04166 

.04321 

.04475 

.04629 

THE  BAROMETER. 


339 


Atmospheric  Pressure.— The  term  barometric  pressure  is  the  pressure  caused 
bv  the  weight  of  the  atmosphere  above  a given  point.  It  is  measured  by  the 
barometer,  and  this  gives  rise  to  the  synonymous  term  barometric  pressure. 
Atmospheric  pressure  is  usually  stated  in  pounds  per  square  inch,  while 
barometric  pressure  is  stated  in  inches  of  mercury.  Thus,  at  sea  level,  the 
atmospheric  pressure  under  normal  conditions  of  the  atmosphere  is  14./  lb. 
per  sq.  in.,  while  the  barometric  pressure  at  the  same  level  is  30  in.  of 
mercury  column,  or  simply  30  in.  , . ' , . 

Barometric  Variations.— The  pressure  of  the  atmosphere  is  not  constant,  but 
is  subject  to  fluctuations  depending  on  the  condition  of  the  atmosphere. 
Besides  these,  there  are  fluctuations  that  are  more  or  less  regular  and  are 
called  barometric  variations.  There  is  both  a yearly  and  a diurnal,  or  daily, 
variation.  Of  these  two,  the  more  important  and  the.  more  regular  is  the 
daily  variation,  in  which  the  barometer  attains  a maximum  height  from  9 to 
10  o’clock  a.  m.,  and  a minimum  about  4 o’clock  p.  m.  Other  maximum  and 
minimum  readings  are  obtained  at  10  p.  m.  and  3 a.  m.,  respectively;  but 
these  are  not  as  pronounced  as  those  occurring  in  the  daytime.  The  daily 
barometric  variations  range  from  .01  to  .08  in.  

Mercurial  Barometer.— This  barometer  is  often  called  the  cistern  barometer; 
or  when  the  lower  end  of  the  tube  is  bent  upwards  instead  of  the  mouth  of 
the  tube  being  submerged  in  a basin,  it  is  known  as  the  siphon  barometer. 
The  instrument  is  constructed  by  filling  a glass  tube  3 ft.  long,  and  having  a 
bore  of  £ in.  diameter,  with  mercury,  which  is  boiled  to  drive  off  the  air. 
The  thumb  is  now  placed  tightly  over  the  open  end,  the  tube  inverted,  and 
its  mouth  submerged  in  a basin  of  mercury.  When  the  thumb  is  withdrawn, 
the  mercury  sinks  in  the  tube,  flowing  out  into  the  basin,  until  the  top  of 
the  mercury  column  is  about  30  in.  above  the  surface  of  the  mercury  m the 
basin,  and  after  a few  oscillations  above  and  below  this  point,  comes  to  rest. 
The  vacuum  thus  left  in  the  tube  above  the  mercury  column  is  as  perfect 
a vacuum  as  it  is  possible  to  form,  and  is  called  a Torricelli  vacuum,  after  its 
discoverer.  There  being  evidently  no  pressure  in  the  tube  above  the 
mercury  column,  and  as  the  weight  of  this  column  standing  above  the  sur- 
face of  the  mercury  in  the  basin  is  supported  by  the  pressure  of  the  atmos- 
phere, it  is  the  exact  measure  of  the  pressure  of  the  atmosphere  on  the 
surface  of  the  mercury  in  the  basin.  If  the  experiment  is  performed  at  sea 
level,  the  height  of  the  mercury  will  be  found  to  average  about  30  in.,  at 
higher  elevations  it  is  less,  while  if  we  descend  deep  shafts  below  this  level, 
it  Is  greater.  Roughly  speaking,  an  allowance  of  1 in.  of  barometric  height 
is  made  for  each  900  ft.  of  ascent  or  descent  from  sea  level  (see  calculation  of 
barometric  elevations).  A thermometer  is  attached  to  each  mercurial 
barometer  to  note  the  temperature  of  the  reading,  as  it  is  customary  m all 
accurate  work  with  this  instrument  to  reduce  each  reading  to  an  equivalent 
reading  at  32°  F.,  which  is  the  standard  temperature  for  barometric  readings. 
A scale  is  provided  at  the  top  of  the  mercury  column  with  its  inches  so 
marked  upon  it  as  to  make  due  allowance  for  what  is  called  the  error  of 
capacity.  In  other  words,  the  inches  of  the  scale  are  longer  than  real 
inches,  since  the  level  of  the  mercury  in  the  basin  rises  as  it  sinks  m the  tube, 
and  vice  versa.  The  top  of  the  mercury  column  is  always  oval,  convex 
upwards,  owing  to  capillary  attraction,  and  the  scale  is  read  where  it  is 
tangent  to  this  convex  surface.  , , „ .,  . , 

Aneroid  Barometer.— This  is  a more  portable  form  than  the  mercurial 
barometer.  It  consists  of  a brass  box  resembling  a steam-pressure  gauge, 
having  a similar  dial  and  pointer,  the  dial,  however,  being  graduated  to 
read  inches,  corresponding  to  inches  of  mercury  column,  instead  of  reading 
pounds,  as  in  a pressure  gauge.  Within  the  outer  case  is  a delicate  brass 
box  having  its  upper  and  lower  sides  corrugated,  which  causes  it  to  act  as  a 
bellows,  moving  in  and  out  as  the  atmospheric  pressure  on  it  changes.  The 
air  within  the  box  has  been  partially  exhausted,  to  render  it  sensitive  to 
atmospheric  changes.  The  movement  of  the  upper  surface  of  the  box  is 
communicated  to  the  pointer  by  a series  of  levers^  and  the  dial  is  graduated 
to  correspond  with  the  mercurial  barometer. 

Calculation  of  Atmospheric  Pressure.— The  weight  of  the  mercury  column 
of  the  barometer  is  the  exact  measure  of  the  pressure  of  the  atmosphere, 
since  it  is  the  downward  pressure  of  the  atmosphere  that  supports  the 
mercury  column,  area  for  area;  that  is  to  say,  the  pressure  of  the  atmosphere 
on  1 sq.  in.  supports  a column  of  mercury  whose  area  is  1 sq.  in.,  and  whose 
height  is  such  that  the  weight  of  the  mercury  column  is  equal  to  the  weight 
of  the  atmospheric  column.  Hence,  since  1 cu.  in.  of  mercury  weighs  .49  lb., 


340 


VENTILATION  OF  MINES. 


the  atmospheric  pressure  that  supports  30  in.  of  mercury  column  is  .49  X 30 
= 14.7  lb.  per  sq.  in.  In  like  manner,  the  atmospheric  pressure  correspond- 
ing to  any  height  of  mercury  column  may  be  calculated.  It  will  be  observed 
that  the  sectional  size  of  the  mercury  column  is  not  important,  since  it  is 
supported  by  the  atmospheric  pressure  on  an  equal  area,  but  the  calculation 
of  pressure  is  based  on  1 sq.  in. 

Water  Column  Corresponding  to  Any  Mercury  Column.— The  density  of  mercury 

referred  to  water  is  practically  13.6;  hence,  the  height  of  a water  column 
corresponding  to  a given  mercury  column  is  13.6  times  the  height  of  the 
mercury  column.  For  example,  at  sea  level,  where  the  average  barometric 
pressure  is  30  in.  of  mercury,  the  height  of  water  column  that  the  atmos- 
pheric pressure  will  support  is  13.6  X = 34  ft.  This  is  the  theoretical 
height  to  which  it  is  possible  to  raise  water  by  means  of  a suction  pump,  but 
the  length  of  the  suction  pipe  should  not  exceed  75 $ or  80$  of  the  theoretical 
water  column.  . , , , 

Calculation  of  Barometric  Elevations.— Such  elevations,  although  approxi- 
mate, are  useful  for  many  purposes.  The  barometric  readings  are  reduced 
to  equivalent  readings  at  the  standard  temperature  of  32°  F.,  and  for  deter- 
mining differences  in  elevation,  the  readings  of  two  barometers  should  be 
taken,  if  possible,  at  the  same  time.  It  must  not  be  supposed,  however,  that 
the  barometer  alwavs  reads  the  same  for  the  same  elevation  at  this  tempera- 
ture. The  temperature  of  the  atmosphere  has  indeed  very  little  effect  on 
the  atmospheric  pressure,  which  is  due  to  the  weight  of  air  above  the  point 
of  observation,  aerial  currents,  and  other  phenomena. 

In  the  more  accurate  determinations  of  vertical  height  or  elevation  by 
means  of  the  barometer,  the  following  formula  is  usually  employed: 


R = reading  of  barometer  (inches)  at  lower  station; 
r — reading  of  barometer  (inches)  at  higher  station; 

T = temperature  (F.)  at  lower  station; 
t = temperature  (F.)  at  higher  station; 

H = difference  of  level  in  feet  between  the  two  stations. 

H=  56,300  (log  B- log  0(l  + ^)- 


log  R 


H 


56,300  1 + 


(i+— -1 

\ + 900  I 


+ log  r. 


More  simply:  H = 49,000 (§^)  (l  + ) . 


R = 


’49,000  (900  + T+  t)  -f  90017] 
.49,000  (900  + T+  t)  - 900  id  * 


Correction  for  Temperature.— Mercury  expands  about  .0001  of  its  volume 
for  each  degree  Fahrenheit.  To  reduce,  therefore,  a reading  at  any  tem- 
perature to  the  corresponding  reading  at  the  standard  temperature  of  32°  F., 
subtract  of  the  observed  height  for  each  degree  above  32°;  or,  if  the 
temperature  is  below  32°,  add  TT,^  for  each  degree. 

Thus,  30.667  in.  at  62°  F.  is  equivalent  to  a reading  of  30.555  in.  at  32°  F., 


since  30.667 -^-^=(30.667)  - 30.667 -.092  = 30.555  in. 

Depth  of  Shafts.— The  barometer  is  often  employed  to  determine  the 
depth  of  a shaft  or  the  depth  of  any  point  in  a mine  below  a corresponding 
point  on  the  surface.  The  aneroid  is  employed  for  this  work,  being  more 
portable.  Allowance  must  always  be  made  in  such  cases  for  the  venti- 
lating pressure  of  the  mine.  A simple  formula  often  used  for  such  calcu- 
lations is  the  following:  • 

H=  55,OOo(l-^), 


in  which  the  letters  stand  for  the  same  factors  as  designated  above. 

The  most  important  use  of  the  barometer  in  mining  practice,  however,  is 
found  in  the  warning  that  it  gives  of  the  decrease  of  atmospheric  pressure, 
and  the  expansion  of  mine  gases  that  always  follows. 


CHEMISTRY  OF  GASES. 


341 


CHEMISTRY  OF  GASES. 

All  matter  exists  in  one  of  three  forms,  solid , liquid , or  gaseous,  according  to 
the  predominance  of  the  attractive  or  the  repulsive  forces  existing  between  the 
molecules  For  example,  water  exists  as  ice,  or  in  a solid  form,  when  the 
attractive  force  exceeds  the  repulsive  force  between  its  molecules  As 
the^enmeratu^  is  raised  or  heat  is  applied,  the  ice  assumes  the  liquid  form 
due  to^hl  more  rapid  vibration  of  the  molecules  of  which  it  is  composed. 
In  other  words,  the  repulsive  force  existing  between  the  molecules  is 
increased  aid  the  result  is  a liquid.  If  we  still  further  raise  the  tempera- 
S%  bv  applying  more  heat,  the  vibration  of  the  molecules  becomes  yet 
more  rapid,  the  repulsive  force  is  increased  between  the  molecules,  and  a 
gas  or  vapor  called  steam  is  formed.  . . • 

An  atom  is  the  smallest  conceivable  division  of  matter 
A molecule  is  a collection  of  two  or  more  atoms,  united  by  affinity. 

The  atom  cannot  consist  of  more  than  one  element.  The  molecule  may 
be  either  simple  or  compound.  If  compound,  it  is  a chemical  compound, 

itS  Che^afcomp^nTs^  compound  is  one  formed  by  the  union 

of  two  or  more  atoms  chemically,  such  atoms  uniting  always  in  fixed  or 
definite°proportions.  The  properties  of  a chemical  compound  are  always 

Mechanical  Mixture. — A mechanical  mixture  is_  composed  of  different  sub- 
stances that  are  not  chemically  united,  and  which  are  mixed  in  no  fixed 
Smmrtion  The  properties  of  a mechanical  mixture  present  a regular 
proportion,  ine  p p iTnllTn  to  a minimum  state.  Thus,  a solution  of 
gradation  from  a is  not  a chemical  compound  of  salt  and  water, 

bTCplv  a mechanical  mixture  of  the  salt  in  the  water.  If  more  salt  is 

Slo  t^tPr  thp  strength  of  the  mixture  or  the  brine  is  increased; 
added  to  the  water  the  strengm  onu«mt  .g  legg>  Qn  the  other  hand, 

anit  -^if?s  ! chemffial  compound  formed  by  the  union  of  1 atom  of  sodium 
withTatoin  of  chlorine,  the  two  atoms  being  bound  together  by  chemical 
Affinity,  and  always  uniting  in  the  same  proportion,  1 atom  of  each,  to  form 

SalThe  air  that  we  breathe  is  a mechanical  mixture  of  nitrogen  and  oxygen 
gases  with  small  amounts  of  other  ingredients.  The  nitrogen  and  oxygen 
gases’ are  in  a free  state;  that  is  to  say,  they  are  not  combined  as  in  a chem- 
fca?  compound.  This  Is  true,  although  the  proportion  of  these  two  gases, 
oxvgen  and  nitrogen,  in  the  atmosphere,  is  uniformly  in  the  ratio  of  say, 
1 volume  of  oxygen  to  4 of  nitrogen.  Firedamp  is  another  example  of  true 
mechanical  mixture,  consisting  chiefly  of  a mixture  of  marsh  gas  CH±  and 
Sfwith  smaU  amounts  of  other  hydrocarbons  and  a varying  amount  of 
carbonic-acid  gas,  which  is  always  present  in  firedamp.  These  gases  are  not 
combined  chemically,  but  are  mixed  in  varying  proportions. 

Atomic  volume,  or  specific  volume , means  simply  relative  volume.  These 
terms  refer  to  the  relative  volume  of  gases  resulting  from  any  particular 
reaction.  By  means  of  the  laws  of  atomic  volume,  we  can  ascertain  the 
volumes  of  the  different  gases  resulting  from  any  particular  reaction.  1 he 
chemical  reaction  that  takes  place  between  the  elements  constituting 
the  different  gases  is  expressed  by  means  of  a chemical  equation.  When 
we  have  expressed  such  reaction  by  a chemical  equation,  we  can  then 
calculate  the  volumes  of  the  gases  formed,  with  respect  to  the  original 
volumes  of  the  gases  entering  into  the  reaction.  It  must  be  observed,  how- 
ever, that  the  atomic  volumes  express  merely  the  relative^  volumes  of  gases; 
or,  in  other  words,  the  ratio  of  the  volumes  of  gases  before  and  after  the 

reaLawToTvollmea— The  following  laws  of  volume  refer  to  gases  only,  and 

^First—  EquaWoVum^of  all  gases,  under  the  same  conditions  of  tempera- 
ture and  pressure,  contain  the  same  number  of  molecules.  Hence,  the 
molecules  of  all  simple  gases  are  of  the  same  size.  - 

Second.— The  molecules  of  compound  gases,  under  like  con ditions  of  tem- 
perature and  pressure,  occupy  twice  the  volume  of  an  atom  of  hydrogen  gas. 

There  are  very  few  exceptions  to  these  two  laws  of  gaseous  volume,  and 
the  exceptions  are  unimportant  so  far  as  mining  practice  concerned.  _ 
An  element  is  a form  of  matter  that  is  composed  wholly  of  like  atoms. 
Thus  hvdrogen,  oxygen,  iron,  copper,  gold,  and  silver  are  elements. 

Chemical  Symbols  and  Equations.— To  facilitate  the  writing  of  chemical 


342 


VENTILATION  OF  MINES. 


equations  expressing  the  reaction  that  takes  place  between  elements  under 
certain  conditions,  it  is  usual  to  express  the  elements  by  letters  called 
symbols.  These  symbols  stand  for  the  elements  that  they  represent,  and  are 
written  as  capital  letters,  except  where  two  letters  are  used  to  express  a 
symbol,  in  which  case  the  first  letter  only  is  a capital.  Thus,  C is  the 
symbol  for  the  element  carbon,  but  Cu  is  the  symbol  for  copper  (cuprum) 
and  Co  is  the  symbol  for  cobalt.  It  is  important  that  these  symbols  be 
written  exactly  in  this  manner;  otherwise  they  are  liable  to  be  frequently 
misconstrued.  For  example,  Co  stands  for  cobalt,  while  the  symbol  CO 


Table  of  Elements. 


Element. 

Symbol. 

Atomic 

Weight. 

Element. 

Symbol. 

Atomic 

Weight. 

Aluminum  

Al 

27.5 

Manganese 

Mn 

55.0 

Antimony  (stibium) 

Sb 

120.0 

Molybdenum 

Mo 

96.0 

Argon(?)  

A 

Neodymium(?) 

Nd 

Arsenic 

As 

75.0 

Nickel  

Ni 

58.8 

Barium  

P'7- 

137  0 

Niobium  . 

Nb 

94.0 

Beryllium 

Be 

0 4 

Nitrogen 

N 

14.0 

Bismuth 

Bi 

208.0 

Osmium  

Os 

191.0 

Boron 

B 

11.0 

Oxygen 

O 

16.0 

Bromine 

Br 

80.0 

Palladium 

Pd 

106.5 

Cadmium 

Cd 

112.0 

Phosphorus. 

P 

3L0 

Caesium 

Cs 

133.0 

platinum 

Pt 

197.0 

Calcium 

Ca 

4o!o 

Potassium  (kalium) 

K 

39!o 

Carbon  

C 

12.0 

Praseodymium(?)  

Pr 

Cerium  

Ce 

138.0 

Rhodium 

Eh 

104.0 

Chlorine 

Cl 

35.5 

Rubidium 

Eb 

85.0 

Chromium 

Cr 

52^5 

Ruthenium 

Eu 

10L0 

Cobalt 

Co 

59.0 

Samarium(?) 

Sa 

Columbium 

Cb 

93.7 

Scandium  

Sc 

Copper  (cuprum) 

Cu 

63.0 

Selenium 

Se 

79.0 

Didymium  

D 

147.0  • 

Silicon 

Si 

28.0 

Erbium(?) 

Er 

169.0 

Silver  (argentum) 

Ag 

108.0 

Fluorine 

F 

19.0 

Sodium  (natrium)  

Na 

23.0 

Gallium 

Ga 

69.0 

Strontium  

Sr 

87.5 

Germanium 

Ge 

Sulphur  

S 

32.0 

Gold  (aurum) 

Au 

196.7 

Tantalum  

Ta 

182.0 

Helium(?) 

He 

Tellurium  

Te 

127.0 

TTvrlrn^pn 

H 

1.0 

Thallium 

Tl 

205.0 

Xlj  

Tnrlinm 

In 

113.4 

Thorium 

Th 

231.5 

TodinP!  

I 

127.0 

Tin  (stannum) 

Sn 

108.0 

Iridium 

Ir 

193.0 

Titanium 

Ti 

48.0 

Iron  (ferrum)  

Fe 

56.0 

Tungsten  (wolfram) ... 

W 

184.0 

Lanthanum 

La 

139.0 

Uranium 

U 

240.0 

Lead  (plumbum) 

Pb 

207.0 

Vanadium  

V 

51.2 

Lithium 

Li 

7.0 

Ytterbium 

Yb 

Magnesium 

Mg 

24.0 

Yttrium 

Y 

89.0 

Mercury  (hydrargy- 

Zinc   

Zn 

65.0 

rum)  

Hg 

200.0 

Zirconium 

Zr 

90.0 

stands  for  carbonic-oxide  gas,  which  is  a chemical  compound  composed  ot 
two  elements,  carbon  and  oxygen.  ...... 

A molecule  is  expressed  by  writing  the  symbols  of  its  elementary  atoms. 
Where  more  than  1 atom  of  a substance  or  element  enters  into  the  compo- 
sition of  a molecule,  the  number  of  atoms  of  such  element  is  expressed  by  a 
small  subscript  letter  written  immediately  after  the  symbol  of  the  element. 
Thus  carbonic-acid  gas  is  composed  of  1 atom  of  carbon  chemically  united 
with’ 2 atoms  of  oxygen,  and  is  expressed  by  the  symbol  C02.  Where  the 
symbol  is  written  without  such  subscript  figure,  1 atom  only  is  meant. 
Thus  carbonic-oxide  gas  being  composed  of  1 atom  of  carbon  chemically 
united  to  1 atom  of  oxygen,  is  expressed  by  the  symbol  CO. 


CHEMISTRY  OF  GASES. 


343 


A large  figure  written  before  the  symbols  expressing  the  molecule  indi- 
cates the  number  of  molecules  entering  into  the  reaction.  A large  figure  is 
sometimes  used  before  the  symbol  of  a single  element  to  indicate  the  number 
of  atoms  of  that  element  that  enter  the  reaction.  In  any  reaction  occurring 
between  atoms  of  matter,  no  matter  is  destroyed.  In  any  reaction,  there 
are  always  the  same  number  of  atoms  after  the  reaction  as  before  the 
reaction  took  place.  A chemical  equation  is  therefore  an  expression  of 
equality  between  the  atoms  before  and  after  a reaction  takes  place.  The 
first  member  of  the  equation  contains  the  substances  that  act  upon  each 
other  while  the  second  member  of  the  equation  contains  the  substances 
that  are  formed  by  the  reaction.  The  number  of  atoms  is  the  same  in  each 
member  of  the  equation.  „ , . , . 

Example.— To  express  the  reaction  that  takes  place  when  carbonic- 
oxide  gas  burns  in  the  air  to  produce  carbonic-acid  gas,  we  write 
CO  -+•  0 -H  4 N — C02  -f-  4 N 

In  this  equation,  each  molecule  of  carbonic-oxide  gas  CO  takes  up  1 atom 
of  the  free  oxygen  of  the  atmosphere  to  form  carbonic-acid  gas  C02.  The 
nitrogen  in  the  atmosphere  being  4 times  the  volume  of  oxygen,  is  expressed 
as  4 atoms  in  the  equation.  This  nitrogen,  however,  remains  inactive,  and 
takes  no  part  in  the  reaction.  It  is  written  on  both  sides  of  the  equation  for 
the  purpose  of  determining  the  atomic  volumes  of  the  gases  before  and  after 
the  reaction,  as  explained  below. 

The  reaction  for  an  explosion  of  firedamp  is 

+ 40  + 16N  = 002  + 2 H,0  + 16 N m 

In  this  equation,  each  molecule  of  marsh  gas  CH*  is  dissociated;  that  is 
to  say,  its  atoms  are  separated.  The  atom  of  carbon  in  the  molecule  unites 
with  2 atoms  of  the  oxygen  of  the  air  to  form  carbonic-acid  gas  C02.  The 
4 atoms  of  hydrogen,  in  like  manner,  combine  with  two  atoms  of  oxygen  in 
the  air  to  form  2 molecules  of  water  or  steam  2 (HO),  or  2 H20.  The  nitro- 
gen in  this  equation  is  equal  to  4 times  the  volume  of  the  oxygen  consumed, 
and  is  therefore  written  as  1 6N,  since  a total  of  4 atoms  of  oxygen  have 
been  used.  The  nitrogen  is  however  inert,  and  plays  no  part  in  the  reac- 
tion itself,  but  is  written  here  on  both  sides  of  the  equation,  as  in  the 
previous  equation,  in  order  to  properly  represent  the  atomic  volumes  of 
the  gases  or  their  relative  volumes  before  and  after  the  reaction  takes  place. 

Calculation  of  the  Relative  Volumes  of  Gases— To  calculate  the  relative 
volumes  of  the  gases  before  and  after  the  reactions  expressed  in  each  of  the 
equations  given  in  the  preceding  paragraphs,  write  beneath  the  symbol 
of  each  molecule  or  atom  its  atomic  volume.  In  the  chemical  equation 
expressing  the  reaction  that  takes  place  when  carbonic-oxide  gas  CO  burns 
to  carbonic-acid  gas  C02 , we  have  as  follows: 

CO  + O + 4N  = C02+  4 N 

Atomic  volumes,  2+1+4=  2+ 4 

or  in  this  reaction,  7 volumes  have  been  reduced  to  6 volumes.  Such  a 
change  of  volume  often  takes  place  in  chemical  reactions.  All  attempts  to 
explain  the  cause  of  this  change  of  volume,  however,  have  thus  far  failed; 
but  that  the  change  of  volume  does  take  place  has  been  demonstrated  by  a 
large  number  of  experiments.  . ' _ . . . , 

To  calculate  the  volume  of  air  consumed  in  the  complete  explosion  of 
100  cu.  ft.  of  carbonic-oxide  gas  CO,  we  write  the  ratio  of  the  relative  volumes 
of  carbonic-oxide  gas  and  air,  which  is  2 : (1  + 4),  or  2 : 5;  and  to  obtain  the 
actual  volume  of  air  consumed  in  the  explosion  of  100  cu.  ft.  of  carbonic- 

oxide  gas,  we  write  the  proportion  2 : 5 : : 100  : x,  or  x = — ^ — = 250  cu.  ft. 

To  find  the  volume  of  carbonic-acid  gas  C02  produced  in  the  complete 
explosion  of  100  cu.  ft.  of  earbonic-oxide  gas  CO,  write  the  ratio  of  the  atomic 
volumes  of  these  two  gases  2 : 2,  which  shows  no  change  of  volume,  and. 
therefore,  the.  volume  of  carbonic-acid  gas  C02  produced  will  be  the  same  as 
the  volume  of  carbonic-oxide  gas  CO  burned. 

To  find  the  volume  of  air  consumed  m the  complete  explosion  of  100 
cu.  ft.  of  marsh  gas  CHh  write  the  equation  expressing  the  reaction  that 
takes  place  in  this  explosion  as  given  above, 

CH±  + 40  + 16 N = C02  -f  2 H20  + 1 6N 

Atomic  volumes,  2 + 4 + 16  = 2 + 4 + 16 

There  is  no  change  of  volume  caused  by  the  explosion,  since  22  volumes 
on  one  side  of  the  equation  produce,  likewise,  22  volumes  on  the  other  side; 
or  22  volumes  before  the  explosion  produce  22  volumes  after  the  explosion. 


344 


VENTILATION  OF  MINES. 


To  find  the  volume  of  air  consumed,  we  write  the  ratio  of  the  atomic 
volumes  of  marsh  gas  and  air  2 : (4  + 16),  or  2 : 20,  or  1 : 10;  that  is  to 
say,  roughly  speaking,  the  amount  of  air  consumed  in  the  complete  explo- 
sion of  marsh  gas  is  10  times  the  volume  of  the  marsh  gas.  This  is  not  exact, 
however,  as  the  volume  of  nitrogen  in  the  air  is  3.83  times  the  volume  of 
oxygen.  Making  this  correction,  the  volume  of  air  consumed  in  the  complete 
explosion  of  marsh  gas  is  9.66  times  the  volume  of  the  gas. 

To  determine  the  percentage  of  pure  marsh  gas  in  the  above  firedamp 
mixture  (marsh  gas  and  air),  we  write  the  ratio  of  the  atomic  volumes  of 

these  two,  2 : (2  + 4 + 15.32),  or  1 : 10.66;  and  — X 100  = 9.38$  of  CH±. 

1 U*  DO 

The  volume  of  carbonic-acid  gas  formed  in  this  reaction  is  equal  to  the 
volume  of  marsh  gas  consumed,  and  the  volume  of  watery  vapor  is  double 
the  volume  of  marsh  gas  consumed;  the  total  volume  of  gas  and  vapor 
formed  by  the  reaction  is  the  same  as  the  original  volume  of  marsh  gas  and 
air,  or  firedamp  mixture,  since  the  sum  of  the  atomic  volumes  on  each  side 
of  the  equation  is  the  same. 

Atomic  weight  is  the  relative  weight  of  an  atom  of  an  element  compared 
with  an  atom  of  hydrogen.  Atomic  weight  is,  then,  not  an  absolute  weight 
to  be  expressed  in  pounds,  ounces,  or  any  other  denomination,  but  is  simply 
relative  weight.  The  atomic  weight  of  each  of  the  elements  is  given  in  the 
table  on  page  342. 

Molecular  weight  is  the  sum  of  the  atomic  weights  of  the  elements  forming 
the  molecule,  taking  the  atomic  weight  of  each  element  as  many  times  as 
there  are  atoms  of  that  element  in  the  molecule.  A molecule  of  water  is 
composed  of  2 atoms  of  hydrogen  and  1 atom  of  oxygen,  and  as  the  atomic 
weight  of  hydrogen  is  1 and  that  of  oxygen  16,  the  molecular  weight  of 
water  is  (2  X 1)  +16  = 18.  In  the  same  manner,  since  a molecule  of  marsh 
gas  CH4  is  composed  of  4 atoms  of  hydrogen  and  1 of  carbon,  and  the  atomic 
weight  of  hydrogen  is  1 and  that  of  carbon  12,  the  molecular  weight  of  marsh 
gas  is  (4  X 1)  + 12  = 16. 

The  density  of  a gas  is  the  weight  of  any  volume  compared  with  the 
weight  of  the  same  volume  of  hydrogen  or  some  other  standard.  The 
density  of  a gas  is  constant  at  all  temperatures  and  pressures,  the  change 
of  temperature  and  pressure  affecting  the  gas  in  question  and  the  standard 
alike.  The  density  of  air  referred  to  hydrogen  is  14.38. 

(a)  The  density  of  any  simple  gas,  referred  to  hydrogen  as  unity,  is  equal  to 
its  atomic  weight.  ( b ) The  density  of  any  compound  gas , referred  to  hydrogen 
as  unity,  is  one-half  of  its  molecular  weight. 

Specific  Gravity  of  Gases.— The  specific  gravity  of  a gas  is  the  weight  of 
that  gas  referred,  to  the  weight  of  a like  volume  of  air  as  a standard.  It  is, 
in  other  words,  the  ratio  between  the  weight  of  like  volumes  of  any  gas  and 
air,  both  the  air  and  gas  being  subject  to  the  same  temperature  and  pressure. 
Thus,  since  the  weight  of  1 cu.  ft.  of  air  at  a temperature  of  60°  F.  and  30  in. 
barometric  pressure  is  .0766  lb.,  and  the  weight  of  1 cu.  ft.  of  carbonic-acid 
gas  C02  is  .11712  lb.  at  the  same  temperature  and  pressure,  the  specific 

.11712 

gravity  of  carbonic-acid  gas  is  --y—  = 1.529. 

Weight  of  Gases.— The  weight  of  1 cu.  ft.  of  any  gas  at  any  given  tempera- 
ture and  pressure  is  found  by  first  calculating  the  weight  of  1 cu.  ft.  of  dry 
air  at  the  same  temperature  and  pressure  by  means  of  the  formula  given  on 
page  338  for  air,  and  then  multiplying  this  weight  by  the  specific  gravity  of 
the  gas  referred  to  air  as  a standard. 

Example.— To  determine  the  weight  of  1 cu.  ft.  of  carbonic-acid  gas  at  a 
temperature  of  60°  F.,  and  30  in.  barometric  pressure,  we  multiply  the 
weight  of  1 cu.  ft.  of  dry  air,  at  this  temperature  and  pressure,  as  found 
above  (.0766  lb.),  by  the  specific  gravity  of  carbonic-acid  gas  (1.529).  Thus, 
.0766  X 1.529  = .11712  lb. 

The  table  on  page  349  gives  the  specific  gravity  of  the  gases  common  in 
mining  practice,  referred  to  air  as  a standard. 

Expansion  of  Air  and  Gases.— All  air  and  gases  expand  uniformly  at  the 
same  rate.  The  expansion  and  contraction  of  air  and  gases  follow  two 
simple  laws  that  we  will  consider  under  the  heads  (a)  Ratio  of  volume  and 
absolute  temperature  and  ( b ) Ratio  of  volume  and  absolute  pressure. 

Absolute  temperature  means  the  temperature  as  reckoned  from  absolute 
zero,  which  is  the  point  on  the  temperature  scale  below  which  it  is  assumed 
that  no  substance  can  exist  in  a gaseous  state.  * The  absolute  zero  of  the 


PRESSURE. 


345 


» 


Fahrenheit  scale  is  assumed  in  mining  practice  as  459°  below  zero.  Hence, 
the  absolute  temperature  corresponding  to  any  common  temperature  is 
found  by  adding  459°  to  the  common  temperature.  Thus,  the  absolute 
temperature  corresponding  to  60°  F.  is  459  + 60  = 519°. 

Absolute  Pressure.— The  term  absolute  pressure  refers  to  the  total  pressure 
supported  by  air  or  gas;  i.  e.,  the  pressure  above  a vacuum.  Gauge  pressure 
is  the  pressure  above  the  atmosphere.  Absolute  pressure  is  always  the 
atmospheric  pressure  plus  the  gauge  pressure.  If  a gauge  pressure  on  a 
boiler  indicates  60  lb.  per  sq.  in.,  the  absolute  pressure  supported  by  the 
steam  in  the  boiler  will  be  60  + 14.7  = 74.7  lb.  per  sq.  in.  Or,  if  the  ventila- 
ting pressure  in  a mine  is  equal  to  13  lb.  per  sq.  ft.,  the  absolute  pressure 
supported  by  the  air  in  the  airways  will  be  13  + (14.7  X 144)  = 2,129.8  lb. 
ner  so  ft 

Relation  of  Volume  and  Absolute  Temperature  ( Charles ’ or  Gay  Lussac's  law). 
The  volume  of  any  air  or  gas  varies  directly  as  its  absolute  temperature. 

Relation  of  Volume  and  Absolute  Pressure  ( Boyle's  or  Mariotte’s  law).— The 
volume  of  any  air  or  gas  varies  inversely  as  the  absolute  pressure  it  supports. 
For  example,  if  we  double  the  absolute  pressure  supported  by  air  or  gas, 
the  volume  of  the  air  or  gas  will  be  reduced  to  one-half  its  original  volume; 
if  we  multiply  the  absolute  pressure  3 times,  we  reduce  the  volume  to  one- 
third  the  original  volume;  etc.  „ „ . 

Example.— The  intake  current  of  a mine  is  50,000  cu.  ft.  of  air  per  minute; 
the  ventilating  pressure  is  13  lb.  per  sq.  ft.  The  temperature  of  the  intake  is 
20°  F.;  the  temperature  of  the  return  air  is  70°  F.  Calculate  the  volume  of 
the  return  air-current  per  minute,  according  to  the  rules  of  expansion  of  air, 
due  to  the  increase  of  temperature  and  decrease  of  pressure,  in  the  return 
current. 

The  increased  volume  of  the  return  air,  due  to  the  decrease  of  pressure 
and  increase  of  temperature,  is  found  by  writing  a compound  proportion, 
the  first  member  of  which  consists  of  two  ratios,  viz.,  the  direct  ratio  of  the 
absolute  temperatures,  and  the  inverse  ratio  of  the  absolute  pressures,  accord- 
ing to  the  two  laws  stated  above.  That  is,  we  write 


Or, 


(459  + 20)  : (459  + 70) 
2,116.8  : 2,129.8 


529  X 2,129.8  X 50,000 
479X2,116.8 


50,000  : x. 


55,558  cu.  ft. 


Example— In  a compressed-air  plant,  the  gauge  shows  a pressure  of  80  lb. 
per  sq.  in. ; the  area  of  the  piston  is  20  sq.  in.,  and  its  stroke  10  in.  The  pump 
makes  100  strokes  per  minute.  Assuming  there  is  no  leakage  of  air  past  the 
piston,  what  will  be  the  volume  of  air  discharged  from  the  pump  into  the 
mine  per  minute?  , „ , 

The  volume  of  air  discharged  from  the  pump  cylinder  per  minute 


= 20  X 10  X 100  _ 11<57  cu  ft  (cylinder  pressure).  The  absolute  pressure 

on  the  air  in  the  cylinder  is  80  + 14.7  = 94.7  lb.  The  absolute  pressure  on 
the  discharged  air  is  simply  the  atmospheric  pressure  (14.7  lb.).  Hence,  we 

write  the  proportion  14.7  : 94.7  : : 11.57  : x ; or,  x = — ; X 11.57  = 74.54  cu.  ft. 


per  minute,  nearly.  , . . , 

In  calculating  the  expanded  volume  of  air  or  gas,  it  will  be  observed  that 
the  ratio  of  the  original  volume  to  the  expanded  volume  is  always  equal  to 
the  product  of  the  direct  ratio  of  the  absolute  temperatures  and  the  inverse 
ratio  of  the  absolute  pressures,  which  gives  a compound  proportion,  the  first 
member  of  which  consists  of  two  ratios,  the  one  a direct  ratio  and  the  other 
an  inverse  ratio.  r A . . - 

Weight  Produces  Pressure.— In  the  study  of  the  barometer  as  a means  of 
measuring  atmospheric  pressure,  we  observe  that  the  weight  of  the  atmos- 

ghere  produced  the  atmospheric  pressure.  In  like  manner,  the  weight  of  all 
uids  produces  pressure,  and  this  pressure  acts  equally  in  all  directions. 
This  is  an  important  consideration  in  the  study  of  mine  ventilation,  since  it 
has  given  rise  to  the  measurement  of  pressure  by  air  or  motive  columns. 

Calculation  of  Pressure.— An  air  column,  or  motive  column,  in  ventilation, 
is  a column  of  air  having  a base  of  1 sq.  ft.,  and  of  such  height  that  its  weight 
shall  be  equal  to  any  given  pressure.  To  calculate  the  height  of  air  column 
corresponding  to  any  given  pressure,  divide  the  pressure  in  pounds  per 
square  foot  by  the  weight  of  1 cu.  ft.  of  the  air.  Mine  pressure  is  also 


346 


VENTILATION  OF  MINES. 


measured  by  the  water  column  that  it  will  support,  as  in  the  water  gauge,  or  by 
the  mercury  column,  as  in  the  barometer.  In  the  measurement  of  pressure 
by  means  of  the  water  column,  the  weight  of  the  water  column  must  be 
equal  to  the  pressure,  ( ireafor  area. 

Since  the  weights  of  these  columns  are  proportional  to  their  sectional  areas, 
it  makes  no  difference  what  this  area  may  be,  the  weight  of  the  column 
calculated  for  a sectional  area  of  1 sq.  in.  will 
equal  the  pressure  per  square  inch  that  supports 
the  same. 

Hence,  since  1 cu.  in.  of  mercury  weighs  .49  lb., 
.49  X 30  = 14.7  lb.  is  the  atmospheric  pressure 
corresponding  to  a height  of  30  in.  of  mercury,  or, 
as  we  say,  30  in.  of  barometer.  If  we  consider  a 
cubical  box,  as  shown  in  the  accompanying 
figure,  holding  exactly  1 cu.  ft.  of  water,  and 
assume  the  weight  of  the  water  to  be  62.5  lb., 
as  is  usual  in  practice,  and  divide  the  bottom  of 
the  box  into  144  sq.  in.,  as  showTn  in  Fig.  1,  we 
observe: 

(a)  The  pressure  of  the  water  on  the  bottom 
of  the  box  is  equal  to  the  weight  of  the  water, 

62.5  lb.;  that  is  to  say,  the  pressure  per  square  foot  due  to  lft.  of  water  column 
is  62.5  lb. 

( b ) The  pressure  on  the  bottom  of  the  box,  when  the  water  is  only 
1 in.  deep,  is  equal  to  the  weight  of  a layer  of  water  1 in.  thick,  or 
62  5 

— = 5.2  lb.;  or,  the  pressure  per  square  foot  due  to  1 in.  of  water  column 
12 

is  5.2  lb. 

(c)  The  pressure  per  square  inch  on  the  bottom  of  the  box  is  equal  to 
the  weight  of  a prism  of  water  1 ft.  high,  and  having  a base  of  1 sq.  in. 

= .434;  or,  the  pressure  per  square  inch  due  to  1 ft.  of  water  column  is  .454  lb. 

These  principles  relating  to  the  pressure  of  fluids  are  important  to  the 
student  of  mining,  of  which  the  following  are  examples: 

1.  In  a mountainous  country,  several  thousand  feet  above  sea  level, 
where  the  barometer  registers,  say,  only  21  in.,  it  is  desired  to  know  the 
theoretical  height  a pump  will  draw.  .49  X 21  = 10.29  lb.  atmospheric 

pressure,  and  = 24  ft.,  nearly.  The  theoretical  suction,  in  this  instance, 

is  24  ft.,  nearly,  but  the  actual  draft  or  suction  would  vary  from  f to  $ of 
this,  according  to  the  perfection  of  the  pump. 

2.  The  water-gauge  reading  between  the  intake  and  return  airways  of  a 
certain  mine  is  2.5  in.;  to  determine  the  pressure  per  square  foot,  we  have, 

2.5  X 5.2  = 13  lb.  per  sq.  ft. 

3.  To  determine  the  pressure  per  square  foot  on  a mine  dam,  due  to  a 
vertical  head  of  200  ft.,  62.5  X 200  = 12,500  lb. 

4.  To  express  in  air  column  or  motive  column,  a mine  pressure  equivalent 
to  a water-gauge  reading  of  3 in.,  assuming  the  temperature  of  the  air  to  be 
60°  F.  and  the  barometric  pressure  30  in.,  we  have  for  the  weight  of  1 cu.  ft. 

1 3253  X 30 

of  air  at  this  temperature  and  pressure  w = — — y = .0766  lb.  The 

pressure  per  square  foot  due  to  3 in.  of  water  gauge  is  3 X 5.2  = 15.6.  Then, 

15  6 

we  have  for  motive  column,  m = = 204  ft. 

.0766 

Diffusion  and  Transpiration  of  Gases.— Diffusion  of  gases  means  the  mixing 
of  the  gaseous  volumes.  Graham  took  several  glass  tubes,  and  inserting  in 
one  end  of  each  a plug  of  plaster  of  Paris  that  was  porous,  he  filled  each 
tube  with  a different  gas;  as  for  example,  oxygen,  hydrogen,  nitrogen,  etc. 
He  then  placed  the  open  end  of  each  inverted  tube  in  a basin  of  mercury, 
supporting  the  tubes  in  an  erect  position.  The  gas  in  each  tube  immedi- 
ately began  to  diffuse  through  the  porous  plaster  plug  into  the  atmosphere, 
and  it  was  observed  that  the  mercury  rose  in  each  tube  to  take  the  place  of 
the  gas  that  passed  into  the  atmosphere.  The  mercury  rose  in  the  hydrogen 
tube  4 times  as  fast  as  in  the  oxygen  tube,  and  in  the  other  tubes  the  mer- 
cury rose  at  different  rates. 

Rate  of  Diffusion  (Graham’s  Law).— The  rate  of  diffusion  of  gases  into  air  is 


~~7 

% 

'\ 

m 

62 

S /As 

— jg  . 

Fig.  1. 


DIFFUSION  OF  GASES. 


347 


in  the  inverse  ratio  of  the  square  roots  of  their  densities.  The  density  of 
oxvaen  being  16  and  hydrogen  1,  the  rate  of  diffusion  of  oxygen  as  compared 
with  hytogfn  is  1 to  4;  that  is  to  say,  the  rate  of  diffusion  of  oxygen  is  only 
one-fourth  that  of  hydrogen. 

Table  Showing  the  Corresponding  Mercury  and  Air  Columns,  and 
Pressure  per  Square  Foot  for  Each  Inch  of  Water  Column. 


0) 

bo 

03  <D 

© P 
C31”"1 
£ 


P 

a 

p . 

7?  M 

M P 

O 

© 


.0735 

.1471 

.2206 

.2941 

.3676 


aw 

£o~ 

8% 

© 

© 


68 

136 

204 

272 

340 


© ■ 
M a* 
PGO 

8§J 

rQ 

w 


5.2 

10.4 

15.6 

20.8 

26.0 


© 

bo 

a °° 

03  n; 

O.P 
© 
© P 


6 

7 

8 
9 

10 


P 

a 

p . 

02 

83 

frS 

PH 

O 

u 

© 


.4412 

.5147 

.5882 

.6618 

.7353 


aw 

.JhH 

© 

© 


407 

475 

543 

611 

679 


© • 
U U* 
p CQ 

*3 


31.2 

36.4 

41.6 

46.8 

52.0 


Table  Showing  the  Corresponding  Water  Column,  and  Pressure  per 


Barometer. 

Inches. 

Water  Column J 
Feet. 

Pressure. 

Lb.  per  Sq.  In. 

Barometer. 

Inches. 

Water  Column. 
Feet. 

Pressure. 

Lb.  per  Sq.  In. 

1 

1.13 

.49 

. 16 

18.13 

7.84 

2 

2.27 

.98 

17 

19.27 

8.33 

3 

3.40 

1.47 

18 

20.40 

8.82 

4 

4.54 

1.96  ! 

19 

21.53 

9.31 

5 

5.67 

2.45 

20 

22.67 

9.80 

5 

6.80 

2.94 

21 

23.80 

10.29 

7 

7.93 

3.43 

22 

24.93 

10.78 

8 

9.06 

3.92 

23 

26.07 

11.27 

9 

10.20 

4.41 

24 

27.20 

11.76 

10 

11.33 

4.90 

25 

28.33 

12.25 

11 

12.46 

5.39 

26 

29.47 

12.74 

12 

13.60 

5.88 

27 

30.60 

13.23 

13 

14.73 

6.37 

28 

31.73 

13.72 

14 

15.87 

6.86 

29 

32.87 

14.21 

15 

17.00 

7.35 

30 

34.00 

14.70 

t a picDBuiovi  iu. 

30  in.,  is  *h;  the  weighty  of 


wqater  hutVeTato  of  til  to  watTr'i^oftSfaiumed  ’aJl.2:Y,Udo  forVick 
calculation.  The  ;Speciflc.gjavity  ofm 


calculation.  j.ixc  opci/im/  

ture  for  barometric  readings)  is  13.62;  and  a nVrpn  ft 

temperature  weighs  849  lb.  For  ordinary  calculation  tne  weight  of  1 cu.  ft. 
of  water  is  taken  as  62.5  lb.  The  exact  weight  of  1 cu.  ft.  of  pure  water,  at  a 
temperature  of  32°  F.t  is,  however,  62.418  lb. 


The  diffusion  of  marsh  gas  (Sp.  Gr.  .559)  is  much  more  rapid  than  that  of 
carbonic-acid  gas  (Sp.  Gr.  1.529).  The  diffusion  of  gases,  however,  is  greatly 
assisted  by  the  movement  of  the  air-current;  or  by  the  movement  of  the  gas 
as  it  tends  to  rise  or  fall,  according  to  its  relative  densityand  Positionmthe 
airway.  For  example,  suppose  a gas  feeder  to  be  located  in .the * floor : of an 
airway.  The  marsh  gas  given  off  from  the  feeder,  being  lighter  than  air, 


348 


VENTILATION  OF  MINES. 


tends  to  rise  toward  the  roof.  The  action  of  rising  helps  a diffusion  of  this 
gas  very  much.  On  the  other  hand,  a feeder  located  in  the  roof  gives  off  the 
same  gas,  which  tends  to  accumulate  along  the  roof,  and  if  "the  air-current 
is  at  all  sluggish  at  this  point,  the  diffusion  of  the  marsh  gas  will  be  compar- 
atively slow.  It  often  happens  that  a feeder  in  the  roof  or  other  high  point 
of  the  workings  gives  off  gas  more  quickly  than  diffusion  can  take  place, 
where  the  air-current  is  sluggish.  This  results  in  the  accumulation  of  a 
body  of  pure  marsh  gas  at  this  point.  In  like  manner,  we  often  have  an 
accumulation  of  a large  body  of  carbonic-acid  gas,  or  blackdamp,  near  the 
floor  or  other  low  place  in  the  mine  workings,  where  the  air-current  is 
sluggish  and  where  the  blackdamp  is  formed  quicker  than  diffusion  takes 
place. 

Limit  of  Diffusion. — The  diffusion  of  gases  continues  to  take  place  until  the 
mixture  of  the  gases  is  uniform.  It  is  a curious  fact  that  this  takes  place 
earlier  or  quicker  in  the  case  of  gases  whose  densities  differ  widely,  than  where 
the  densities  of  the  two  gases  are  nearly  alike.  Thus,  saturation  will  take 
place  more  quickly  in  the  diffusion  of  carbonic-acid  gas  into  air  than  in  the 
diffusion  of  firedamp  into  air,  although  the  rate  of  diffusion  of  the  latter  is 
greater  than  of  the  former,  firedamp  being  lighter  than  carbonic-acid  gas. 

The  property  of  diffusion  is  of  the  greatest  importance  in  the  ventilation 
of  mines,  since  it  is  owing  to  this  that  the  air-current  is- enabled  to  sweep 
away  these  gases  from  their  lurking  places  in  the  workings  more  rapidly 
and  effectually  than  it  otherwise  could. 

Transpiration  of  gases  is  the  exuding  of  the  gases  from  the  pores  of  the  coal 
in  which  they  are  contained.  It  is  a well-known  fact  that  transpiration 
takes  place  more  rapidly  from  a newly  exposed  face  of  coal.  This  is  owing 
to  the  fact  that  the  gas  pent  up  in  the  coal,  or  occluded  in  the  seam,  tends 
to  escape  at  the  first  opportunity,  when  the  seam  is  exposed  to  the  atmos- 
phere. The  gas  is  under  a certain  pressure,  as  we  have  previously  observed, 
and,  as  the  mine  workings  penetrate  the  coal  seam,  the  gases  are  forced 
outward  from  the  coal  by  their  own  pressure,  thus  expanding  into  the  air  of 
the  mine. 

The  transpiration  of  gas  from  coal  seams  differs  very  widely,  in  some 
seams  it  being  so  rapid  and  violent  as  to  splinter  and  break  the  coal  in  its 
effort  to  escape.  It  frequently  causes  a crackling  sound  peculiar  to  a very 
gaseous  seam,  and  in  some  cases,  causes  fine  coal  to  be  thrown  into  the  face 
of  the  miner. 


GASES  FOUND  IN  MINES. 

Oxygen  0 is  a colorless,  odorless,  tasteless,  non-poisonous  gas.  It  is  heavier 
than  air,  having  a specific  gravity  of  1.1056.  It  is  the  great  supporter  of  life 
and  combustion.  Oxidation , or  the  union  of  any  of  the  elements  with 
oxygen,  is  simply  another  term  for  combustion  in  its  broadest  sense.  Most 
forms  of  matter  containing  carbon  are  easily  decomposed  at  certain  temper- 
atures, through  carbon  seeking  to  combine  with  the  oxygen  of  the  air  to 
form  carbonic-acid  gas  C02.  This  union  of  the  oxygen  with  other  elements, 
or  oxidation,  takes  place  at  all  temperatures.  It  is  less  active  when  the 
temperature  is  low,  and  is  then  known  as  slow  combustion.  An  example  of 
this  is  found  in  the  gob  fires  that  occur  so  frequently  in  mine  workings. 
The  fine  coal  that  is  so  often  thrown  back  into  the  gob  is  acted  on  first  by 
moisture,  and  as  its  temperature  rises,  carbonic-oxide  gas  is  formed  in  small 
quantities  by  the  union  of  the  carbon  of  the  coal  with  the  oxygen  of  the  air; 
as  the  temperature  rises,  more  gas  is  formed.  Heat  is  caused  by  the  chemical 
action  due  to  the  interchange  of  the  atoms,  this  heat  being  often  sufficient  to 
ignite  the  gas  formed,  spontaneous  or  active  combustion  resulting.  Oxygen 
is  the  element  in  the  atmosphere  on  which  all  life  depends. 

Nitrogen  A is  a colorless,  odorless,  and  tasteless  gas:  it  is  neither  combus- 
tible nor  a supporter  of  combustion;  it  is  not  poisonous,  and  is  lighter  than 
air,  having  a specific  gravity  of  .9713.  Nitrogen  is  a particularly  inert  gas;  it 
takes  no  active  part  in  any  combustion,  in  the  sense  of  causing  such  com- 
bustion. Its  province  is  to  dilute  oxygen  of  the  atmosphere,  on  which 
life  depends.  Were  it  not  for  this  dilution,  oxidation  would  be  too  rapid, 
and  not  as  completely  under  control  as  at  present.  The  effect  of  nitrogen 
on  human  life  would  be  to  suffocate,  if  breathed  pure,  inasmuch  as  it  would 
exclude  oxygen  from  the  lungs.  Nitrogen  itself  has  no  life-giving  power. 

Marsh  gas  CHh  often  called  light  carbureted  hydrogen , or  methane,  is  a 
chemical  compound,  consisting  of  4 atoms  of  hydrogen  to  1 atom  of  carbon. 


GASES  FO  UND  IN  MINES. 


349 


It  is  one  of  the  chief  gases  occluded  in  coal  seams,  and  results  from  the 
metamorphism  of  the  carbonaceous  matter  from  which  coal  is  formed,  when 
such  metamorphism  has  taken  place  with  the  exclusion  of  air,  and  m presence 
of  water.  Pure  marsh  gas  is  colorless,  odorless,  and  tasteless,  and.  is  iignter 
than  air.  Its  specific  gravity  is  .559,  and  it  diffuses  rapidly  in  the  air,  forming 
a firedamp  mixture.  Marsh  gas  burns  with  a blue  flame,  but  it  will  not 
support  combustion,  and  a lamp  placed  in  it  is  immediately  extinguished. 
In  the  mine,  it  is  a difficult  matter  to  place  a lamp  m a body  of  pure  marsh 
gas,  since  the  gas  diffuses  so  rapidly  that  a firedamp  mixture  always  sur- 
rounds a body  of  pure  gas,  which  may  exist  high  up  m some  cavity  of  the 
roof,  or  at  the  face  of  a steep  pitch  where  the  circulation  is  slow  and  the 
feeder  at  the  face  is  giving  off  a large  amount  of  gas.  The  flaming  of 
the  lamp  in  passing  through  a fir  edamp  mixture  would  at  once  cause  the 
withdrawal  of  the  lamp  before  reaching  the  body  of  pure  marsh  gas.  But 
could  a lamp  be  placed  in  a body  of  pure  marsh  gas,  it  would  be  extinguished 
at  once.  Marsh  gas  is  not  poisonous,  and  when  mixed  with  air  m sufficient 
proportion,  it  may  be  breathed  for  a considerable  time  with  impunity  (see 
Firedamp).  Pure  marsh  gas  does  not  support  life,  but  suffocates  by  exclu- 
ding oxygen  from  the  lungs.  , , , . , 

Other  Hydrocarbons.— All  gases  that  are  compounds  of  carbon  and  hydrogen 
are  called  hydrocarbons.  Qf  these,  the  chief  member  is  marsh  gas,  or  light 
carbureted  hydrogen,  described  in  the  preceding  paragraph;  the  other 
hydrocarbons  are  called  heavy  hydrocarbons.  The  chief  of  these  are  olefiant 
gas  CM f4,  and  ethane  C2HQ.  Both  of  these  gases,  like  marsh  gas,  are  the 
result  of  the  metamorphism  of  carbonaceous  matter,  during  the  formation  of 
the  coal,  but  unlike  marsh  gas,  they  have  been  produced  in  the  absence  of 
water,  and  as  a result  they  contain  a larger  percentage  of  carbon  than 
marsh  gas.  They  always  exist  in  common  with  marsh  gas,  as  occluded  gases 
in  coal  seams,  but  to  a far  less  extent.  Each  of  these  gases  possesses  a higher 
illuminating  power,  burning  with  a brighter  flame  than  marsh  gas.  This  is 
due  to  the  larger  percentage  of  carbon  present  in  their  composition.  Their 
remaining  properties  are  very  similar  to  the  properties  given  for  marsh  gas; 
thev,  however,  when  present  in  a firedamp  mixture,  lower  the  temperature 
of  ignition,  and  render  the  mixture  more  dangerous  than  it  would  be 
otherwise.  , , 

Constants  for  Mine  Gases— The  following  table  shows  the  symbols,  specific 
gravities,  and  relative  velocities  of  diffusion  and  transpiration  of  the  principal 
mine  gases,  arranged  in  the  order  of  their  specific  gravities,  air  being  taken  asl. 
The  values  given  in  the  next  to  the  last  column  of  this  table  were 
obtained  by  experimenting  with  the  gases,  and  agree  quite  closely  with 
the  calculated  values  given  in  the  preceding  column.  From  this  column 
we  see  that  1,344  volumes  of  marsh  gas  will  diffuse  in  the  same  time  as  1,000 
volumes  of  air,  or  812  volumes  of  carbonic-acid  gas. 

Table  of  Mine  Gases. 


Name  of  Gas. 

Symbol. 

Specific 

l 

Relative  Velocity  [Relative  Velocity 
r»f  Diffnsirn.  of  Transniration. 

Gravity. 

V Sp.  Gr- 

(Air  = 1.) 

(Air  = 1.) 

Air  

1.00000 

1.0000 

1.000 

1.0000 

Carbonic  acid 

co2 

1.529 

.8087 

.812 

1.2371 

Sulphureted  hy- 
drogen  

'MS 

1.1912 

.9162 

.95 

.903 

Oxygen  

0 

1.1056 

.9510 

.9487 

Olefiant  

c2h4l 

.978 

1.0112 

1.0191 

1.788 

Nitrogen 

N 

.9713 

1.0147 

1.0143 

1.0303 

Carbonic  oxide  ... 

CO 

.967 

1.0169 

1.0149 

1.034 

Steam 

Marsh  gas 

MO 

CHt 

.6235 

.559 

1.2664 

1.3375 

1.344 

1.639 

Hvdrogen 

M 

.06926 

3.7794 

3.83 

2.066 

Carbonic-oxide  gas  CO,  often  called  whitedamp , is  a chemical  compound 
consisting  of  1 atom  of  carbon  united  to  1 atom  of  oxygen.  To  a certain 


350 


VENTILATION  OF  MINES. 


extent  it  occurs  as  an  occluded  gas  in  coal.  It  is  chiefly  formed,  however, 
in  coal  mines,  by  the  slow  combustion  of  carbonaceous  matter  in  the  gobs  or 
waste  places  of  the  mine,  where  the  supply  of  air  is  limited.  It  is  always  the 
product  of  the  slow  combustion  of  carbon  in  a limited  supply  of  air.  It  is 
therefore  one  of  the  chief  products  of  gob  fires,  and  is  also  a product  of  the 
explosion  of  powder  in  blasting.  This  gas  often  fills  the  crevice  made 
behind  a standing  shot,  and  causes  the  flash  that  takes  place  when  the 
miner  puts  his  lamp  behind  such  shot  to  examine  the  same.  This  gas  is 
formed  in  large  quantities  whenever  the  flame  of  a blast  or  explosion  is 
projected  into  an  atmosphere  in  which  coal  dust  is  suspended.  The  force  of 
a blast  often  blows  the  dust  into  the  air,  and  the  flame  acting  on  it  distils 
carbonic-oxide  gas. 

Carbonic-oxide  gas  is  lighter  than  air,  having  a specific  gravity  of  .967, 
and  it  thereicre  accumulates  near  the  roof  and  in  the  higher  working- 
places.  It  is  colorless,  odorless,  and  tasteless.  It  is  combustible,  burning 
with  a light-blue  flame.  This  is  the  flame  often  seen  over  a freshly  fed 
anthracite  fire.  It  is  also  a supporter  of  combustion,  being  the  only  mine 
gas  that  burns  and  also  supports  combustion.  This  property  leads  to  very 
important  results  in  mines,  inasmuch  as  it  lengthens  the  flame  of  a lamp  or 
the  flame  of  a blast.  Any  flame  is  fed  by  this  gas,  and  is  thereby  transmitted 
through  the  mine  airways,  from  one  point  to  another.  The  same  property 
extends  very  widely  an  otherwise  local  explosion.  This  gas  has  the  widest 
explosive  range  of  any  gas  known  to  mining,  except  hydrogen.  The  effect 
of  its  presence  in  firedamp  mixtures  is  always  to  widen  the  explosive  range 
of  the  firedamp,  causing  it  to  become  explosive  in  larger  and  smaller 
proportions  than  it  otherwise  would.  Carbonic-oxide  gas  is  a very  poison- 
ous gas,  and  acts  on  the  human  system  as  a narcotic,  producing  drowsiness 
or  stupor,  followed  by  acute  pains  in  the  head,  back,  and  limbs,  and  after- 
ward by  delirium.  It  acts,  when  breathed  into  the  lungs,  to  absorb  the 
oxygen  from  the  blood,  or,  in  other  words,  poisons  the  blood. 

Carbonic-oxide  gas  is  detected  in  mine  workings  by  its  effect  on  the  flame 
of  a lamp,  wThich  burns  more  brightly  in  the  presence  of  the  gas,  and  reaches 
upwards  as  a slim,  quivering  taper,  having  often  a pale-blue  tip  that, 
however,  is  not  readily  observed. 

Carbonic-acid  gas  CO 2,  often  called  blackdamp  or  chokedamp , is  a chemical 
compound  consisting  of  1 atom  of  carbon  united  to  2 atoms  of  oxygen.  It  is 
heavier  than  air,  having  a specific  gravity  of  1.529.  It  therefore  accumulates 
near  the  floor  or  in  the  low  places  of  the  mine  workings.  It  is  always  the 
result  of  the  complete  combustion  of  carbon  in  a plentiful  supply  of  air,  and 
is  a product  of  the  breathing  of  men  and  animals,  burning  of  lamps,  or  any 
other  complete  combustion.  It  is  always  present  in  occluded  gases. 

Carbonic-acid  gas  is  a colorless,  odorless  gas,  but  possesses  a peculiarly 
sweet  taste,  which  may  be  detected  in  the  mouth  when  it  is  inhaled  in  large 
quantities.  It  is  not  combustible,  nor  is  it  a supporter  of  combustion. 
Lamps  are  at  once  extinguished  by  it.  It  diffuses  slowly  into  the  atmosphere, 
and  is  a difficult  gas  to  remove  in  ventilating.  It  is  not  poisonous,  but  acts 
to  suffocate  by  excluding  oxygen  from  the  lungs.  Its  effect,  when  breathed 
for  any  length  of  time,  is  to  cause  headache  and  nausea,  followed  by  weak- 
ness and  pains  in  the  back  and  limbs;  when  present  in  larger  quantities,  it 
causes  death  by  suffocation.  This  gas,  when  present  in  firedamp  mixtures, 
has  the  opposite  effect  from  that  of  carbonic-oxide  gas,  inasmuch  as  it 
narrows  the  explosive  range  of  the  firedamp,  and  renders  such  mixtures 
inexplosive,  which  would  otherwise  be  explosive  (see  Firedamp). 

Carbonic-acid  gas  is  detected  in  the  mine  air  by  the  dimness  of  the  lamps 
and  by  their  extinguishment  when  present  in  larger  quantities.  It  should 
always  be  looked  for  at  the  floor,  and  in  low  places  of  the  mine  workings. 

Sulphureted  hydrogen  H2S  occurs  at  times  as  an  occluded  gas  in  coal  seams, 
but  more  often  exudes  from  the  strata  immediately  underlying  or  over- 
lying  those  seams.  It  is  generally  supposed  to  be  formed  by  the  disintegra- 
tion of  pyrites  in  the  presence  of  moisture.  It  is  heavier  than  air,  having  a 
specific  gravity  of  1.1912.  It  is  a colorless  gas,  having  a very  disagreeable 
odor  resembling  that  of  rotten  eggs,  and  is  known  to  the  miners  as  stinkdamp. 
It  is  an  exceedingly  dangerous  gas  when  occurring  in  considerable  quan- 
tities. When  mixed  with  7 times  its  volume  of  air,  it  is  violently  explosive. 
It  is  extremely  poisonous,  acting  to  derange  the  system  when  breathed 
in  small  quantities,  and,  when  inhaled  in  larger  quantities,  it  produces 
unconsciousness  and  prostration.  Its  smell  serves  as  the  best  means  for  its 
detection. 


GASES  FOUND  IN  MINES. 


351 


Firedamp. — The  general  term  firedamp  relates  to  any  explosive  mixture  of 
marsh  gas  and  air,  although  in  some  localities  this  term  is  understood  as 
referring  to  any  mixture  of  marsh  gas  and  air  whatever,  whether  explosive 
or  otherwise.  Many  persons  speak  of  pure  marsh  gas  as  firedamp.  The  first 
meaning  given  above,  however,  is  the  general  acceptation  of  the  term. 

Pure  marsh  gas  when  present  in  small  quantities  in  the  air  burns  m the 
flame  of  the  lamp  without  explosion.  As  the  quantity  of  the  gas  is 
increased,  the  effect  on  the  flame  of  the  lamp  is  at  once  noticeable.  As  the 
proportion  of  gas  in  the  air  is  further  increased,  and  approaches  the  lower 
explosive  limit,  the  lamp  flame  enlarges,  snaps,  and  crackles.  When  the 
proportion  of  gas  to  air  is  1 to  IB,  slight  explosions  occur  within  the  lamp, 
the  flame  of  the  lamp  jumping  violently.  As  the  proportion  of  gas  is 
increased,  the  violence  of  the  explosion  is  augmented  until  it  reaches  a 
maximum,  when  the  proportion  of  gas  to  air  is  1 to  9i  (exactly,  1:  9.38). 
This  is  the  proportion  of  gas  and  air  in  firedamp,  when  at  its  maximum 
explosive  violence.  From  this  point,  as  the  quantity  of  gas  is  still  further 
increased,  the  violence  of  the  explosion  decreases,  until  it  becomes  very 
feeble  when  the  proportion  of  gas  and  air  is  1 to  5i,  and  ceases  altogether 
beyond  this  point.  The  explosive  limits  of  marsh  gas,  or  the  limits  of  fire- 
damp mixtures,  are  then  as  follows:  Lower  limit,  1 volume  of  gas  to  13 
volumes  of  air;  higher  limit,  1 volume  of  gas  to  5£  volumes  of  air.  These 
limits  refer  to  pure  firedamp,  or,  in  other  words,  a firedamp  mixture  con- 
sisting of  pure  marsh  gas  and  air.  , . . , . . , 

It  rarely  happens  that  firedamp,  as  found  m mine  workings,  is  pure,  but 
contains  admixtures  of  other  gases,  such  as  carbonic-acid  gas  CO 2,  carbonic- 
oxide  gas  CO,  and  heavy  hydrocarbons.  . j A 

Afterdamp. — The  term  afterdamp  relates  to  the  gaseous  mixture  that  exists 
in  mine  workings  after  an  explosion  of  gas.  The  composition  of  afterdamp 
is  exceedingly  variable,  and  admits  of  no  general  analysis  that  can  be 
applied  with  certainty  to  any  one  explosion.  The  conditions  that  obtain 
in  an  explosion  are  so  manifold,  and  control  so  completely  the  character  of 
the  gases  formed,  that  it  is  impossible  to  give  more  than  a general  analysis 
of  afterdamp.  . „ , 

The  chief  products  of  the  complete  explosion  of  pure  firedamp  are  car- 
bonic-acid gas,  watery  vapor,  and  nitrogen  (see  page  343).  The  explosion  of 
firedamp  is  seldom,  however,  complete.  Where  a large  body  of  gas  has 
exploded,  the  air-current  in  the  mine  workings  does  not  furnish  sufficient 
air  for  the  complete  combustion  of  the  firedamp,  and  as  a result,  a large 
amount  of  carbonic-oxide  gas  is  formed,  and  is  present  in  the  afterdamp  of 
the  explosion.  The  presence  of  this  gas  (CO)  renders  the  afterdamp  far 
more  dangerous  than  it  would  otherwise  be,  for  two  reasons:  The  gas  itself 
is  very  poisonous,  and  its  presence  is  not  at  once  detected  by  the  zealous 
men  that  are  working  to  rescue  their  fellow  workmen.  The  lamps  burn 
very  brightly  in  this  gas,  and  the  rescuers  press  forward  unconscious  of  their 
real  danger  until  overcome  by  the  effects  of  the  gas.  The  presence  of  coal 
dust  in  suspension  in  the  mine  air  at  the  time  of  the  explosion,  or  thrown 
into  the  air  by  the  force  of  the  explosion,  results  at  once  in  the  production 
of  a large  amount  of  carbonic-oxide  gas.  It  is  a well-known  fact,  also,  that 
carbonic-acid  gas  CO2,  formed  as  a direct  product  of  the  explosion,  or  which 
may  be  present  in  the  mine  air  before  the  explosion,  coming  in  contact 
with  the  incandescent  carbon  of  the  coal  dust,  is  converted  by  it,  at  the  high 
temperature  of  the  flame,  into  carbonic-oxide  gas  CO.  We  observe,  there- 
fore, that  an  explosion,  in  all  its  effects,  tends  to  the  rapid  and  abundant 
production  of  this  most  dangerous  gas. 

The  other  products  of  an  explosion  are  numerous,  but  for  the  larger  part, 
unimportant,  except  as  they  do  not  support  life.  We  have  mentioned  and 
described  only  those  gases  forming  the  larger  portion  of  the  afterdamp,  or 
constituting  the  active  agents  in  an  explosion. 

Occurrence  of  Oases  in  Mines.— Most  of  the  gases  occurring  m mines  are 
occluded  in  the  coal  or  the  strata  adjacent  to  the  coal  seam.  These  occluded 
gases  differ  widely  in  different  coals,  but  are  chiefly  marsh  gas  with  varying 
quantities  of  heavy  hydrocarbons  (olefiant  gas,  ethane,  etc.)  and  carbonic- 
acid  gas  to  a limited  extent.  In  some  coals,  a large  percentage  of  nitrogen 
gas  is  occluded,  which,  however,  transpires  very  slowly  into  the  atmosphere. 
Sulphureted  hydrogen,  when  present,  usually  exudes  from  the  underlying 
or  overlying  strata  of  the  coal  seam.  These  occluded  gases  are  the  result  of 
coal  formation,  according  to  the  best  authorities  and  evidence.  They  exist 
in  the  pores  of  the  coal  under  considerable  pressure  due  to  the  weight  of  the 


352 


VEX  TIL  A TIOX  OF  MIXFX. 


superincumbent  strata.  When  the  strata  adjacent  to  the  coal  seam  are 
impervious  to  gases,  the  occluded  gases  remain  pent  up,  and  we  have  what 
is  called  a gaseous  seam.  The  tendency  of  the  gas  is  alwavs  to  escape  to  the 
surface  or  into  the  mine  workings,  at  the  first  opportunity. 

These  gases  have  each  their  separate  effects,  and  their  combined  effect  is 
sometimes  very  complicated.  We  can  only  study  to  become  familiar  with 
the  separate  characteristics  of  each  of  these  gases,  and  judge  of  their  com- 
bined effect  when  present  in  firedamp  mixtures.  For  example,  one  effect  of 
all  these  gases  when  present  in  firedamp  mixtures  is  to  dilute  the  firedamp, 
and  to  that  extent  weaken  its  explosive  force.  Dilution  of  the  firedamp  bv 
carbonic-acid  gas  CO*  decreases  very  rapidly  the  explosiveness  of  the  fire- 
damp. When  carbonic-acid  gas  is  present  in  firedamp  to  the  extent  of  one- 
seventh  its  volume,  explosion  ceases  altogether;  in  other  words,  the 
firedamp  is  rendered  inexplosive.  The  effect  of  smaller  quantities  of  this 
gas  is  to  contract  the  explosive  limits  of  the  firedamp  as  well  as  to  weaken 
the  explosion.  The  effect  of  carbonic-oxide  gas  CO  when  present  in  fire- 
damp mixtures  is  likewise  to  dilute  the  firedamp.  The  flame,  however,  is 
lengthened  by  this  gas.  and  the  explosive  limits  of  the  firedamp  mixture  are 
widened.  In  other  words,  mixtures  of  marsh  gas  and  air.  which  were  not 
explosive  mixtures,  are  rendered  explosive  by  the  presence  of  carbonic- 
oxide  gas. 

The  chief  source  of  the  other  mine  gases  lies  in  the  slow  combustion 
of  carbonaceous  matter  in  the  gob.  gob  fires,  burning  of  lamps,  breathing 
of  men  and  animals,  etc.  The  table  on  page  353  shows  the  percentage  of 
occluded  gases  in  a number  of  coals  and  their  volume  at  normal  temper- 
ature and  pressure. 

Gas  Feeders  i Pockets!. — The  occluded  gas  of  a coal  seam  escapes  when- 
ever opportunity  is  offered,  and  accumulates  in  the  pockets  and  crevices 
of  the  adjoining  strata,  forming  what  are  called  gas  feeders.  These  consti- 
tute a very  dangerous  element  in  the  mining  of  gaseous  seams,  inasmuch  as 
when  such  a crevice  or  feeder  is  tapped  by  the  miner’s  drill,  the  gas,  which 
is  usually  under  heavy  pressure,  blows  out  in  a large  volume,  at  times  even 
blowing  the  drill  from  the  hole. 

Pressure  of  Occluded  Gases. — Occluded  gases  exist  under  a pressure  that  is 
proportionate  to  the  weight  of  the  overlying  strata.  Numerous  experiments 
in  England.  France,  and  Belgium  show*  that  the  pressure  of  gases  occluded 
in  coal  seams  frequently  amounts  to  from  10  to  16  atmospheres,  and  in  some 
cases  has  reached  32  atmospheres.  These  high  pressures  of  occluded  gases 
manifest  themselves  frequently  in  the  boring  of  gas  wells,  where  the  tools 
are  at  times  blown  from  the  bore  hole. 


Pressure  of  Occluded  Gas. 


Name  of  Mine. 

Depth  of  Hole. 
Feet. 

Pressure. 

Pounds. 

Elmore  mine,  main  bed 

8.53 

4.36 

Hetton  mine,  Hutton  bed 

8.98 

6.96 

Eppleton  mine,  Hutton  bed... 

46.90 

36.14 

Balden  mine,  Bensham  bed... 

31.85 

71.41 

Harris  Navigation  mine 

32.80 

22.04 

Merthvr  Vale  mine  

49.20 

39.67 

Celvnen  mine 

54.48 

68.32 

Harton  mine  (1,214  ft.  deep) 

16.24 

196.30 

Harton  mine  

27.55 

230.44 

Harton  mine  

37.13 

294.45 

Amount  of  Gas. — Experiments  made  by  the  Prussian  Firedamp  Commission 
have  given  results  varying  from  357  to  2,400  cu.  ft.  of  gas  liberated  per  ton  of 
coal  mined.  Mr.  Chesneau  gives  1,377  cu.  ft.  at  the  Herin  mine,  Anzin. 
Experiments  at  the  Ronchamp  mines  give  883  cil  ft. 

Outbursts  of  gas  are  frequent  occurrences  in  some  coal  seams.  They  are 
caused  by  the  occluded  gas  finding  its  way  to  a vertical  crevice  or  cleat  in  the 


gases  found  in  mines. 


353 


Gases  Enclosed  in  the  Pores  of  Coal  and  Evolved  in  Vacuo 
at  212°  F.— (Thomas.) 


Name  of  Colliery. 

Quality. 

C02 

0 

CHt 

N 

Quar 

. <* 
o>  3 

60 

68 

rH 

itity. 

d 

-M  O 

fa  u H 
U £ 

CC 

Navigation 

Steam. 

13.21 

.49 

81.64 

4.66 

250.0 

80 

Dunraven  

Steam. 

5.46 

.44 

84.22 

9.88 

218.0 

70 

Cyfarthfa  

Steam. 

18.90 

1.02 

67.47 

12.61 

147.0 

47 

Bute 

Steam. 

9.25 

.34 

86.92 

3.49 

375.0 

120 

Bonville’s  Court 

Anthracite. 

2.62 

93.13 

4.25 

555.0 

178 

Watney’s 

Anthracite. 

14.72 

84.18 

1.10 

600.0 

192 

Plymouth  Iron  Works 

Bituminous. 

36.42 

.80 

62.78 

55.9 

18 

Cwm  Clydach 

Bituminous. 

5.44 

1.05 

63.76 

29.75 

55.1 

18 

Bettwys  

Bituminous. 

22.16 

6.09 

2.68 

69.07 

1 

24.0 

8 

Gases  Enclosed  in  the  Pores  of  Coal  and  Evolved  in  Vacuo 
at  212°  F.— (If.  LeChatellier.) 


Locality. 

CH4 

C02 

N 

0 

Analyst. 

Dunraven  mine  (blowers) 

96.70 

.47 

2.79 

J.  W.  Thomas. 

Dunraven  mine  (bore  hole) 

96.50 

.44 

3.02 

J.  W.  Thomas. 

Garswood  mine 

84.16 

.86 

12.30 

2.65 

W.  Kellner. 

Garswood  mine  (blowers) 

88.86 

.41 

8.90 

1.83 

W.  Kellner. 

Glamorgan  mine  (blowers) 

93.01 

.27 

5.94 

.78 

W.  Kellner. 

Dombran  mine  (blowers) 

95.11 

.48 

4.07 

.34 

f Austrian  Firedamp 

Karwin  mine 

94.59 

.18 

4.48 

.75 

| Commission. 

Karwin  mine  (blowers)  

99.10 

.20 

.70 

Hruschau  mine 

79.16 

.19 

17.04 

.61 

Hruschau  mine  (blowers)  

87.93 

.83 

10.25 

.99 

Peters wald  mine  (blowers) 

90.00 

.15 

9.25 

.60 

Segen  Gottes  mine  

83.51 

1.17 

15.02 

.30 

Sauer. 

Segen  Gottes  mine  (borehole) 

87.16 

1.11 

11.73 

Sauer. 

Liebe  Gottes  mine  (borehole) 

77.69 

3.77 

18.48 

.06 

Sauer. 

Gases  Enclosed  in  the  Pores  of  Coal  and  Evolved  in  Vacuo 
at  212°  F .—{Schondorfr.) 


Locality. 

Clh 

CiH, 

II 

C02 

N+O 

Blowers. 

Bonifacius  mine  at  Kray  (Essen)  

Consolidation  mine  at  Schalk  ( Westphalia  1 
Konig  mine  at  Neunkirchen  (Saarbruck) 

Oberkirchen  mine  at  Schaumburg  

Cavities  in  the  roof,  Lothringen  mine  at 

Castrop  (Westphalia)  

New  Iserlohn  mine  at  Lawgendren  (West- 
phalia)  

90.94 

89.88 

84.89 
(60.46 
1 93.66 

27.95 
( 4.75 
\ 4.00 

1.62 

37.64 

.88 

.06 

1.40 

5.84 

2.11 

1.35 

.09 

.30 

.67 

.65 

2.56 

.63 

.45 

1.34 

.40 

7.36 

3.61 

12.84 

4.80 

70.25 

65.00 

95.00 

354 


VENTILATION  OF  MINES. 


Fig.  2. 


coal  seam,  as  illustrated  in  Fig.  2,  and  the  pressure  of  the  gas  thus  becomes 
distributed  over  a large  area.  Thus,  a pressure  of  10  atmospheres  of  a gas 
feeder  becoming  distributed  over  an  area  of  200  sq.  ft.  results  in  a total  pres- 
sure of  upwards  of  2,000  tons,  upon  a comparatively  small  area  of  coal. 

As  mine  openings  approach  proximity 
to  such  a locality,  this  pressure  man- 
ifests itself  by  bursting  the  coal  from 
its  position  in  the  face,  and  throwing 
it  into  the  entries,  in  some  cases  com- 
pletely blocking  the  openings  or  pas- 
sageways. Such  an  occurrence  is 
termed  an  outburst.  It  is  frequently 
accompanied  by  thunderings  and 
poundings,  which  manifest  themselves 
for  several  days  previous  to  the  actual 
outburst  of  gas.  These  poundings  are 
_ taken  as  a warning  by  the  miners 

S • experienced  in  such  regions.  The 
' s? poundings  are  probably  the  result  of 

the  gas  working  its  way  from  one 
crevice  to  another,  always  advancing 
closer  and  closer  to  the  mine  openings,  where  they  finally  burst  forth  with 
extreme  violence. 

Testing  for  Gas’ by  Lamp  Flame.— Marsh  gas  and  firedamp  are  detected  in 
mine  workings  by  the  small  flame  cap  that  envelopes  and  surmounts  the 
flame  of  the  lamp  in  a firedamp  mixture.  This  flame  cap  is  caused  by  the 
gaseous  mixture,  which  burns  as  it  comes  in  contact  with  the  flame. 
The  proportion  of  gas  in  the  mixture  determines  the  height  of  the  flame  cap. 
When  testing  for  gas,  the  lamp  flame  is  first  reduced  to  a small,  uniform 
size,  and  although  this  is  not  a universal  practice,  it  has  the  advantage  of 
giving  uniform  results.  The  lamp  is  held  in  an  upright  position,  m one 
hand,  while  the  eyes  are  carefully  screened  by  the  other  hand  from  the 
glare  of  the  light,  the  lamp  being  slowly  raised  toward  the  root  where  gas  is 
suspected.  The  flame  is  carefully  watched  for  the  first  appearance  of  a cap, 
and  the  height  of  the  cap  is  carefully  noted.  Many  lamps  are  provided  with 
a graduated  scale  set  opposite  to  the  flame,  so  that  the  height  of  a cap  may 
be  estimated  with  accuracy.  After  the  observation,  the  lamp  is  quietly  and 
promptly  withdrawn  from  the  gas.  Should  flaming  occur  within  the  lamp, 
as  sometimes  happens  when  it  is  raised  too  quickly,  or  when  the  gaseous 
mixture  is  strong,  the  lamp  should  be  withdrawn  carefully  and  not  with 
undue  haste,  as  there  is  danger  of  the  flame  of  the  gases  burning  within  the 
lamp  being  forced  through  the  gauze  by  a rapid  movement.  This  requires 
great  presence  of  mind  on  the  part  of  the  person  using  the  lamp. 

In  Fig.  3 the  heights  of  flame  cap  due  to  the  presence  of  different  proportions 
of  marsh  gas  are  shown.  These  heights,  as  given,  refer  to  the  experimental 
heights  of  flame  cap  ob- 
tained with  pure  marsh 
gas.  It  should  be  ob- 
served, however,  that  the 
presence  of  other  gases 
in  the  firedamp  will  vary 
its  explosive  character, 
and  this  fact  very  mate- 
rially modifies  the  explo- 
siveness of  certain  caps. 

For  example,  in  the  ex- 
periments on  pure  marsh 
gas,  a 2"  flame  cap  w as 
found  to  be  inexplosive; 
while,  in  the  mine,  and 
with  the  variable  char-  „ . 

acter  of  the  firedamp  mixtures  usually  found  there,  a flame  ot  1T%  in.  is 
often  found  to  indicate  explosive  conditions.  Again,  flames  of  even  less 
height  than  this  often  indicate  dangerous  conditions,  especially  where 
the  coal  is  inflammable  and  there  is  much  fine  dust  present  m the 
atmosphere.  These  conditions  account  readily  for  the  various  statements 
that  we  commonly  see  in  regard  to  the  explosiveness  of  certain  flames.  In 
fact,  each  fire  boss  learns,  after  years  of  experience,  to  depend  wholly  on  his 


1:50  LAO 


1:30  1:25 

Fig.  3. 


1:20  1:18  1:16 


SAFETY  LAMPS. 


355 


own  knowledge,  guided  by  tbe  conditions  tbat  exist  in  tbe  workings  and 
with  which  he  has  become  familiar. 


SAFETY  LAMPS. 

The  safety  lamp  is  designed  to  give  light  in  gaseous  workings  without  the 
danger  of  igniting  the  gases  present  in  the  atmosphere.  The  principle  of 
the  safety  lamp  depends  on  the  cooling  effect  that  an  iron-wire  gauze  exerts 
on  flame.  It  is  a well-known  fact  that  all  gases  ignite  at  certain  fixed 
temperatures,  and  if  this  temperature  is  decreased  from  any  cause,  the  flame 
is  extinguished.  , „ . 

Use  of  Safety  Lamps.— Safety  lamps  are  used  for  two  general  purposes  in 
the  mine,  and  may  be  classified  under  two  heads:  (a)  lamps. for  general  use; 
(b)  lamps  for  testing  for  gas.  , „ , . , 

Safety  Lamps  for  General  Work.— The  essential  features  of  a lamp  designed 
for  general  mine  work  are:  (1)  safety  in  strong  currents;  (2)  good  illuminating 
power;  (3)  security  of  lock  fastening;  (4)  freedom  from  flaming;  (5)  security 
against  accident;  (6)  simplicity  of  construction.  The  conditions  under 
which  a lamp  is  placed  at  the  working  face  differ  from  those  that  attend 
the  testing  for  gas.  The  illuminating  power  of  the  lamp  must  be  good,  so 
that  the  workman  can  see  clearly  what  he  is  doing.  The  lamp  must  not 
be  too  sensitive  to  gas,  or  its  tendency  to  flame  will  necessitate  that  a care- 
ful watch  be  kept  of  it,  and  this  would  interfere  with  the  prosecution  of  the 
miner’s  work.  Again,  the  miner  is  too  often  careless  or  neglectful  of  his 
lamp,  and  would  fail  to  give  it  the  required  attention  The  lamp  is  often 
upset,  and  is  apt  to  be  broken  by  flying  coal,  or  by  a fall,  unless  carefully 
protected.  The  lamp  should  be  so  securely  locked  as  not  to  permit  of  any 
tampering  on  the  part  of  the  miner  without  its  being  detected  in  the  lamp 
room.  In  order  that  the  lamp  may  be  thoroughly  and  rapidly  cleaned,  its 
construction  should  be  simple.  The  lamp  should  be  easily  taken  apart  and 
put  together  again  after  it  is  cleaned.  _ . . . 

Lamps  for  Testing.— The  essential  features  of  a lamp  for  testing  purposes 
are*  (1)  free  admission  of  air  below  the  flame;  (2)  no  reflecting  surface 
behind  the  flame;  (3)  ability  to  test  for  a thin  layer  of  gas  at  the  roof. 
When  testing  for  gas,  it  is  important  to  have  a free  admission  of  the  air 
below  and  around  the  flame,  as  the  flame  cap  is  very  sensitive  and  is  inter- 
fered with  seriously  by  the  conflicting  ascending  and  descending  currents 
in  a lamp  in  which  the  air  enters  above  the  flame.  A more  uniform  cap  will 
be  given  where  the  currents  ascend  quietly  around  the  flame.  # This  feature 
is  very  important  to  the  production  of  a good  flame  cap,  and  it  is  this  feature 
that  makes  the  Davy  lamp  such  a favorite  among  fire  bosses.  In  order  that 
a flame  cap  shall  be  readily  observed,  there  should  be  no  reflection  behind 
it,  as  the  eye  is  easily  deceived  under  these  conditions.  A scale  by  which, 
the  height  of  the  flame  cap  may  be  accurately  measured,  is  a convenient 
feature  in  many  lamps  for  testing  purposes. 

In  the  use  of  the  common  Davy  lamp  in  testing  for  gases,  it  is  a common, 
although  dangerous,  practice  to  turn  the  lamp  on  its  side  and  place  it  close 
up  against  the  roof.  In  this  position,  the  flame  is  very  apt  to  pass  through  the 
gauze,  from  two  causes:  The  gauze  is  readily  heated,  because  the  flame  cap 
is  close  against  it,  and  when  heated,  affords  no  protection  against  the 
passage  of  the  flame  and  the  ignition  of  the  gas  outside  the  lamp.  Again, 
in  this  position,  small  particles  from  the  roof  are  apt  to  fall  upon  the  gauze, 
and  this  may  often  assist  in  the  passage  of  the  flame  through  the  gauze.  A 
dirty  gauze  is  unsafe.  When  the  lamp  is  turned  sideways,  the  gauze  may 
become  smoked  by  contact  with  the  flame,  and  this  smoke,  or  deposit  of 
carbon,  assists  greatly  the  passage  of  flame  through  the  gauze.  Another 
common  and  dangerous  practice  on  the  part  of  the  fire  boss  is  to  brush  the 
gas  down  on  the  lamp  with  his  cap.  By  so  doing,  there  is  great  danger  of 
the  flame  being  blown  through  the  gauze  and  igniting  the  gas  that  may  be 
present.  On  these  accounts,  it  is  essential  that  a good  lamp  for  testing  pur- 
poses shall  be  able  to  draw  its  air  from  a point  close  to  the  roof,  in  cases 
where  it  is  necessary  to  do  so.  This  is  often  accomplished  by  an  extra  tube, 
which  is  supplied  with  the  lamp,  and  which  may  be  taken  off  the  lamp 

__i j.  nrui  ~ nrv  Ck  rvn  t Girl  A nf  t.np  IRTT1T)  TO  tllft  TOT). 


its  flame.  A more  uniform 
the  lard  oil  commonly  used  in  the  safety  lamp. 


356 


SAFETY  LAMPS. 


Detection  of  Small  Percentages  of  Gas.— The  Davy  lamp  in  the  hands  of  a 
careful  person  may  be  made  to  detect  the  presence  of  gas  in  quantities  as 
low  as  3f*.  It  is  claimed  by  some  tire  bosses  that  2 $ of  gas  may  be  detected 
with  a good  Davy.  For  the  detection  of  small  quantities  of  gas,  specially 
constructed  lamps  have  been  used.  These  lamps  are  designed  to  burn 
alcohol  or  hydrogen,  giving  a non-luminous  flame.  Among  these  may  be 
mentioned  the  Pieler  lamp,  burning  alcohol,  which  it  is  claimed  will  detect 
as  small  a quantity  of  gas  as  A device  known  as  the  Clowes  gas  tester 
has  been  invented,  and  may  be  attached  to  many  safety  lamps.  It  consists 
of  a hydrogen  tube  that  is  designed  to  furnish  a small  stream  of  hydrogen 
to  the  lamp  flame  when  testing  for  gas.  Surrounding  the  wick  of  the  lamp 
is  a closely  fitting  cone,  to  which  the  hydrogen  from  the  tube  is  supplied. 
When  the  lamp  is  to  be  used  for  testing  for  gas,  the  wick  is  lowered, 
extinguishing  the  oil  flame  after  the  hydrogen  is  turned  on.  It  is  claimed 
that  gas  may  be  detected  in  as  small  quantities  as  iJo  by  this  apparatus 
attached  to  any  good  safety  lamp  admitting  its  air  below  the  flame. 

The  Shaw  gas  tester  is  useful  for  determining  the  percentage  of  marsh 
gas  in  the  mine  air,  but  it  cannot  be  applied  at  the  face,  and  samples  of  gas 
must  be  taken  to  the  surface  for  analysis.  . 

Oils  for  Safety  Lamps.— Most  safety  lamps  burn  vegetable  oils,  which  are 
considered  the  safest  for  mining  use,  and  so  reported  by  the  English  Mine 
Commission.  Such  oils  are  rape-seed  oil  and  colza  oil,  made  from  cabbage 
seed.  Seal  oil  is  also  largely  used,  and  was  regarded  as  a safe  oil  by  the 
English  Mine  Commission.  Seal  oil  affords  a better  light  than  vegetable  oils, 
and  in  its  use  there  is  less  charring  of  the  wick.  A mixture  of  1 part  of  coal 
oil  to  2 parts  of  rape  or  seal  oil  is  often  used,  and  improves  the  light,  but  the 
smoke  from  the  flame  is  increased.  The  Ashworth-Hepplewhite-Gray  lamp 
is  constructed  to  burn  coal  oil,  or  a mixture  of  coal  and  lard  oil.  The  Wolf 
lamp  is  especially  designed  for  burning  naphtha  or  benzine.  Special  tests 
have  been  made  to  prove  the  safety  of  using  such  a fluid  in  this  lamp,  and 
resulted  in  demonstrating  the  fact  that  the  lamp  was  safe  under  any  condi- 
tions that  might  arise.  A thorough  test  was  made,  the  oil  vessel  of  the 
burning  lamp  being  heated  to  180°  F.,  at  which  point  the  lamp  was 
extinguished  without  ma  nifesting  any  dangerous  results. 

Types  of  Safety  Lamps.-  In  the  year  1815,  Sir  Humphrey  Davy  and  George 
Stevenson,  the  latter  a poor  miner,  discovered,  simultaneously,  that  flame 
would  not  pass  through  small  openings  in  a perforated  iron  plate.  This  led 
to  the  construction  of  what  are  known  as  the  Davy,  and  the  Stevenson  or 
“ Geordy,”  lamps.  The  Davy  lamp  is  still  a great  favorite  among  fire  bosses 
for  the  detection  of  gas  in  mine  air.  Inasmuch  as  all  safety  lamps,  of  which 
there  are  a large  number,  depend  on  the  same  principle,  we  will  only 
describe  such  lamps  as  possess  essential  features,  and  which  show  important 
improvements  and  the  gradual  developments  in  safety -lamp  construction. 

Davy  Lamp.— Fig.  4 (a)  shows  a wire  gauze  cylinder  about  5 in.  in  height 
and  1£  in.  in  diameter,  surmounted  by  a gauze  cap  2 in.  in  depth.  The 
gauze,  which  has  28  wires  to  the  inch,  or  784  apertures  to  the  square  inch,  is 
fastened  to  a brass  standard,  which  secures  it  to  the  oil  cup  or  lamp  below. 
The  gauze  at  the  top  of  the  lamp  is  doubled  by  the  cap,  which  gives  greater 
security  at  this  point,  where  the  flame  tends  to  pass  through  the  gauze  more 
quickly,  and  where  the  gauze  is  more  readily  burned  out.  The  mixture  of 
gas  and  air  enters  the  lamp  in  the  lower  part  of  the  gauze,  and  burns  within 
the  lamp,  the  products  of  combustion  passing  out  through  the  upper  portion 
of  the  gauze  cylinder.  This  lamp  gives  a good  flame  cap,  on  account  of  the 
free  access  of  the  air  below  the  flame,  which  prevents  smoking  and  increases 
the  illuminating  power  of  the  lamp.  As  a lamp  for  general  use,  the  Davy 
lamp,  however,  is  unsafe,  on  account  of  its  liability  to  flame.  In  many 
mining  localities  the  use  of  this  lamp  is  prohibited  by  law,  except  for 
purposes  of  examining  for  gas,  when  it  must  be  used  solely  by  properly 
authorized  fire  bosses.  The  flame  of  the  lamp  is  also  unprotected  from  the 
force  of  rapid  air-currents,  and  is  not  safe  when  the  velocity  of  the  current 
exceeds  6 ft.  per  second.  The  illuminating  power  of  the  lamp  is  also  not 
sufficient  for  general  work.  , . , , , 

Clanny  Lamp.— The  unbonneted  Clanny  lamp,  Fig.  4 (6),  is  constructed 
according  to  the  same  principles  as  the  Davy  lamp,  differing  only  in  the 
fact  that  the  lower  part  of  the  wire  gauze  surrounding  the  flame  is  replaced 
by  a strong  glass  cylinder  or  chimney.  The  purpose  of  this  is  to  increase 
the  illuminating  power  of  the  lamp.  The  lamp,  when  clean,  gives  a good 
light,  but  the  entrance  of  the  air  at  a point  above  the  flame,  and  its  descent 


(dJ  (e) 

Fig.  4. 


(f> 


358 


SAFETY  LAMPS. 


within  the  lamp  to  the  flame,  causes  the  lamp  to  smoke,  due  to  the  conflict 
of  the  ascending  and  descending  air-currents  within  the  lamp.  The  smoke 
becomes  deposited  on  the  glass  chimney,  which  interferes  greatly  with  the 
light.  This  lamp  is  not  a good  one  for  gas  testing,  and  in  fact  cannot  be 
used  for  that  purpose  to  any  advantage.  The  unbonneted  Clanny  is  not 
safe  in  an  air-current  having  a velocity  greater  than  8 ft.  per  second.  The 
bonneted  Clanny  obviates  this  difficulty  to  a large  extent,  but  increases  the 
tendency  of  the  lamp  to  smoke. 

Mueseler  Lamp.— This  lamp,  Fig.  4 (c),  in  all  respects  resembles  the  Clanny 
lamp  just  described,  except  that  the  tendency  in  the  Clanny  lamp  to  smoke 
is  overcome  in  the  Mueseler  by  increasing  the  draft  by  means  of  an  interior 
wrought-iron  chimney  or  tube,  supported  within  the  lamp,  and  reaching 
down  to  within  an  inch  of  the  base  of  the  flame.  The  air  enters  the  lamp 
as  in  the  Clanny,  above  the  flame,  but  is  deflected  downwards  by  the  central 
tube,  and  passes  under  the  edge  of  this  tube,  ascending  through  it  to  the  top 
of  the  lamp,  where  it  escapes.  The  Mueseler  lamp  is  a better  lamp  for 
illuminating  purposes  than  the  Clanny,  and  presents  more  security,  when 
bonneted,  against  explosions  within  the  lamp.  This  lamp  will  withstand  a 
current  of  very  much  higher  velocity  than  the  Clanny  lamp,  and  is 
reputed  to  be  safe  in  a current  having  a velocity  of  100  ft.  per  second.  The 
lamp  is  not  a good  lamp  for  the  detection  of  gas.  It  does  not  flame, 
however,  as  quickly  as  the  Clanny  lamp. 

Marsaut  Lamp— This  lamp,  Fig.  4 (d),  is  built  after  the  Clanny  lamp  in 
every  respect,  but  is  supplied  with  multiple-gauze  chimneys,  one  within  the 
other,  the  effect  of  which  is  to  increase  the  security  against  explosion  of  gas 
within  the  lamp.  The  bonneted  Marsaut  lamp  is  a peculiarly  strong  lamp 
in  this  respect.  The  gauze  used  in  the  caps  of  this  lamp  has  984  apertures  to 
the  square  inch.  This  lamp  is  often  extinguished  in  an  explosive  mixture 
by  the  force  of  the  explosion  within  itself.  It  gives  a good  light  and  is  a good 
lamp  for  general  work;  it  is  not,  however,  a good  lamp  for  testing  for  gas. 

Ashworth-Hepplewhite-Gray  Lamp.— This  lamp,  Fig.  4 (e),  combines  a number 
of  characteristic  features.  It  is  designed  for  general  work,  as  well  as  for 
testing  for  gas.  It  often  happens  that  gas  accumulates  in  a thin  layer  along 
the  roof  of  an  entry  or  working  place,  and  is  not  detected  by  the  use  of  the 
Davy  lamp  or  any  ordinary  lamp.  The  Gray  lamp  is  so  arranged  that  it 
can  be  made  to  draw  its  air  from  the  top  of  the  lamp,  by  means  of  openings 
in  the  top  of  the  four  standards  of  the  lamp,  the  air  passing  down 
through  the  standards,  and  into  the  lamp,  below  the  flame.  When  not 
in  use  for  testing,  openings  can  be  made  in  the  lower  part  of  the  stand- 
ards by  moving  a slide,  and  air  enters  at  these  openings.  The  lamp  is  essen- 
tially a bonneted  Clanny.  The  glass  chimney,  however,  as  well  as  the  gauze 
that  surmounts  it,  is  made  in  a conical  form,  the  purpose  of  this  being  to 
diffuse  the  light  upward  for  examination  of  the  roof  of  the  mine.  The 
conical  form  given  to  the  gauze  also  strengthens  the  lamp  against  explo- 
sions of  gas  within.  This  lamp  is  a very  good  all-around  lamp,  and  possesses 
good  illuminating  power.  . , . . 

Wolf  Lamp.— The  Wolf  lamp,  Fig.  4 (/),  is  rapidly  growing  m popularity 
having  been  already  introduced  in  a large  number  of  mines  in  America  ana 
England,  and  on  the  Continent.  This  lamp  is  essentially  a Clanny  lamp 
with  a free  admission  of  air.  It  is  compact  and  efficient,  and  has  good 
illuminating  power,  and  is  also  constructed  in  different  forms,  combining, 
as  desired,  any  or  all  of  the  features  of  previous  lamps.  Two  of  its  charac- 
teristic features,  however,  consist  in  a self-lighting  arrangement  accom- 
plished by  means  of  a percussive  device,  which  ignites  a wax  taper  within 
the  lamp,  and  a locking  device,  which  can  be  opened  only  with  a powerful 
magnet.  This  relighting  device  is  an  important  feature  in  any  safety  lamp 
for  general  use,  inasmuch  as  the  most  dangerous  conditions  exist  immedi- 
ately after  an  explosion,  and  the  miners  are  always  left  to  grope  their  way 
in  the  dark.  A large  number  of  lives  are  lost,  owing  to  the  confusion  that 
ensues,  the  men  becoming  bewildered  and  losing  their  wav,  when  they  are 
shortly  overcome  by  the  afterdamp  of  the  explosion.  This  lamp  permits  of 
immediate  relighting  with  safety  to  the  men.  „ , _ . , _ 

Locking  Lamps.— The  ordinary  lock  consists  of  a lead  plug,  which,  when 
inserted  in  the  lamp,  will  show  the  least  tampering  on  the  part  of  the 
miner.  Other  locks  consist  of  an  ordinary  turnbolt  operated  by  a peculiar 
key.  Magnetic  locks  allow  of  the  opening  of  the  lamp  only  by  means  of  a 

Strong  magnet  kept  in  the  lamp  room. 

Cleaning  Safety  Lamps.— Safety  lamps  should  be  thoroughly  and  regularly 


CARE  OF  SAFETY  LAMPS. 


359 


cleaned  and  filled  between  each  shift.  Each  lamp  should  then  be  lighted 
and  inspected  by  a competent  person  before  being  given  to  the  miner.  A 
careful  inspection  of  the  gauze  of  the  lamp  is  necessary,  as  well  as  of  all  the 
joints  by  which  air  may  enter  the  lamp.  It  should  be  known  to  a certainty 
that  each  lamp  is  securely  locked  before  leaving  the  lamp  room. 

Relighting  Stations.— These  stations  are  located  at  certain  places  in  gaseous 
mines  where  they  can  be  supplied  with  a current  of  fresh  air,  and  where 
there  is  no  danger  from  the  gases  of  the  mine.  The  lamp  is  apt  to  be 
overturned,  or  to  fall,  and  is  often  extinguished  thereby;  and  if  these 
stations  were  not  provided,  the  man  would  have  to  return  with  his  lamp  to 
the  surface  in  order  to  have  it  relighted.  Such  a station  is  always  located  at 
the  entrance  of  the  gaseous  portion  of  a mine,  in  cases  where  the  entire 
mine  does  not  liberate  gas. 

Illuminating  Power  of  Safety  Lamps.— The  following  table  gives  the  illumi- 
nating power  or  candlepower  of  some  of  the  principal  lamps.  The  light  of  a 
sperm  candle  is  taken  as  1,  or  unity. 


f 


Name  of  Lamp. 


Illuminating  Power 
of  Lamp. 


Davy  

Geordy  

Clanny •. 

Mueseler  

Evan  Thomas. 

Marsaut,  3 gauzes 

Marsaut,  2 gauzes 

Marsaut,  with  Ho  wat’s  deflector 

Ashworth-Hepplewhite-Gray 

Wolf  


.16 

.10 

.20 

.35 

.45 

.45 

.55 

.65 

.65 

.90 


EXPLOSIVE  CONDITIONS  IN  MINES. 

In  the  ventilation  of  gaseous  seams,  the  air-current  may  be  rendered 
explosive  by  the  sudden  occurrence  of  any  one  of  a number  of  circum- 
stances that  cannot  be  anticipated.  Among  these  are  the  following:  (1) 
Derangement  of  the  ventilating  current.  (2)  Sudden  increase  of  gas  due  to 
outburts,  falls  of  roof,  feeders,  fall  of  barometric  pressure,  etc.  (3)  Presence 
of  coal  dust  thrown  into  suspension  in  the  air,  in  the  ordinary  working  of 
the  mine,  or  by  the  force  of  blasting  at  the  working  face,  or  by  a blown-out, 
or  windy,  shot.  (4)  Pressure  due  to  a heavy  blast,  or  any  concussion  of  the 
air  caused  by  closing  of  doors,  etc.  (5)  Rapid  succession  of  shots  in  close 
workings.  (6)  Accidental  discharges  of  an  explosive  in  a dirty  atmosphere. 
Any  or  all  of  these  causes  may  precipitate  an  explosion  at  any  moment. 
Hence,  the  condition  of  the  air-current  should  be  maintained  far  within  the 
explosive  limit.  The  explosive  conditions  vary  considerably  in  different 
coal  seams.  The  nature  of  the  coal  and  its  enclosing  strata,  its  friability 
and  inflammability,  together  with  the  character  of  its  occluded  gases,  deter- 
mine, to  a large  extent,  the  explosive  conditions  in  the  seam.  Experience 
in  any  particular  seam  or  district  must  always  be  the  best  guide,  and  furnish 
the  best  standard  for  determining  the  explosiveness  of  any  given  lamp 
flame.  For  example,  a 2"  flame  may  be  comparatively  safe  in  a small  mine 
where  the  coal  is  hard  and  not  particularly  flammable,  while  a li"  flame 
cap  would  be  considered  unsafe  in  mines  where  the  conditions  are  more 
favorable  to  the  generation  of  gas  and  formation  of  coal  dust.  The  daily 
output  of  the  mine  and  the  general  care  that  is  enforced  upon  the  miners 
at  the  working  face  are  factors  that  should  always  be  considered  and  taken 
into  serious  account  in  determining  explosive  conditions  (see  Testing  for 
Gas  by  Lamp  Flame). 

Derangement  of  Ventilating  Current.— The  flow  of  the  air-current  must  be 
uniform  and  continuous.  Doors  must  be  kept  closed,  since  the  mere  setting 
open  of  a door,  for  a short  period  of  time,  is  sufficient  to  precipitate  a serious 
explosion.  Any  contemplated  change  in  the  current,  by  the  erection  of 
brattices,  air  bridges,  stoppings,  etc.,  should  be  carefully  considered  before 
the  work  is  begun,  and  every  precaution  adopted  to  secure  the  safety  of  the 


360 


VENTILATION  OF  MINES. 


men.  Derangement  of  the  current  may  occur  through  a fall  of  roof  upon 
the  main  airway,  by  which  the  area  of  the  airway  is  reduced,  which  results 
in  the  reduction  of  the  quantity  of  air  passing  in  the  mine.  If  this  fall  is 
not  noticed  at  once,  serious  results  may  happen.  The  utmost  vigilance  is 
therefore  required  on  the  part  of  fire  bosses  and  all  connected  with  mine 
workings.  The  failure  of  the  ventilating  apparatus  is  another  source  that 
gives  rise  to  the  derangement  of  the  current.  As  a rule,  furnaces  are  not 
now  employed  for  the  ventilation  of  gaseous  seams.  There  are,  however, 
some  furnaces  in  use  in  such  seams,  and  these  require  constant  attention 
lest  the  fire  should  burn  low.  Upon  any  accident  occurring  to  the  ventila- 
ting machinery,  notice  should  at  once  be  given  to  the  inside  foreman,  and 
the  men  withdrawn  as  rapidly  as  possible. 

A sudden  increase  of  gas  may  occur  at  any  time  in  a gaseous  seam,  owing 
to  an  outburst,  which  suddenly  yields  a large  volume  of  gas  and  may 
render  the  mine  air  in  that  section  extremely  explosive.  The  men  working 
on  the  return  of  such  a current  must  be  hastily  withdrawn,  and  all  lights 
extinguished.  A heavy  fall  of  coal  in  the  mine  workings  or  in  the  airways, 
or  the  tapping  of  a large  gas  feeder,  produces  the  same  effect  in  a less  degree. 
The  nearer  the  fall  of  roof  takes  place  to  the  face  of  the  workings,  the  more 
liable  it  is  to  be  followed  with  a large  flow  of  gas,  inasmuch  as  the  gas  near 
the  face  has  not  had  time  to  drain  off,  as  in  the  case  of  old  workings.  This 
fact  is  always  true  in  reference  to  new  workings  in  a gaseous  seam.  The  gas 
continues  to  flow  freely  for  a considerable  period,  wrhen  its  flow  gradually 
decreases  until  it  about  ceases.  When  a large  feeder  has  been  tapped,  it 
may  be  plugged  for  a time,  if  necessary,  but  the  better  practice  is  to  allow  it 
to  flow  freely  and  diffuse  into  the  air-current,  which  should  be  sufficiently 
increased  to  dilute  the  quantity  of  gas  given  off  and  to  render  it  inexplosive. 
The  men  upon  the  return  air  should  be  notified.  It  is  dangerous  practice  to 
light  these  feeders. 

When  there  is  a large  area  of  abandoned  workings  m the  mine,  any 
considerable  fall  of  barometric  pressure  is  usually  followed  by  a large 
outflow  of  gas  from  the  gobs  or  waste  places  of  the  mine.  A fall  of  1 in.  m 
5 hours  represents  a very  rapid  decrease  of  barometric  pressure.  At  all  large 
collieries  there  is,  or  should  be,  a good  standard  barometer  located  upon  the 
surface  near  the  shaft.  In  many  cases,  these  barometers  are  self-recording, 
and  are  often  provided  with  an  automatic  alarm  that  gives  warning  when- 
ever a fall  of  barometric  pressure  occurs.  This  warning  should  at  once  be 
conveyed  to  the  men  in  the  workings,  and  every  precaution  adopted  to 
avoid  evil  results.  The  fact  is  fairly  well  established  that  a fall  of  atmos- 
pheric pressure  is  not  followed  by  an  outflow  of  gas  from  the  mine  workings 
for  the  space  of,  say,  3 hours  after  such  fall  occurs.  This  statement  must  be 
regarded  with  caution,  however,  as  it  largely  depends  on  the  condition  and 
extent  of  the  abandoned  workings.  Where  these  are  full  of  gas,  its  expan- 
sion affects  the  condition  of  the  airways  much  more  quickly  than  m cases 
where  these  working  places  are  partly  ventilated. 

Effect  of  Coal  Dust  in  Mine  Workings —According  to  the  greater  or  less  flam- 
mability of  the  coal,  the  presence  of  fine  dust  in  the  airways  and  workings  of 
the  mine  becomes  a dangerous  factor.  Certain  coals  are  extremely  friable 
and  are  reduced  readily  to  fine  dust,  which  is  thrown  into  suspension  m the 
air-current  by  the  ordinary  operations  of  the  miners  in  their  work,  as  well 
as  by  the  concussion  of  the  air  from  numerous  causes,  and  by  the  movement 
of  cars  and  the  traveling  of  men  and  animals  upon  the  various  haul- 
ways  and  passageways.  For  a long  time  it  was  questioned  whether  the 
presence  of  dust  was  a dangerous  factor,  except  where  there  was  also  a 
small  percentage  of  gas  in  the  air.  Evidence,  however,  has  well  established 
the  fact  that  coal  dust  of  itself  is  a dangerous  element,  and  may  often  be  the 
sole  cause  of  an  explosion,  when  acted  upon  by  a flame  of  sufficient  intensity 
and  magnitude.  The  action  of  the  flame  is  to  distil  carbonic-oxide  gas  (70 
from  the  fine  particles  of  dust  suspended  in  the  air.  The  explosion  of  the 

§as  thus  formed  causes  a further  disturbance  and  raises  a larger  supply  oi 
ust,  which  likewise  contributes  to  the  liberation  of  fresh  quantities  of  gas, 
and  thus  an  explosion  is  generated  and  transmitted.  Small  quantities  of 
marsh  gas  greatly  increase  the  violence  of  this  action,  but  explosions  in 
flouring  mills  and  w7 ell-ventilated  coal  bins  establish  the  fact  that  such 
occurrences  are  not  dependent  on  the  presence  of  marsh  gas.  .... 

Too  much  faith  must  not  be  placed  in  the  use  of  water  by  sprinkling  lor 
laying  the  dust.  This  has  a beneficial  effect  in  the  immediate  vicinity,  but 
a large  amount  of  water  is  required  to  render  an  untidy  working  place  safe 


MINE  EXPLOSIONS. 


361 


at  firing  time.  Better  practice  is  to  allow  no  accumulations  of  dust  at  the 
face.  This  should  be  regularly  loaded  out  with  the  coal. 

Pressure  as  Affecting  Explosive  Conditions.— Gaseous  mixtures  that  are  not 
explosive  in  the  ordinary  condition  of  a mine,  often  become  explosive 
under  the  momentary  pressure  to  which  they  are  subjected  by  heavy 
blasting,  and,  in  some  instances,  this  may  occur  from  the  concussion 
of  the  air  caused  by  the  quick  shutting  of  a door.  In  the  latter  case,  how- 
ever, the  explosive  condition  of  the  air  would  necessarily  have  to  be  close  to 
the  limit,  in  order  for  such  a slight  occurrence  to  precipitate  an  explosion. 
The  factor  of  pressure  as  increasing  the  explosiveness  of  gaseous  mixtures 
should  be  considered  and  constantly  borne  in  mind. 

Rapid  Succession  of  Shots  in  Close  Workings.— It  constantly  happens  that 
two,  three,  or  more  shots  are  fired  by  means  of  fuse  or  touch  squibs  in  a 
single  chamber  or  heading,  where  the  circulation  of  air  is  not  always  the 
best.  The  practical  effect  is  that  a considerable  quantity  of  carbonic-oxide 
gas  CO  is  produced  by  the  firing  of  the  first  shot,  and  this  gas  does  not  have 
time  to  diffuse  or  become  diluted  by  the  air-current  before  it  is  fired  by  the 
flame  of  the  following  shots.  An  explosion  may  often  be  precipitated  by  such 
an  occurrence,  if  the  workings  are  at  all  dusty.  Two  shots  at  the  most  are  all 
that  should  be  fired  at  one  time  in  a close  chamber  or  heading. 

Mine  Explosions.— The  explosion  of  gas  in  a mine  usually  arises  from  the 
ignition  of  an  explosive  mixture  of  gas  and  air  called  firedamp , which  has 
accumulated  in  some  unused  chamber  or  cavity  of  the  roof,  or  in  the  waste 
places  of  the  mine,  and  has  been  ignited  by  a naked  light,  by  the  flame  of  a 
shot,  or  by  a mine  fire.  The  initial  force  of  an  explosion  is  generally 
expended  locally,  but  the  flame  continues  to  feed  upon  the  carbonic-oxide 
gas  generated  by  the  incomplete  combustion  of  the  firedamp  mixture, 
and  distilled  also  from  the  coal  dust  thrown  into  the  air  by  the  agitation. 
Air  is  required  to  burn  this  carbonic-oxide  gas;  this  causes  the  flame  to 
travel  against  the  air-current,  or  in  the  direction  in  which  fresh  air  is  found. 
In  the  other  direction,  or  behind  the  explosion,  the  flame  is  soon  extin- 
guished in  its  own  trail  when  the  initial  force  of  the  explosion  is  expended. 
The  explosion  continues  to  travel  along  the  airways  against  the  current  as 
long  as  there  is  sufficient  gas  or  coal  dust  for  it  to  feed  upon,  or  until  its 
temperature  is  cooled  below  the  point  of  ignition,  by  some  cause  such  as,  for 
example,  the  rapid  expansion  of  the  area  of  the  workings.  We  observe  the 
chief  factor  in  transmitting  an  explosion  is  the  presence  of  carbonic-oxide 
gas,  which  lengthens  the  flame  and  extends  the  effect. 

The  recoil  of  an  explosion  is  the  return  of  the  flame  along  the  path  that  it 
has  just  traversed.  In  the  recoil,  the  flame  burns  more  quietly,  advances 
more  slowly,  and  travels  close  to  the  ropf.  The  evidence  found  at  the  point 
where  a recoil  took  place,  or  an  explosion  turned  back,  has  been  sufficient 
to  establish  the  fact  that  the  recoil  is  caused  primarily  by  a cooling  of  the  tem- 
perature, probably  caused  very  largely  by  an  expansion  of  the  area  of  the 
airway.  Soot  is  often  deposited  at  this  point  in  considerable  quantity,  if  the 
action  of  the  flame  is  not  such  as  to  consume  it.  This  fact  alone  shows  the 
combustion  at  this  point  to  have  been  incomplete.  Immediately  in  the  rear 
of  the  flame  is  a mixture  of  carbonic-oxide  gas  CO,  which  bursts  into  flame 
at  the  sudden  stoppage  of  the  advancing  explosion.  This  is  rendered 
possible  by  the  flow  of  cold  air  from  the  adjacent  chambers  and  workings 
along  the  floor  of  the  airway.  The  flame  now  retreats,  burning  the  trail  of 
carbonic-oxide  gas  along  the  roof,  fed  by  the  cold  air  along  the  floor. 

To  Explore  Workings  After  a Serious  Explosion.— The  shafts  or  slopes  and  the 
ventilating  machinery  should  claim  the  first  attention  of  those  on  the 
surface,  and  an  effort  should  be  made  to  reach  the  bottom  as  expeditiously 
as  possible.  Assistance  from  neighboring  collieries,  both  in  the  way  of 
skilled  labor  and  advice,  should  also  be  requested.  Should  the  shaft  or  slope 
need  repairs  before  communication  between  top  and  bottom  is  restored,  the 
person  in  charge  on  the  surface  should,  in  the  meantime,  see  that  props  of 
the  lengths  in  ordinary  use,  brattice  boards,  brattice  cloth,  and  nails  are 
brought  to  a convenient  place  for  putting  on  the  cage  or  car,  and  he  ought 
also  to  collect  all  the  tools  likely  to  be  required,  such  as  axes,  saws,  ham- 
mers, etc.  It  is  also  important  that  rough  tracings  of  the  workings  be 
prepared  for  the  use  of  the  leader  of  each  squad  of  explorers.  Officials  will 
understand  how  useful  these  will  be  to  those  that  are  penetrating  into  work- 
ings about  which  every  man  of  his  squad  may  have  been  heretofore  ignorant. 

When  the  explorers  have  arrived  at  the  bottom  and  are  ready  to  proceed, 
there  should  be  for  each  section,  if  more  than  one  is  operated  upon,  two 


362 


VENTILATION  OF  MINES. 


managers,  each,  having  his  own  squad  of  men,  and  his  own  particular  duty 
to  do.  One  may  take  charge  of  restoring  the  ventilation,  the  inspection  of 
the  workings,  and  the  clearing  of  the  roads;  the  other  may  appoint  and 
have  charge  of  the  bottom  man,  the  conveying  of  material,  and  the  detailing 
of  stretcher  companies  where  required.  They  can  consult  and  help  each 
other  in  every  difficulty,  but  system  is  necessary  if  the  work  is  to  be  done  in 
the  shortest  possible  time.  . A . _ ... 

The  manager  who  has  charge  of  the  men  m front  should  appoint  two 
experienced  men  with  good  nerves  to  act  as  foremen,  instructing  them  to 
inspect  and  report  to  him  the  condition  of  the  workings  within  a short 
radius.  He  should  then  form  the  rest  of  his  men  into,  say,  three  squads  of 
three  each,  who  will  work  together  at  stoppings  or  falls  until  separated  by 
him  or  until  the  end  of  the  shift.  Being  near  the  bottom,  it  will  probably 
be  found  that  all  is  clear  for  three  or  four  breast  or  stoop  lengths,  and  stop- 
pings are  required  to  be  put  up.  Material  will  be  required  for  this,  and 
when  the  cage  is  first  sent  to  the  top  for  it,  it  should  not  be  kept  there  to 
enable  the  top  man  to  put  on  a big  load,  but  it  should  be  sent  down  with  all 
despatch,  loaded  with  a half  dozen  each  of  props  and  brattice  boards,  with 
one  piece  of  cloth  and  nails.  This  will  allow  a start  to  be  made,  and  will 
prevent  the  anxious  men  from  worrying  over  what  to  them  is  an  unac- 
countable delay.  Larger  loads  can  be  sent  down  in  subsequent  trips.  For 
convenience  in  carrying,  the  brattice  cloth  may  be  cut  in  lengths  to  suit  the 
gangways  or  headings  with  2 or  3 ft.  to  spare.  Squad  No.  1 should  be 
detailed  to  the  first  stopping.  This  may  be  put  up  with  boards  at  top  and 
bottom  and  cloth  between.  If  the  air-current  is  strong,  a few  of  the  follow- 
ing stoppings  may  be  put  up  by  squads  No.  2 and  No  3,  with  cloth  only 
stretched  between  two  props.  These  can  be  very  rapidly  put  up  and  will 
drive  the  ventilation  forwards,  thus  allowing  the  firemen  to  extend  rapidly 
the  area  of  inspection.  These  stoppings  can  be  completed  by  No.  1 detail. 
In  a short  time  it  may  become  impossible  to  proceed  in  this  manner,  lhe 
foul  air  will  in  all  probability  become  more  difficult  to  dislodge,  and  eventu- 
ally one  detail  may  be  able  to  put  up  stoppings  as  quickly  as  the  firedamp  or 
chokedamp  can  be  carried  off.  Part  of  what  may  be  called  the  ventilaung 
detail  can  now  be  transferred  to  the  bearer  detail,  the  duties  of  the  latter 
having  become  heavier  as  the  stoppings  advanced.  It  is  not  an  easy  task  to 
carry  props  long  distances  in  a stooping  posture,  and  when  to  that  is  added, 
it  may  be,  the  carrying  out  of  the  living  or  dead  bodies,  the  men  begin  to 
fag  very  soon.  But  the  person  in  charge  here  must  see  that  the  forward 
party  is  kept  in  material  for  stoppings  so  that  no  delay  may  occur  on  that 
account.  A system  of  staging  gives  relief  to  the  carrying  parties. 

To  conclude  with  a few  general  remarks Let  those  that  nave  never  yet 
assisted  to  explore  a mine  after  an  explosion  be  assured  of  this,  that  the 
chief  requisites  in  a leader  are  a capacity  for  hard  work  and  the  ability  to 
organize  his  men  into  a system,  however  roughly,  whereby  work  will  be  best 
forwarded.  It  mil  not  speed  the  work  to  say  to  a dozen  or  more  men, 
generally,  do  this  or  that,  neither  is  it  beneficial  to  allow  all  the  workmen 
to  discuss  matters  and  suggest  plans.  Those  in  charge  ought  to  arrange  what 
is  to  be  done.  Anything  else  results  in  noise  and  confusion.  And  let  men 
that  are  sent  from  other  collieries  take  with  them  their  own  toefis  and  lamps. 
Those  in  charge  ought  to  take  note  of  the  position,  etc.  of  bodies  found,  and 
of  every  point  which  is  likely  to  throw  light  on  the  cause  or  origin  of  the 
explosion.  This  can  be  more  correctly  done  before  the  roads  are  disturbed 
by  oust  and  travel.  These  notes  might  not  only  be  the  means  of  ascertain- 
ing the  cause  of  explosion,  but  also  of  pointing  out  a way  of  prevention  m 

In  no  case  after  an  explosion  should  the  air-current  of  the  mine  be 
reversed  from  its  usual  course,  except  only  after  careful  consideration, 
because  of  the  reliance  placed  by  the  entombed  workmen  on  their  knowl- 
edge of  the  direction  in  which  the  air  should  be  moving-  and  the  reversal 
of  the  current  may  drive  the  gases  of  the  explosion  upon  them  with  disas- 
trous results.  Conditions  must  be  allowed  to  remain  as  they  exist,  and  the 
rescuers  conform  themselves  to  such  conditions  in  the  best  manner  possible. 

QUANTITY  OF  AIR  REQUIRED  FOR  VENTILATION. 

The  quantity  of  air  required  for  the  adequate  ventilation  of  a mine  can- 
not be  stated  as  a rule  applicable  in  every  case.  Regulations  tlmt  would 
supply  a proper  amount  of  air  for  the  ventilation  of  a tlnck  seam  would  be 


ELEMENTS  IN  VENTILATION. 


363 


found  to  cause  great  inconvenience  if  applied  without  modification  to  the 
workings  in  a thin  seam.  Likewise,  the  ventilation  of  an  old  mine  with 
extended  workings,  a large  area  of  which  has  been  abandoned,  and  m many 
cases  not  properly  sealed  off,  will  require,  naturally,  a larger  quantity  of  air 
per  capita  than  a newly  opened  mine  or  shaft.  The  natural  conditions 
existing  in  rise  and  dip  workings,  with  respect  to  the  gases  that  may  be 
liberated  or  generated  in  those  workings,  call  for  the  modification  of  the 
quantity  of  air  required  in  each  case.  For  example,  dip  workings,  where 
much  blackdamp  is  generated,  will  require  a larger  quantity  of  air,  or 
higher  velocity  at  the  working  face,  to  carry  off  such  damps;  and  rise  work- 
ings, liberating  a large  amount  of  marsh  gas,  will  likewise  require  a higher 
velocity  at  the  working  face.  On  the  other  hand,  a reversal  of  these 
conditions,  such  as  a large  quantity  of  marsh  gas  being  liberated  m dip 
workings,  or  a similar  amount  of  blackdamp  being  generated  in  rise  work- 
ings, will  require  a comparatively  low  velocity  of  the  air  at  each  respective 

Quantity  Required  by  State  Laws.— The  quantity  of  air  required  by  the 
laws  of  the  several  States  is  generally  specified  as  100  cu  ft.  per  man 
per  minute,  and  in  many  cases  an  additional  amount  of  500  cu.  it.  per 
animal  per  minute  is  stated.  This  quantity  is  m no  case  stated  as  the 
actual  amount  of  air  required  for  the  use  of  each  man  or  animal,  but  is  only 
the  result  of  experience,  as  showing  the  quantity  of  air  required  for  the 
proper  ventilation  of  the  average  mine,  based  on  the  number  of  men  and 
animals  employed.  The  number  of  men  employed  m a mine  is  an  indica- 
tion of  the  extent  of  the  working  face,  while  the  number  of  animals 
employed  is  an  indication  likewise  of  the  extent  of  the  haulage  roads,  or  the 
development  of  the  mine.  These  amounts  refer  particularly  to  non-gaseous 

SeaThe  Bituminous  Mine  Law  of  Pennsylvania  specifies  that  there  shall  be 
not  less  than  100  cu.  ft.  per  minute  per  person  m any  mine,  while  150  cu.  it. 
are  required  in  a mine  where  firedamp  has  been  detected. . > 

The  Anthracite  Mine  Law  of  Pennsylvania  specifies  a minimum  quantity 
of  200  cu.  ft.  per  minute  per  person.  Each  of  these  laws  contains  modifying 
clauses,  which  specify  that  the  amount  of  air  in  circulation  shall  be  sufficient 
to  “dilute,  render  harmless,  and  sweep  away”  smoke  and  noxious  or 

da  Quantity  of  Air  Required  for  Dilution  of  Mine  G.*...-To  determiiie > this 
requires  a knowledge  of  the  quantity  of  gas  generated  °^llb^ted  m the 
workings.  The  quantity  of  air  for  dilution  should  be  ample,  and  should  be 
such  as  not  to  permit  the  condition  of  the  current  to  approach  the  explosive 
point.  The  ventilation  should  be  ample  at  the  face.  - r . 

Quantity  of  Air  Required  to  Produce  the  Necessary  Velocity  of  Current  at  the 
Face  — This  consideration  modifies  considerably  the  quantity  of  air  required 
for  the  ventilation  of  thick  and  thin  seams.  The  velocity  of  the  current  is 
dependent  not  only  on  the  quantity  of  air  in  circulation,  but  on  the  area  of  the 
air  passage.  This  area  is  quite  small  in  thin  seams,  and  often  very  large  in 
thick  seams.  As  a result,  the  velocity  is  often  low  at  the  face  of  thick 
seams,  and  insufficient  for  the  proper  ventilation  of  the  face,  although  the 
quantity  of  air  passing  into  such  a mine  may  be  very  large.  A certain 
velocity  of  the  current  is  always  required  in  order  to  sweep  away  the  gases. 
This  velocity  depends  on  the  character  of  the  gases  and  the  position  ot  the 
workings.  Heavy  damps  are  hard  to  move  from  dip  workings  where  they 
have  accumulated;  and,  likewise,  lighter  damps  accumulating ’at 'the: face 
of  steep  pitches  are  hard  to  brush  away,  and  the  velocity  of  the  current  in 
these  cases  must  be  equal  to  the  task  of  driving  out  these  gases. 


ELEMENTS  IN  VENTILATION. 

The  elements  in  any  circulation  of  air  are  (a)  horsepower  or  power 
applied;  (5)  resistance  of  the  airways,  or  mine  resistance,  which  gives  rise 
to  the  total  pressure  in  the  airway;  (c)  velocity  generated  by  the  power 
applied  against  the  mine  resistance.  ,.  , . 

Horsepower  or  Power  of  the  Cur  rent. -The  power  applied  is  often ^spoken 
of  as  the  power  upon  the  air.  It  is  the  effective  power  of  the  ventilating 
motor,  whatever  this  may  be,  including  all  the  ventilating , ^£eJ^cies, 
whether  natural  or  otherwise.  The  power  upon  the  air  may  be  the  power 
exerted  by  a motive  column  due  to  natural  causes,  or  to  a furnace,  or  may 


364 


VENTILATION  OF  MINES. 


be  the  power  of  a mechanical  motor.  The  power  upon  the  air  is  always 
measured  in  foot-pounds  per  minute,  which  expresses  the  units  of  work 
accomplished  in  the  circulation. 

Mine  Resistance.— The  resistance  offered  by  a mine  to  the  passage  of  an 
air-current,  or  the  mine  resistance,  is  due  to  the  friction  of  the  air  rubbing 
along  the  sides,  top,  and  bottom  of  the  air  passages.  This  friction  causes  the 
total  ventilating  pressure  in  the  airway,  and  is  equal  to  it.  Calling  the 
resistance  E,  the  unit  of  ventilating  pressure  (pressure  per  square  foot)  p, 
and  the  sectional  area  of  the  airway  a,  we  have,  E = pa;  that  is  to  say,  the 
total  pressure  is  equal  to  the  mine  resistance. 

Velocity  of  the  Air-Current.— Whenever  a given  power  is  applied  against  a 
given  resistance,  a certain  velocity  results.  For  example,  if  the  power  u 
(foot-pounds  per  minute)  is  applied  against  the  resistance  pa,  a velocity  v 
(feet  per  minute)  is  the  result;  and  since  the  total  pressure  pa  moves  at 
the  velocity  v,  the  work  performed  each  minute  by  the  power  applied  is  the 
product  of  the  total  pressure  by  the  space  through  which  it  moves  per 
minute,  or  the  velocity.  Thus,  u = (pa)  v. 

Relation  of  Power,  Pressure,  and  Velocity.— The  relation  of  these  elements  of 
ventilation  is  not  a simple  relation.  For  example,  a given  power  applied  to 
move  air  through  an  airway  establishes  a certain  resistance  and  velocity  in 
the  airway.  The  resistance  of  the  airway  is  not  an  independent  factor;  that 
is  to  say,  it  does  not  exist  as  a factor  of  the  airway  independent  of  the 
velocity,  but  bears  a certain  relation  to  the  velocity.  Power  always  produces 
resistance  and  velocity,  and  these  two  factors  always  sustain  a fixed  relation. 

This  relation  is  expressed  as  follows:  The  total  pressure  or  resistance  varies 
as  the  square  of  the  velocity;  i.  e.,  if  the  power  is  sufficient  to  double  the 
velocity,  the  pressure  will  be  increased  4 times;  if  the  power  is  sufficient  to 
multiplv  the  velocity  B times,  the  pressure  will  be  increased  9 times.  Thus, 
we  observe  that  a change  o*f  power  applied  to  any  airway  means  both  a 
change  of  pressure  and  a change  of  velocity. 

Again,  since  the  power  is  expressed  by  the  equation  u = (pa)  v,  and  since 
p a,  or  the  total  pressure,  varies  as  v 2,  the  work  varies  as  vK  From  this  it 
follows  that,  if  the  velocity  is  multiplied  by  2,  and,  consequently,  the  total 
pressure  by  4,  the  work  performed  (pa)  v will  be  multiplied  by  23  = 8.  We 
thus  learn  that  the  power  applied  varies  as  the  cube  of  the  velocity. 


MEASUREMENT  OF  VENTILATING  CURRENTS. 

The  measurement  and  calculation  of  any  circulation  in  a mine  airway 
includes  the  measurement  of  (a)  the  velocity  of  the  air-current,  (b)  of  pres- 
sure, (c)  of  temperature,  (d)  calculation  of  pressure,  quantity,  and  horse- 
power of  the  circulation. 

These  measurements  should  be  made  at  a point  in  the  airway  where  the 
airway  has  a uniform  section  for  some  distance,  and  not  far  from  the  foot  of 
the  downcast  shaft  or  the  fan  drift. 

Measurement  of  Velocity.— For  the  purpose  of  mine  inspection,  the  velocity 
of  the  air-current  should  be  measured  at  the  foot  of  the  downcast,  at  the 
mouth  of  each  split  of  the  air-current,  and  at  each  inside  breakthrough,  in 
each  split.  These  measurements  are  necessary  in  order  to  show  that  all  the 
air  designed  for  each  split  passes  around  the  face  of  the  workings. 

The  measurement  of  the  velocity  of  a current  is  best  made  by  means  of 
the  anemometer.  This  instrument  consists  of  a vane  placed  in  a circular 
frame  and  having  its  blades  so  inclined  to  the  direction  of  its  motion  that 
1 ft.  of  lineal  velocity  in  the  passing  air-current  will  produce  1 revolution  of 
the  vane.  These  revolutions  are  recorded  by  means  of  several  pointers, 
each  having  a separate  dial  upon  the  face  of  the  instrument,  the  motion 
being  communicated  by  a series  of  gear-wheels  arranged  decimally  to  each 
other.  Most  anemometers  are  provided  with  a large  central  pointer  that 
makes  1 revolution  for  each  100  revolutions  of  the  vane.  The  dial  for  this 
pointer  is  marked  by  100  divisions,  which  record  the  number  of  lineal  feet 
of  velocity.  In  very  accurate  work  with  the  anemometer,  certain  constants 
are  used  as  suggested  by  the  instrument  maker,  but  these  constants  are  of 
little  value  in  ordinary  practice  and  are  of  doubtful'  value  even  in  more 
accurate  observations. 

The  measurement  of  the  velocity  of  an  air-current  must  necessarily 
represent  only  approximately  the  true  velocity  in  the  airway.  The  air 
travels  with  a greater  velocity  in  the  center  of  the  airway,  and  is  retarded  at 


MEASUREMENT  OF  PRESSURE. 


385 


the  sides,  top,  and  bottom  by  the  friction  of  these  surfaces.  Hence,  the 
air  to  a large  extent  rolls  upon  these  surfaces,  which  naturally  generates  an 
eddy  at  the  sides  of  airways.  When  measuring  the  air,  the  anemometer 
should  be  held  in  a position  exactly  perpendicular  to  the  direction  of  the 
current,  and  moved  to  occupy  different  positions  in  the  airway,  being 
held  an  equal  time  in  each  position,  or  it  may  be  moved  continuously 
around  the  margin  of  the  airway,  and  through  the  central  portion.  The 
person  taking  the  observation  should  observe  the  caution  of  not  obstruct- 
ing the  area  of  the  airway  by  his  body,  as  the  area  is  thereby  reduced,  and 
the  velocity  of  the  current  increased.  The  area  of  the  airway  is  accurately 
measured  at  the  point  where  the  observations  are  taken. 

To  obtain  the  quantity  of  air  passing  (cubic  feet  per  minute),  multiply 
the  area  of  the  airway,  at  the  point  where  the  velocity  is  measured,  by  the 
velocity. 

Example.— The  anemometer  gives  a reading  of  1,320  ft.  in  2 minutes,  the 
height  of  the  airway  is  6 ft.  6 in.,  and  its  average  width  8 ft.  8 in.  What 
volume  of  air  is  passing  in  the  airway  per  minute? 

1 320 

X 8f  X — 37,180  cu.  ft.  per  min. 

The  measurement  of  the  ventilating  pressure  is  made  by  means  of  a water 
column  in  the  form  of  a water  gauge. 

Water  Gauge.— The  water  gauge  is  simply  a glass  U tube  open  at  both  ends. 
Water  is  placed  in  the  bent  portion  of  the  tube,  and  stands  at  the  same 
height  in  both  arms  of  the  tube  when  each  end  of  the  tube  is  subjected  to 
the  same  pressure.  If, 
however,  one  end  of  the 
tube  is  subjected  to  a 
greater  pressure  than 
the  other  end,  the  water 
will  be  forced  down  in 
that  arm  of  the  tube, 
and  will  rise  a corre- 
sponding height  in  the 
other  arm,  the  differ- 
ence of  level  in  the  two 
arms  of  the  tube  repre- 
senting the  water  col- 
umn balanced  by  the 
excess  of  pressure  to 
which  the  water  in  the 
first  .arm  is  subjected. 

An  adjustable  scale 
graduated  in  inches 
measures  the  height  of 
the  water  column.  The 
zero  of  the  scale  is  ad- 
justed to  the  lower 
water  level,  and  the  Fig.  6. 

upper  water  level  will 
then  give  the  reading  of  the  water  gauge.  One  end  of  the  glass  tube  is 
drawn  to  a narrow  opening  to  exclude  dust,  while  the  other  end  is  bent  to 
a right  angle,  and  passing  back  through  the  standard  to  which  the  tube  is 
attached,  is  cemented  into  the  brass  tube  that  passes  through  a hole  in-  the 
partition  or  brattice,  when  the  water  gauge  is  in  use.  The  bend  of  the  tube 
is  contracted  to  reduce  the  tendency  to  oscillation  in  the  height  of  water 
column.  (See  Fig.  5.) 

When  in  use,  the  water  gauge  must  be  in  a perpendicular  position.  It  is 
placed  upon  a brattice  occupying  a position  between  two  airways,  as  shown 
at  A,  Fig.  6.  The  brass  tube  forming  one  end  of  the  water  gauge  is 
inserted  m a cork,  and  passes  through  a hole  bored  in  the  brattice.  The 
water  gauge  must  not  be  subjected  to  the  direct  force  of  the  air-current,  as 
m this  case  the  true  pressure  will  not  be  given.  Fig.  6 shows  the  instrument 
as  occupying  a position  in  the  breakthrough,  between  two  entries.  It  will 
be  observed  that  the  water  gauge  records  a difference  of  pressure,  each  end 
of  the  water  gauge  being  subject  to  atmospheric  pressure,  but  one  end  in 
addition  being  subject  to  the  ventilating  pressure,  which  is  the  difference  of 


Fig.  5. 


366 


VENTILATION  OF  MINES, 


pressure  between  the  two  entries.  The  water  gauge  thus  enables  us  to 
measure  the  resistance  of  the  mine  inbye  from  its  position  between  tw  o 
airways.  If  placed  in  the  first  breakthrough,  at  the  foot  of  the  shaft,  it 
measures  the  entire  resistance  of  the  mine,  but  if  placed  at  the  mouth  ot  a 
split  it  measures  only  the  resistance  of  that  split.  It  never  measures  the 
resistance  outbye  from  its  position  in  the  mine,  but  always  inbye  (see  Calcula- 
tion of  Pressure).  ,«  , . 

Measurement  of  Temperature.— It  is  important  to  measure  the  temperature 
of  the  air-current  at  the  point  where  the  velocity  is  measured,  as  the  tem- 
perature is  an  important  factor  of  the  volume  of  air  passing  (see  Expan- 
sion of  Air  and  Gases,  etc.).  , __  . . _ 

Thermometers.— Thermometers  measure  changes  m the  temperature  ot  the 
atmosphere  bv  the  contraction  and  expansion  of  mercury  or  spirits;  or  they 
may  be  made  entirely  of  metal,  and  the  changes  of  temperature  are  then 
measured  by  the  expansion  and  contraction  of  the  sensitive  metallic 
portion  These  latter  are  known  as  aneroid  thermometers.  The  Fahren- 
heit thermometer  is  the  one  most  commonly  used  in  America.  By  this 
scale,  the  freezing  point  of  water  at  the  sea  level  is  placed  at  32°  above  zero; 
the  boiling  point  of  water  at  sea  level  is  placed  at  212°  above  zero,  so  that  the 
space  between  these  two  points  is  divided  into  180°.  ^ . 

Reaumur  and  Centigrade  thermometers  are  used  on  the  continent  ot 
Europe.  Of  these  two,  the  first  is  generally  used  in  Germany,  and  the 
second  in  France,  but  the  latter  is  almost  exclusively  used  by  the  scientists 

of  all  nations.  . _ ^ . . , , 

In  the  Reaumur  thermometer,  the  freezing  and  boiling  points  are  placed 
at  0°  and  80°,  respectively.  In  the  Centigrade,  the  freezing  and  boiling 
points  are  placed  at  0°  and  100°,  respectively.  _ ,.  .,  .. 

To  Convert  Fahrenheit  Into  Centigrade— (1)  Subtract  32  and  divide  the 
remainder  by  1.8,  or  multiply  by  f . A ... ...  . , , 

If  a Fahrenheit  thermometer  registers  16/°,  what  will  be  the  register  by  a 
Centigrade  thermometer  ? 

167  - 32  (167  - 32)5 


1.8 


= 75°  Centigrade. 


75°  Centigrade. 


To  Convert  Centigrade  Into  Fahrenheit. — (1)  Multiply  by  1.8,  or  f,  and  add  32. 

• Ars  75°,  what  will  be  the  register  by  a 


If  the  Centigrade  thermometer  registers 
Fahrenheit  thermometer? 

75  X 1.8  + 32  = 167°  Fahrenheit.  + 32 


167°  Fahrenheit. 


To  Convert  Fahrenheit  Into  Reaumur.— (1)  Subtract  32,  and  divide  by  2.25, 

°r  mhe'Fahrenheit  thermometer  registers  113°,  what  will  be  the  register  by 
the  Reaumur  thermometer? 


113  — 32 
2.25 


= 36°  Reaumur. 


I113 — 32^  = 36°  Reaumur. 
9 


To  Convert  Reaumur  Into  Fahrenheit— (1)  Multiply  by  2.25,  or  multiply  by  f, 

If  the  Reaumur  thermometer  registers  36°,  what  will  be  the  register  by 
the  Fahrenheit  thermometer? 

36  X 2.25  + 32  = 113°  Fahrenheit.  + 32  = 113°  Fahrenheit. 

To  Convert  Reaumur  Into  Centigrade.— Multiply  by  1-25.  . . 

If  a Reaumur  thermometer  registers  32°,  what  will  be  the  register  by 
a Centigrade  thermometer? 

32  X 1.25  = 40°  Centigrade. 

To  Convert  Centigrade  Into  Reaumur.— Multiply  by  .8.  . . 

If  a Centigrade  thermometer  registers  40°,  what  will  be  the  register  by 
a Reaumur  thermometer? 

40  x .8  = 32°  Reaumur. 

Calculation  of  Mine  Resistance— The  mine  resistance  is  equal  to  the  total 
pressure  p a that  it  causes.  This  mine  resistance  is  dependent  upon  tnree 
factors:  (a)  The  resistance  k offered  by  1 sq.  ft.  of  rubbing  surface  to 

a current  naving  a velocity  of  1 ft.  per  minute.  The  coefficient  of  friction  k, 
or  the  unit  of  resistance , is  the  resistance  offered  by  the  unit  of  rubbing  sur- 
face to  a current  of  a unit  velocity.  This  unit  resistance  has  been  variously 
estimated  by  different  authorities  (see  following  table).  The  value  most 
universally  accepted,  however,  is  that  known  as  the  Atkinson  coefficient 


THE  EQ  UIVALENT  ORIFICE. 


367 


(.0000000217).  (b)  The  mine  resistance,  which  varies  as  the  square  of  the 
velocity.  ( c ) The  rubbing  surface.  Hence,  if  we  multiply  the  unit  resist- 
ance by  the  square  of  the  velocity,  and  by  the  rubbing  surface,  we  will 
obtain  the  total  mine  resistance  as  expressed  by  the  formula  pa  = ksv *. 

Table  of  Various  Coefficients  of  Friction  of  Air  in  Mines. 

Pressure  per 
Sq.  Ft.  Decimals 
of  a Pound. 


J.  J.  Atkinson’s  treatise 

A.  Devillez  in  Ventilation  des  Mines: 

Forchies - 

Crachet-Picquery  

Grand  Baisson 

Average  of  2,  3,  and  4 

Used  in  Ventilation  des  Mines 

Arched  Tunnels 

Along  a working  face  of  coal 

G.  G.  Andre,  Atmosphere  of  Coal  Mines 

Peclet,  Cheminee  (Devillez,  p.  112) 

j)  Clark  

According  to  Goupiiliere’s  Cours  d’  Exploitation  des  Mines, 
Vol.  II,  p.  389: 

D’Aubuisson - 

Navier 

W.  Fairley 

J.  Stanley  James 

D.  Murgue 


.0000000217 

.000000008211 

.000000008928 

.000000008611 

.000000008585 

.000000009511 

.000000002113 

.000000014266 

.000000022424 

.000000003697 

.000000002272 


.000000001955 

.000000001872 

.00000001 

.00000000929 

.000000008242 


It  will  be  observed  that  J.  J.  Atkinson’s  coefficient  is  greatly  in  excess  of 
any  other,  with  the  exception  of  Andre’s.  Fairley’s  is  derived  from  an 
average  taken  between  Atkinson,  Devillez,  and  Clark,  and,  undoubtedly,  it 
is  an  exceedingly  simple  coefficient  to  work  out  calculations  with,  as  it  will 
save  a great  mass  of  figures.  James,  in  his  work  on  colliery  ventilation, 
reduces  the  coefficient  still  further  on  the  authority  of  the  Belgian  Mine 
Commission,  but  he  gives  a most  unwieldy  figure  to  use. 

Atkinson’s  figure  is  the  one  most  in  use,  and  if  it  is  too  high,  it  errs  on  the 
side  of  safety,  and  it  is  always  advisable  to  have  plenty  of  spare  ventilating 
power  at  a mine.  For  this  reason,  and  until  a regular  and  thorough  investi- 
gation, made  by  a commission  of  competent  men,  provides  a standard  coef- 
ficient, we  prefer  to  abide  by  Atkinson’s  coefficient,  and  it  is  used  in  all  our 
calculations 

Calculation  of  Power,  or  Units  of  Work  per  Minute. — If  we  multiply  the  total 
pressure  by  the  velocity  (feet  per  minute)  with  which  it  moves,  we  obtain  the 
unite  of  work  per  minute,  or  the  power  upon  the  air.  Hence,  u = pav  = 
ksv*  which  isrthe  fundamental  expression  for  work  per  minute , or  power. 

The  Equivalent  Orifice.— This  term,  often  used  in  regard  to  ventilation, 
evaluates  the  mine  resistance,  or,  as  will  be  seen  from  the  equation  given 
below  for  its  value,  it  expresses  the  ratio  that  exists  between  the  quantity 
of  air  passing  in  an  airway  and  the  pressure  or  water  gauge  that  is  produced 
by  the  circulation.  This  term  was  suggested  by  M.  Daniel  Murgue,  and 
refers  to  the  flow  of  a fluid  through  an  orifice  in  a thin  plate,  under  a given 
head.  The  formula  expressing  the  velocity  of  flow  through  such  an  orifice 
is  v = 1/2 gh]  multiplying  both  members  of  this  equation  by  A,  and  substi- 
tuting for  the  first  member  A v,  its  value  q , we  have,  after  transposing  and 

correcting  for  vena  contracta,  A = - , in  which  .62  is  the  coefficient  for 

.62y  2 g h 

the  vena  contracta  of  the  flow.  Reducing  this  to  cubic  feet  per  minute  and 
inches  of  water  gauge  represented  by  i , we  have,  finally,  the  equation 

A = .0004  X —7=.  By  this  formula,  Murgue  has  suggested  assimilating  the 

V i 

flow  of  air  through  a mine  to  the  flow  of  a fluid  through  a thin  plate;  since, 
in  each  case,  the  quantity  and  the  head  or  pressure  vary  in  the  same  ratio. 
Thus,  applying  this  formula  to  a mine,  Murgue  multiplies  the  ratio  of  the 
quantity  of  air  passing  (cubic  feet  per  minute)  and  the  square  root  of  the 
water  gauge  (inches)  by  .0004,  and  obtains  an  area  A , which  he  calls 
the  equivalent  orifice  of  the  mine.  . , „ 

Potential  Factor  of  a Mine.  ( Proposed  by  J.  T.  Beard.) — Equations  8 and  27, 


368 


VENTILATION  OF  MIXES. 


pages  370-371,  give,  respectively,  the  pressure  and  the  power  that  will  circu- 
late a given  quantitv  of  air  per  minute  in  a given  airway.  These  equations 
may  be  written  as  equal  ratios,  expressed  in  factors  of  the  current  and  the 
* T)  Jc  s u k s 

airway,  respectively;  thus,  — = — ^ , and  — = which  show  that  the  ratio 

between  the  pressure  and  the  square  of  the  quantity  it  circulates  in  any 
given  airwav  is  equal  to  the  ratio  between  the  power  and  the  cube  of  the 
quantity  it  circulates.  Solving  each  of  these  equations  with  respect  to  q, 
we  have  the  following: 

With  respect  to  pressure, 

*-  (a\i rs)^- 

With  respect  to  power, 

*“  (rny*- 


Hence,  we  observe  that,  in  any  airway,  for  a constant  pressure , the  quan- 


tity of  air  in  circulation  is  proportional  to  the  expression  a-y  and,  for  a 

constant  power , the  quantity  is  proportional  to  the  expression  which 

terms  are  called  the  potentials  of  the  mine  with  respect  to  pressure  and 
power,  respectively;  and  their  values  — — and  are  the  potentials  of  the 

Vp 


current  with  respect  to  pressure  and  power,  respectively.  These  factors,  it 
will  be  observed,  evaluate  the  airway,  as  they  determine  the  quantity  of  air 
a given  pressure  or  power  will  circulate  in  that  airway  (cubic  feet  per 
minute).  Bv  their  use.  the  relative  quantities  of  air  any  given  pressure  or 
power  will  circulate  in  different  airways  are  readily  determined.  The  rule 
mav  be  stated  as  follows:  . . . 

Rule. — For  any  given  pressure  or  power,  the  quantity  of  air  in  circulation  is 
always  ' proportional  to  the  potential  for  pressure,  or  the  potential  for  power , as 
the  case  may  he. 

This  rule  finds  important  application  in  splitting  (see  Calculation  of 
Natural  Splitting) . In  all  cases  where  the  potential  is  used  as  a ratio,  the 
relative  potential  maybe  employed  by  omitting  the  factor  k;  or  it  may  be 
employed  to  obtain  the  pressure  and  power,  in  several  splits  by  multiplying 
the  final  result  by  k (see  Formulas  46,  47,  etc.,  page  378). 

Example.—  20,000  cu.  ft.  of  air  is  passing  in  a mine  in  which  the  airway 
is  6 ft.  X 8 ft.,  and  10.000  ft.  long,  under  a certain  pressure;  it  is  required  to 
find  what  quantity  of  air  this  same  pressure  will  circulate  in  a mine  in  which 
the  airwav  is  6 ft.  X 12  ft.,  and  8,000  ft.  long. 

Calculating  the  potential  Xp  with  respect  to  the  pressure  for  each 
of  these  mines,  or  airways,  we  have,  using  the  relative  potential, 


Xi=  6X8< 


6X8 


6X12 


— .62845,  and  X2  — 6 X 12^  2(6  + J2)  x 8,000 


\ 2(6  + 8)  X 10,000 

= 1.1384.  Since  the  ratio  of  the  quantities  is  e^ual  to  the  ratio  of  the 
potentials  with  respect  to  pressure,  in  these  two  mines,  we  write  the  propor- 


20,000  X 1.1384 
.62845 


= 36,229  cu.  ft.  per 


tion  20,000  : q2  : : .62845  : 1.1384,  and  q2  = 

min.  . . . . . ,, 

Example.—  20,000  cu.  ft.  of  air  is  passing  in  a mine  in  which  the  airway 
is  6 ft.  X 8 ft.,  and  10,000  ft.  long,  under  a certain  power;  it  is  required  to  find 
what  quantity  of  air  will  be  circulated  by  this  same  power  m a mine  in 
which  the  airway  is  6 ft.  X 12  ft.,  and  8,000  ft.  long. 

We  calculate  the  potential  Xu  with  respect  to  power  for  each  of  these 

6X8 

mines,  using,  as  before,  the  relative  potential.  Thus,  X\  = ^ io  000 


--  .7337,  and  X2 


6X  12 


f 2(6 


1.0905.  Then,  in  this  case,  since  the 


12)X  8,000 

ratio  of  the  quantities  is  equal  to  the  ratio  of  the  potentials  with 


POTENTIAL  FACTOR. 


369 


respect  to  power,  we  write  the  proportion,  20,000  : q%  : : .7337  : 1.0905,  and 

a = 20,000  X 1^0905  _ 29  726  cu.  ft.  per  min. 
v2  7337 

The  following  table  will  serve  to  illustrate  the  use  of  the  formulas 
employed  in  these  calculations.  It  will  be  observed  that  there  are 
several  formulas  for  quantity,  and  for  velocity,  and  for  work  or  horse- 
power, but  in  each  respective  case  the  several  formulas  are  derived  by 
simple  transposition  of  the  terms  of  the  original  formula,  and  are  tabulated 
here  for  convenience.  Choice  must  be  made  in  the  use  of  any  of  these  for- 
mulas,  according  to  the  known  terms  in  each  example. . Thus,  an  example 
mav  ask-  What  pressure  will  be  produced  in  passing  a given  quantity  of  air 
through 'a  certain  mine,  the  size  and  length  of  the  airways  being  given? 

We  then  use  the  formula  p = if  t^ie  question  asks  what  quan- 

tity of  air  a given  pressure  will  produce  in  this  same  mine,  we  use  the 


formula  q 


-4 


pa 

ks 


Xfl. 


It  will  be  observed  that  this  second  formula  is  a 


simple  transposition  of  the  first.  , „ , x ...  , 

In  like  manner  the  question  maybe  asked,  what  power  will  produce  a 
certain  quantity  of  air  in  a certain  airway;  and  the  expression  used,  in  this 

case,  is  u = k Sy~.  Or,  the  question  may  be  asked,  what  quantity  of  air  will 

be  produced  in  a given  airway  by  means  of  a certain  power^or  work  applied 


to  the  airway.  In  this  case,  the  formula  used  is  q = If  the  fic- 

tion asks  for  the  power  required  to  produce  a given  velocity  in  a fiven  air- 
way the  formula  employed  is  u = ksvs.  All  of  these  formulas  are  derived 

by  combining  the  simple  formulas  p = — — , q = av,  and  u = qp. 

To  illustrate  the  use  of  the  formulas,  we  take  as  an  example  an  under- 
ground road,  5 ft.  wide  by  4 ft.  high,  and  2,000  ft.  in  length,  and  calculate  the 
value  of  each  symbol  or  letter,  assuming  a velocity  of  500  ft.  per  minute. 


Symbol. 

Value  of  Symbol  for  this 
Particular  Example. 

Area  of  airway  (5  ft.  X 4 ft.) 

tinrconowpr  ♦ 

a 

h 

20  sq.  ft. 
2.959  H.  P. 

Pnoffipipnt  of  friction  + 

k 

.0000000217  lb. 

VUCUILIV/Ilt  VII  llibtlL/ll  | 

T nn rrfVi  rtf*  QirWflV  

l 

2,000  ft. 

±J0IlgXIl  U1  dll  WdJ  • • • 

Perimeter  of  airway,  2(5  ft.  + 4 ft.)  

Pressure  (lb.  per  sq.  ft.)  

nna-nfitxr  r»f  nir  fpn  ft,  ner  mm. ) 

0 

P 

q 

18  ft. 

9.765  lb. 
10,000  cu.  ft. 

quantity  ui  an  it. 

A rna  nf  rnhhiTiP1,  SlirftinP  

s 

36,000  sq.  ft. 

AltJd  UI  lUUUIllg  ouiiavyt  

Units  of  work  per  minute  (power) 

Volnpitv  (ft  ripr  min  ^ 

u 

V 

97,650  ft.-lb. 
500  ft. 

V clUtltj  \ A o*  pci  min. ; 

Wotpr  an  n orp  

i 

1.87788  ip. 

vv  dtei  gdugu  - 

TTmiiirolorit  nrifipp  nf  flip  TTVlTlfi  

A 

2.919  sq.  ft. 

JjU  UlValcIll  UllliUC  ui  tiiv  

■prktori+ml  fnr  nowpr  

Xu 

217.16  units. 

i UtUlltldl  lUi  pu  vv  Cl  

■pz-ktcntial  fnr*  tytpwii  re 

Xv 

3,200  units. 

I Utt/Utldl  1U1  piCOOUlC  

Weight  of  1 cu.  ft.  of  downcast  air 

Motive  column  (downcast  air)  

moYvfVi  nf  fnrnflPP  shaft,  

P 

W 

M 

D 

.08098  lb. 
120.5  ft. 
306.77  ft. 

Average  temperature  of  the  upcast  column.. 
Average  temperature  of  the  downcast  column 

T 

t 

350°  F. 
32°  F. 

*A  horsepower  is  equal  to  33,000  units  of  work.  . , , . 

t This  coefficient  of  friction  is  an  invariable  quantity,  and  is  the  same  in  every  calculation 
relating  to  the  friction  of  air  in  mines. 

Note.— The  water  gauge  is  calculated  to  five  decimal  places  to  enable  all 
the  other  values  to  be  accurately  arrived  at.  In  practice,  it  is  only  read  to 
one  decimal  place. 


370 


VENTILATION  OF  MINES. 


FORMULAS. 


On  the  right  side  of  each  formula,  the  various  calculations,  based  on  the 
example  given,  are  worked  out  in  figures. 


To  Find: 

No. 

Formula. 

• 

Specimen  Calculation. 

Rubbing  sur- 
face of  an  air- 
way. (Sq.ft.) 

1 

s — l 0 

2,000  X 18  = 36,000  sq.  ft. 

Area  of  an 
airway.  (Sq.ft.) 

2 

a = — 

V 

20  sq.  ft.  of  area. 

ouU 

Velocity. 
(Ft.  per  min.) 

3 

II 

^^  = 500  ft. 

4 

3 / U 

V ” \ks 

si  97,650 

\ .0000000217  X 36,000 

5 

v JVa 

1 9.765X20 

\ ks 

\ .0000000217  X 36,000 

6 

u 

97,650  cqq  «■ 

9.765  X 20  500  * 

~ pa 

Pressure. 

7 

ksv 2 

.0000000217  X 36,000  X 5002  n 

(Lb.  persq.  ft.) 

P 

a 

20  ~ 9./6D1D. 

8 

k sq2 

J 

.0000000217  X 36,000  X 10,0002 
20s 

= 9.765  lb. 

9 

II 

|g 

10 

p = Mw 

120.58  X .08098  = 9.765  lb. 

11 

p — 5.2  i 

5.2  X 1.87788  = 9.765  lb. 

12 

II 

hk 

cel 

13 

II 

Sc 

Water  gauge. 
(Inches.) 

14 

i - 

5.2 

9'™5  = 1.87788  in. 

Resistance  of 
an  airway. 
(Total  pressure, 

15 

16 

pa  = ksv 2 
u 

pa  = - 

* V 

.0000000217  X 36,000  X 5002  = 195.31b. 
9^°  = 195.3  n>. 

FORMULAS. 


371 


To  Find:  1 

No. 

Formula.  | 

1 

Specimen  Calculation. 

Quantity. 

17 

q ==  av 

20  X 500  = 10,000  cu.  ft. 

(Cu.ft.per  min) 

►c 

It 

•e  18 

97  650 

18 

y/,oou  = 1Q  000  cu  ft 
9.765 

19 

1 9.765  X 20 

\ .0000000217  X 36,000 

= 10,000  cu.  ft. 

20 

9 = ^Xa 

3 1 97,650  ^ 0q 

\ .0000000217  X 36,000 
= 10,000  cu.  ft. 

21 

q = Xufu 

217.16  X ^ 97,650  = 10,000  cu.  ft. 

22 

q = fX/u 

^3,2002  X 97,650  = 10,000  Cu.  ft. 

23 

q = XpVp 

3,200  X V 9-765  = 10,000  cu.  ft. 

Units  of  work 

24 

u = avp 

20  X 500  X 9.765  = 97,650  ft.-lb. 

per  minute,  or 
power  on  the 

25 

II 

8 

10,000  X 9.765  = 97,650  ft.-lb. 

air. 

(Ft.-lb.permin) 

26 

u = ksv* 

.0000000217  X 36,000  X 5003 
= 97,650  ft.-lb. 

ks  q3 

.0000000217  X 36,000  X 10,0003 

27 

U ~~  a3 

203 

= 97,650  ft.-lb. 

28 

u = h 33,000 

2.959  X 33,000  = 97,650  ft.-lb. 

29 

qz 

u = x~z 

■A-u 

= 97,650  ft.-lb. 

30 

q 3 

- 97-65oft-ib- 

Horsepower. 

31 

h U 

“ 33,000 

= 2.959  H.  P. 

33,000 

Power  poten- 
tial. 
(Units.) 

32 

|w 

° £ 
II 

20  — 217.16  units. 

^ .0000000217  X 36,000 

33 

1*1*. 

II 

Hi 

j/lO’OOO2  - 217.16  units. 
\ 9.765 

■y  q 

10,000  _ 2^7  i6  units. 

34 

■A-u  — O/— 

fn 

^97,650 

372 


VENTILATION  OF  MINES. 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Pressure  poten- 
tial. 
(Units.) 

35 

r 

36 

H & 

f " 

11  S 

•ell  *|a 

Co  1 

1 20 

„ 20  \ .0000000217  X 36,000 

= 3,200  units. 

-Q-Q°  = 3,200  Units. 

V 9.765 

Equivalent 
orifice. 
(Sq.  ft.) 

37 

.0004 q 

Vi 

.0004  X 10,°°0  — 2.919  sq.  ft. 
1/1.87788 

Motive  column, 
downcast  air. 
(Feet.) 

38 

39 

K-1>x459+r 

M = -P- 
w 

30M7xm  + ^ - m5ft- 

Motivecolumn, 
upcast  air. 
(Feet.) 

40 

39 

M = 2- 

w 

306-77x!“;32-m7ft; 

mZ  = m7ft- 

Variation  of  the  Elements.— In  the  illustration  of  the  foregoing  table,  we 
have  assumed  fixed  conditions  of  motive  column,  as  well  as  fixed  conditions 
in  the  mine  airways.  It  is  often  convenient,  however,  to  know  how  the 
different  elements,  as  velocity  v,  quantity  q,  pressure  p,  power  u,  etc.,  will 
vary  in  different  circulations;  since  we  may,  by  this  means,  compare  the 
circulations  in  different  airways,  or  the  results  obtained  by  applying  different 
pressures  and  powers  to  the  same  airway.  These  laws  of  variation  must 
always  be  applied  with  great  care.  For  example,  before  we  can  ascertain 
how  the  quantity  in  circulation  will  vary  in  different  airways,  we  must 
-mow  whether  the  pressure  or  the  power  is  constant  or  the  same  for  each 
hrway.  The  following  rules  may  always  be  applied: 


For  a constant  pressure:  v varies  as  q varies  as  (relative  poten- 
tial for  pressure). 


For  a constant  power:  varies  as 


q varies  as  — ^ (relative  potential 


for  power). 

For  a constant  velocity:  q varies  as  a;  p varies  as  — ; u varies  as  lo. 

For  a constant  quantity:  v varies  inversely  as  a;  p varies  inversely  as  Xu3 
(potential  for  power);  u varies  inversely  as  XM3  (potential  for  power)  or 
directly  as  p. 

For  the  same  airway:  The  following  terms  vary  as  each  other:  v , q, 

Vp,  fu. 

Similar  Airways. 


v = length  of  similar  side,  or  similar  dimension. 

For  a constant  pressure:  v varies  as  ^ j ; q varies  as  r 2 X rvariesas 

lv2,  or  V lq2. 


DISTRIBUTION  OF  AIR. 


373 


1.  3 jr2 

For  a constant  power:  v varies  as  q varies  as  r X yjj ; r varies  as 


r^or^«3 


For  a constant  velocity:  q varies  as  r2;  p varies  as  u varies  as  Ir; 


/-l  u 
r varies  as  y g,  or 

For  a constant  quantity:  v varies  inversely  as  r2;  p and  u vary  inversely  as 
or 

Furnace  Ventilation. 

p (motive  column)  varies  as  D;  q varies  as  j/  D. 

Fan  Ventilation. 


rb  . l 

, ; r varies  as  — — 

* V*' 


It  has  been  customary  in  calculations  pertaining  to  the  yield  of  centrif- 
ugal ventilators  to  assume  as  follows:  q varies  as  n;  p varies  as  ?i2; 
u varies  as  n3. 

More  recent  investigation,  however,  shows  that  when  we  double  the 
speed  we  do  not  obtain  double  the  quantity  of  air  in  circulation;  or,  in  other 
words,  the  quantity  does  not  vary  exactly  as  the  number  of  revolutions  of 
the  fan.  Investigation  also  points  to  the  fact  that  the  efficiency  of  centrif- 
ugal ventilators  decreases  as  the  speed  increases.  To  what  extent  this  is  the 
case  has  not  been  thoroughly  established.  The  variation  between  the  speed 
of  a fan  and  the  quantity,  pressure,  power,  and  efficiency,  as  calculated  from 
a large  number  of  reliable  fan  tests,  may  be  stated  as  follows: 

Forthesamefan,  discharging  against  a constant  potential:  q varies  as  n-91. 
p varies  as  it1*94.  Complement  of  efficiency  (1  — K)  varies  as  w425. 

The  efficiency  here  referred  to  is  the  mechanical  efficiency , or  the  ratio 
between  the  effective  work  qp  and  the  theoretical  work  of  the  fan. 


DISTRIBUTION  OF  AIR  IN  IWNE  VENTILATION. 

When  a mine  is  first  opened,  the  air  is  conducted  in  a single  current 
around  the  face  of  all  the  headings  and  workings,  and  returns  again  to  the 
upcast  shaft,  where  it  is  discharged  into  the  atmosphere.  As  the  develop- 
ment of  the  mine  advances,  however,  it  becomes  necessary  to  divide  the  air 
into  two  or  more  splits  or  currents.  This  division  or  splitting  of  the  air- 
current  is  usually  accomplished  at  the  foot  of  the  downcast,  or  as  soon  as 
possible  after  the  current  enters  the  mine.  There  are  several  reasons  why 
the  air-current  should  be  thus  divided.  The  most  important  reason  is  that 
the  mine  is  thereby  divided  into  separate  districts,  each  of  which  has  its 
own  ventilating  current,  which  may  be  increased  or  decreased  at  will. 
Fresh  air  is  thus  obtained  at  the  face  of  the  workings,  and  the  ventilation  is 
under  more  perfect  control.  It  often  happens  that  certain  portions  of  a mine 
are  more  gaseous  than  others,  and  it  is  necessary  to  increase  the  volume  of 
air  in  these  portions,  which  can  be  readily  accomplished  when  each  district 
has  its  own  separate  circulation.  Again,  the  gases  and  foul  air  are  not 
conducted  from  one  district  to  another,  but  each  district  is  supplied  with 
fresh  air  direct  from  the  main  intake.  Should  an  explosion  occur  in  any 
part  of  the  mine,  it  is  more  apt  to  be  confined  to  one  locality  when  a mine  is 
thus  divided  into  separate  districts.  Another  consideration  is  the  reduced 
power  necessary  to  accomplish  the  same  circulation  in  the  mine;  or  the 
increased  circulation  obtained  by  the  use  of  the  same  power. 

Requirements  of  Law  in  Regard  to  Splitting.— The  Anthracite  Mine  Law  of 
Pennsylvania  specifies  that  every  mine  employing  more  than  75  persons 
must  be  divided  into  two  or  more  ventilating  districts,  thus  limiting  the 
number  that  are  allowed  to  work  on  one  air-current  to  75  persons.  The 
Bituminous  Mine  Law  of  Pennsylvania  limits  the  number  allowed  to  work 
upon  one  current  to  65  persons,  except  in  special  cases,  where  this  number 
may  be  increased  to  100  persons  at  the  discretion  of  the  mine  inspector. 

Practical  Splitting  of  the  Air-Current— When  the  air-current  is  divided  into 
two  or  more  branches,  it  is  said  to  be  split.  The  current  may  be  divided  one 
or  more  times;  when  split  or  divided  once,  the  current  is  said  to  be  traveling 


374 


VENTILATION  OF  MINES . 


in  two  splits,  each  branch  being  termed  a split.  The  number  of  splits  in 
which  a current  is  made  to  travel  is  understood  as  the  number  of  separate 
currents  in  the  mine,  and  not  as  the  number  of  divisions  of  the  current. 

Primary  Splits.— When  the  main  air-current  is  divided  into  two  or  more 
splits,  each  of  these  is  called  a primary  split.  . 

Secondary  Splits. — Secondary  splits  are  the  divisions  of  a primary  split. 

Tertiary  Splits.— Tertiary  splits  result  from  the  division  of  a secondary  split. 

Equal  Splits  of  Air.— When  a mine  is  spoken  of  as  having  two  or  more  equal 
splits,  it  is  understood  to  mean  that  the  length  and  the  size  of  the  separate 
airways  forming  those  splits  are  equal  in  each  case.  It  follows,  of  course, 
from  this  that  the  ventilating  current  traveling  in  each  split  will  be  the 
same,  inasmuch  as  they  are  all  subject  to  the  same  ventilating  pressure. 
When  an  equal  circulation  is  obtained  in  two  or  more  splits  by  the  use  of 
regulators,  these  splits  cannot  be  spoken  of  as  equal  splits.  * 

Unequal  Splits  of  Air.— By  this  is  meant  that  the  airways  forming  the  splits 
are  of  unequal  size  or  length.  Under  this  head  we  will  consider  (a)  Natural 
Division  of  the  Air- Current;  ( b ) Proportionate  Division  of  the  Air- Current. 

Natural  Division  of  the  Air-Current.— By  natural  division  of  air  is  meant  any 
division  of  the  air  that  is  accomplished  without  the  use  of  regulators;  or,  in 
other  words,  such  division  of  the  air-current  as  results  from  natural  means. 
If  the  main  air-current  at  any  given  point  in  a mine  is  free  to  traverse  two 
separate  airways  in  passing  to  the  foot  of  the  upcast  shaft,  and  each  of  these 
airways  is  free  or  an  open  split,  i.  e.,  contains  no  regulator,  the  division  of 
the  air  will  be  a natural  division.  In  such  a case,  the  larger  quantity  of  air 
will  always  traverse  the  shorter  split  of  airway.  In  other  words,  an  air-cur- 
rent always  seeks  the  shortest  way  out  of  a mine.  A comparatively  small 
current,  however,  will  always  traverse  the  long  split  or  airway. 

Calculation  of  Natural  Splitting.— It  is  always  assumed,  in  the  calculation 
of  the  splitting  of  air-currents,  that  the  pressure  at  the  mouth  of  each  split, 
starting  from  any  given  point,  is  the  same.  Since  this  is  the  case,  in  order 
to  find  the  quantity  of  air  passing  in  each  of  several  splits  starting  from  a 
common  point,  the  rule  given  under  Potential  Factor  of  a Mine  is  apphed. 
This  rule  may  be  stated  as  follows: 

The  ratio  between  the  quantity  of  air  passing  in  any  split  and  the  pressure 
potential  of  that  split  is  the  same  for  all  splits  starting  from  a common  point. 
Also  the  ratio  between  the.  entire  quantity  of  air  in  circulation  in  the  several 
splits  and  the  sum  of  the  pressure  potentials  of  those  splits  is  the  same  as  the 
above  ratio,  and  is  equal  to  the  square  root  of  the  pressure. 

Expressed  as  a formula,  indicating  the  sum  of  the  pressure  potentials 

(Xi  + X2  + etc.)  by  the  expression  2IP,  this  rule  is  = Jr  = V P- 


Hence,  p = 


and  u = 


express  the  pressure  and  power, 


(2JP) 2 ~ (2XP)2  . . _ 

respectively,  absorbed  by  the  circulation  of  the  splits.  These  are  the  basal 
formulas  for  splitting,  from  which  any  of  the  factors  may  be  calculated  by 
transposition.  They  will  be  found  illustrated  in  the  table  at  the  end  of  this 
section.  We  will  give  here  two  examples  only,  showing  the  calculation  of 
the  natural  division  of  an  air-current  between  several  splits.  \\  e have,  from 

Xi  ^ 

the  above  formulas,  q\  = ^ ^ Q. 

Example. — In  a certain  mine,  an  air-current  of  60,000  cu.  ft.  perminute 
is  traveling  in  two  splits  as  follows:  Split  A,  6 ft.  X 8ft.,  5,000  ft.  long- 
split  B,  5 ft.  X 8 ft.,  10,000  ft.  long.  It  is  required  to  find  the  natural  division 

of  this  air-current.  . , , . , r+ 

Calculating  the  relative  potentials  for  pressure  in  each  split,  we  have 


for  split  A 


for  split  B,  X2 


.*1  -«Vs 

= 4°^ 


48 


2(6  + 8)5,000 
40 

2(5  + 8)10,000 


= .4961 


and  2 Xp  = 1.3849; 


and  substituting  these  values,  we  have, 


Qi 

Q2 


- v 60,000  = 38,506  cu.  ft.  per  min.; 
1.3849 

x 60.000  = 21,494  cu.  ft.  per  min. 

1.3849 


and 


DISTRIBUTION  OF  AIR. 


375 


Example.— In  a certain  mine,  there  is  an  air-current  of  100,000  cu.  ft.  per 
minute  traveling  in  three  splits  as  follows:  Split  A,  6 ft.  X 10  ft.,  8,000  ft.  long; 
split  B , 6 ft.  X 12  ft.,  15,000  ft.  long;  split  C,  5 ft.  X 10  ft.,  6,000  ft.  long.  Find 
the  natural  division  of  this  current  of  air. 

Calculating  the  respective  relative  potentials  with  respect  to  pressure, 
we  have 

for  split  A X,  = 60 y2(6  + 1ffx8,000  - -9185; 

for  split  B,  Xt  = 72^ + - .8314; 

for  split  C,  X3  = 50 V2(5  + 10rx6,-60b  = '8833' 

Adding  these  potentials,  we  have  2 Xp  = .9185  + .8314  + .8333  = 2.5832. 
Then,  applying  the  foregoing  rule,  we  have 

qi  = X 100,000  = 35,556  cu.  ft.  per  min.; 

«2  = ~~  X 100,000  = 32,184  cu.  ft.  per  min.; 

QQOO 

and  x 100’000  = 32,260  cu-  ft-  Per  min- 

Total,  100,000 

Proportional  Division  of  the  Air-Current.— It  continually  happens  that  differ- 
ent proportions  of  air  are  required  in  the  several  splits  of  a mine  than  would 
be  obtained  by  the  natural  division  of  the  air-current.  It  is  usually  the  case 
that  the  longer  splits  employ  a larger  number  of  men,  and  require  a larger 
quantity  of  air  passing  through  them.  They,  moreover,  liberate  a larger 
quantity  of  mine  gases,  for  which  they  require  a larger  quantity  of  air  than 
is  passing  in  the  smaller  splits.  The  natural  division  of  the  air-current 
would  give  to  these  longer  splits  less  air,  and  to  the  shorter  ones  a larger 
amount  of  air,  which  is  directly  the  reverse  of  what  is  needed.  On  this 
account,  recourse  must  be  had  to  some  means  of  dividing  this  air  pro- 
portionately, as  required.  This  is  accomplished  by  the  use  of  regulators,  of 
which  there  are  two  general  types,  the  box  regulator  and  the  door  regulator. 

Box  Regulator. — This  is  simply  an  obstruction  placed  in  those  airways  that 
would  naturally  take  more  air  than  the  amount  required.  It  consists  of  a 
brattice  or  door  placed  in  the  entry,  and  having  a small  shutter  that  can  be 
opened1  to  a greater  or  less  amount.  The  shutter  is  so  arranged  as  to  allow 
the  passage  of  more  or  less  air,  according  to  the  requirements.  The  box 
regulator  is,  as  a rule,  placed  at  the  end  or  near  the  end  of  the  return  air- 
way of  a split.  It  is  usually  placed  at  this  point  as  a matter  of  convenience, 
because,  in  this  position,  it  obstructs  the  roads  to  a less  extent,  the  haulage 
from  the  back  entry  in  this  split  being  carried  over  to  the  main  haulway, 
through  a cross-cut,  before  this  point  is  reached.  The  difficulty,  however, 
can  be  avoided,  in  most  cases,  by  proper  consideration  in  the  planning  of 
the  mine  with  respect  to  haulage  and  ventilation.  The  objection  to  this 
form  of  regulator  is  that,  in  effect,  it  lengthens  the  airway,  or  increases  its 
resistance,  making  the  resistance  of  all  the  airways,  per  foot  of  area,  the 
same.  It  is  readily  observed  that,  by  thus  increasing  the  resistance  of  the 
mine,  the  horsepower  of  the  ventilation  is  largely  increased,  for  the  same 
circulation.  This  is  an  important  point,  as  it  will  be  found  that  the  power 
required  for  ventilation  is  thus  increased  anywhere  from  50$  to  100$  over 
the  power  required  when  the  other  form  of  regulator  can  be  adopted. 

Door  Regulator.— In  this  form  of  regulator,  which  was  first  introduced  by 
Beard,  the  division  of  the  air  is  made  at  the  mouth  of  the  split.  The  regu- 
lator consists  of  a door  hung  from  a point  of  the  rib  between  two  entries, 
and  swung  into  the  current  so  as  to  cut  the  air  like  a knife.  The  door  is 
provided  with  a set  lock,  so  that  it  may  be  secured  in  any  position,  to  give 
more  or  less  air  to  the  one  or  the  other  of  the  splits,  as  required.  The  posi- 
tion of  this  regulator  door,  as  well  as  the  position  of  the  shutter  in  the  box 
regulator,  is  always  ascertained  practically  by  trial.  The  door  is  set  so  as 
to  divide  the  area  of  the  airway  proportionate  to  the  work  absorbed  in  the 


376 


VENTILATION  OF  MINES. 


respective  splits.  The  pressure  in  any  split  is  not  increased,  each  split 
retaining  its  natural  pressure.  . . . , 

Calculation  of  Pressure  for  Box  Regulators— When  any  required  division  of 
the  air-current  is  to  be  obtained  by  the  use  of  box  regulators,  these  are 
placed  in  all  the  splits,  save  one.  This  split  is  called  the  open,  or  free,  split, 

and  its  pressure  is  calculated  in  the  usual  way  by  the  formula  p = ~as~' 

The  natural  pressure  in  this  open  split  determines  the  pressure  of  the  entire 
mine,  since  all  the  splits  are  subject  to  the  same  pressure  in  this  form  of 

^ First*  determine  in  which  splits  regulators  will  have  to  be  placed,  in  order 
to  accomplish  the  required  division  of  the  air.  Calculate  the  natural  pres- 
sure, or  pressure  due  to  the  circulation  of  the  air-current,  for  each  split, 

when  passing  its  required  amount  of  air,  using  the  formula  p = ^ The 

split  showing  the  greatest  natural  pressure  is  taken  as  the  free  split.  In  each 
of  the  other  splits,  box  regulators  must  be  placed,  to  increase  the  pressure 
in  those  splits;  or,  in  other  words,  to  increase  the  resistance  of  those  splits 
per  unit  of  area.  . , . . 

Example. — The  ventilation  required  m a certain  mine  is: 

split  A , 6 ft.  X 9 ft.,  8,000  ft.  long;  40,000  cu.  ft.  per  min. 

split  B , 5 ft.  X 8 ft.,  6,000  ft.  long;  40,000  cu.  ft.  per  min. 

split  a 9 ft.  X 9 ft.,  8,000  ft.  long;  10,000  cu.  ft.  per  min. 

split  D,  6 ft.  X 8 ft.,  10,000  ft.  long;  30,000  cu.  ft.  per  mm. 

In  which  of  these  splits  should  regulators  be  placed,  to  accomplish  the 
required  division  of  air,  and  what  will  be  the  mine  pressure?  . 

Calculating  the  pressure  due  to  friction  in  each  split  when  passing  its 
required  amount  of  air,  we  find, 

.0000000217  X 2(6  + 9)8,000  X 40,0002 
' 5#  ~ 

.0000000217  X 2(5  + 8)6,000  X 40.0002 
~40* 

.0000000217  X 2(9  + 9)8,000  X 10.0002 
813 

.0000000217  X 2(6  + 8)10,000  X 30,0002  = 49  45  lb  per  sq  ft 


for  split  A,  p = 
for  split  B,  p = 


for  split  C,  p = 


= 52.92  lb.  per  sq.  ft.; 
= 84.63  lb.  per  sq.  ft.; 
= 1.176  lb.  per  sq.  ft.; 


for  split  D,  p = 


48* 


Split  B has  the  greatest  pressure,  and  is  therefore  the  free  split.  Box 
regulators  are  placed  in  each  of  the  other  splits  to  increase  their  respective 
pressures  to  the  pressure  of  the  free  split  or  the  mine  pressure.  Therefore, 
the  mine  pressure  in  this  circulation  is  84.63  lb.  per  sq.  ft.  _ 

The  Size  of  opening  in  a box  regulator  is  calculated  by  the  formula  for 
determining  the  flow  of  air  through  an  orifice  in  a thin  plate  under  a certain 
head  or  pressure.  The  difference  in  pressure  between  the  two  sides  of  a box 
regulator  is  the  pressure  establishing  the  flow  through  the  opening,  which 
corresponds  to  the  head  h in  the  formula  v = \Z%9h-.  This  regulator  is 
usually  placed  at  the  end  of  a split  or  airway,  and  since  the  regulator 
increases  the  pressure  in  the  lesser  split  so  as  to  make  it  equal  to  the  pressure 
in  the  other  split,  the  pressure  due  to  the  regulator  will  be  equal  to  the 
ventilating  pressure  at  the  mouth  of  the  split,  less  the  natural . pressure  or 
the  pressure  due  to  friction  in  this  split.  Hence,  when  the  position  of  the 
regulator  is  at  the  end  of  the  split,  the  pressure  due  to  friction  m the  split  is 

first  calculated  by  the  formula  p = ^-2,  and  this  pressure  is  deducted  from 

the  ventilating  pressure  of  the  free  or  open  split,  which  gives  the  pressure 
due  to  the  regulator.  This  is  then  reduced  to  inches  of  water  gauge,  and 

.OCKHq  Tbe  va]ue  0f  ^ thus  obtained  is 


substituted  for  i in  the  formula  A — 


V K 


the  area  (square  feet)  of  the  opening  in  the  regulator. 

Example.—  50,000  cu.  ft.  of  air  is  passing  per  minute  m a certain  mine, 
in  two  equal  splits,  under  a pressure  equal  to  2 in.  of  water  gauge,  and  it  is 
required  to  reduce  the  quantity  of  air  passing  m one  of  these  splits,  by  a box 
regulator  placed  at  the  end  of  the  split,  so  as  to  pass  but  15,000  cu.  ft.  per 


DISTRIBUTION  OF  AIR. 


377 


minute  in  this  split.  Find  the  area  of  the  opening  in  the  regulator,  assu- 
ming that  the  ventilating  power  is  decreased  to  maintain  the  pressure  con- 
stant at  the  mouth  of  the  splits  after  placing  the  regulator.  The  size  and 
length  of  each  split  is  6 ft.  X 10  ft.  and  10,000  ft.  long.  . , „ ^ 

The  natural  pressure  for  the  split  in  which  the  regulator  is  placed  will  be 

.0000000217  X 2(6  + 10)  X 10,000  X 15, OOP2  = ? m lb  per  sq> 


_ ksq 2 __ 


a3 

Then, 


7.233 

5.2 


(6  X 10)3 

1.4  in.  of  water  gauge  (nearly),  due  to  friction  of  the  air- 


current  in  this  split. 

„ . .0004  q 

Finally,  A = — j=-  - 

V 


And,  2 — 1,4  = .6  in.  water  gauge  due  to  regulator. 


.0004  X 15,000 

V -6 


= 7.746  sq.  ft.,  area  of  opening. 


Size  of  Opening  for  a Door  Regulator.— The  sectional  area  at  the  regulator  is 
divided  proportionately  to  the  work  to  be  performed  in  the  respective  splits 
according  to  the  proportion  A\ : A2 ::  U\ : u2.  Or  since  A\-t  A2  = a,  we  have 

A\  :a  ::  U\ : ux  + u2,  and  Ax  = — X a.  This  furnishes  a method  of  pro- 
portionate splitting  in  which  each  split  is  ventilated  under  its  own  natural 
pressure.  The  same  result  would  be  obtained  by  the  placing  of  the  box 
regulator  at  the  intake  of  any  split,  thereby  regulating  the  amount  of  air 
passing  into  that  split,  but  the  door  regulator  presents  less  resistance  to  the 
flow  of  the  air-current.  The  practical  difference  between  these  two  forms 
of  regulators  is  that  in  the  use  of  the  box  regulator  each  split  is  ventilated 
under  a pressure  equal  to  the  natural  pressure  of  the  open  or  free  split 
which  very  largely  increases  the  horsepower  required  for  the  ventilation  of 
the  mine-  while  in  the  use  of  the  door  regulator  each  split  is  ventilated 
under  its  own  natural  pressure,  and  the  proportionate  division  of  the  air  is 
accomplished  without  any  increase  of  horsepower.  This  is  more  clearly 
. , x — — -• — — hs,  and  the  table  showing  the  corn- 


explained  in  the  two  following  parai 
parative  horsepowers  of  the  two  methods. 

Calculation  of  Horsepower  for  Box  Regulators.— By  the  use  of  the  box  regu- 
lator, the  pressure  in  all  the  splits  is  made  equal  to  the  greatest  natural 
pressure  in  any  one.  This  split  is  made  the  open  or  free  split,  and  its  natural 
pressure  becomes  the  pressure  for  all  the  splits,  or  the  mine  pressure.  This 
mine  pressure,  multiplied  by  the  total  quantity  of  air  in  circulation  (the  sum 
of  the  quantities  passing  in  the  several  splits),  and  divided  by  33,000,  gives 
the  horsepower  upon  the  air,  or  the  horsepower  of  the  circulation.  Thus, 
in  the  first  example  given  on  page  376,  in  which  for  split  B the  pressure 
p = 84.63  lb.  per  sq.  ft.  and  the  total  quantity  of  air  passing  per  minute 
is  120,000  cu.  ft.,  we  have 

Calculation  of  Horsepower  for  Door  Regulators. — In  the  use  of  the  door 
regulator,  each  split  is  ventilated  under  its  own  natural  pressure,  and, 
hence,  in  the  calculation  of  the  horsepower  of  such  a circulation,  the  power 
of  each  split  must  be  calculated  separately,  and  the  sum  of  these  several 
powers  will  be  the  entire  power  of  the  circulation.  For  the  purpose  of  com- 
parison, we  tabulate  below  the  results  obtained  in  the  application  of  these 
two  methods  of  dividing  the  air  in  the  above  example. 


Splits. 

Natural 

Division. 

Required 

Division. 

Horsepower. 

Door 

Regulator. 

Box 

Regulator. 

Split  A,  6 ft.  X 9 ft.,  8,000  ft.  long 
Split  B,  5 ft.  X 8 ft.,  6,000  ft.  long 
Split  C,  9 ft.  X 9 ft,,  8,000  ft.  long 
Split  D,  6 ft.  X 8 ft., 10, 000  ft.  long 

Totals  

28,277 

22,360 

47,423 

21,940 

40,000 

40.000 

10.000 
30,000 

64.145 
102.582 
.356 
1 44.955 

102.582 

102.582 

25.645 

76.936 

120,000 

1 

120,000 

212.038 

307.745 

378 


VENTILATION  OF  MINES 


SPLITTING  FORMULAS 

The  following  table  of  formulas  will  serve  to  illustrate  the  methods  of 
calculation  in  splitting.  The  example  assumes  the  same  airway  as  that  given 
on  page  369  and  used  to  illustrate  the  table  of  formulas,  page  370,  but  the  air- 
current  is  divided,  as  specified  in  the  table: 

Natural  Division. 

Primary  Splits— Split  (1)  = 4 ft.  X 5 ft.,  800  ft.  long.  Split  (2)  = 4 ft.  X 5 ft., 
1,200  ft.  long. 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Potential  for 
pressure. 

35 

Y n 1 a 

x*~a\lks' 

U?=  (Xx  + X2 
+ etc.). 

(1)  20^  00000oo217x14,4oo  5’060' 

/ 20  _ . 

(2)  20 0000000217  X 2b 600 

5,060  + 4,131  = 9191. 

Natural  divi- 
sion. 

41 

Xv 

q ~ 2 Xp  X Q' 

(1)  X 10,000  = 5,505  cu.  ft. 

(2)  ^lli  x 10,000  = 4,495  cu‘ ft' 

Or  the  natural  division  may  be  calculated  from  the  pressure  at  the  mouth 
of  the  several  splits  by  using  formula  (23);  thus, 


23 

q^Xp\/  p. 

(1)  5,060  ]/ 1.1838  = 5,505  cu.  ft. 

(2)  4,131  V 1.1838  = 4,495  cu.  ft. 
See  formula  (42). 

Pressure. 

42 

Q2 

P (2  Xp)* 

Power. 

43 

Q3 

(zx„r 

Quantity. 

44 

45 

Q = S.Xpy'p. 

<2  = Xp)-w. 

9,191  V 1.1838  = 10,000  cu.  ft. 
1^9, 1912  X 11,838  = 10,000  cu.  ft. 

Increase  of 
quantity  due 
to  splitting. 
(Pressure  con- 
stant. ) 

46 

2 Xp 

Q = -X 

•A-p  — O 

Q 191 

i~j~  X 10,000  = 28,722  cu.  ft. 

Increase  in 
quantity  due 
to  splitting. 
(Power  con- 
stant.) 

47 

& 

It 

10,00°-V(|^)2  = 20,205  CU,ft 

SPLITTING  FORMULAS 


379 

500  ft.  long. 


Secondary  Splits.  — (1)  4 ft.  X 5 ft.,  800  ft.  Jong.  (2)  4 ft.  X 5ft 
(3)  4 ft.  X 5 ft.,  400  ft.  long.  (4)  4 ft.  X 5 ft.,  300  ft.  long. 

The  calculation  is  often  shortened,  when  many  splits  are  concerned,  by 
using  the  relative  potential , omitting  the  factor  A;;  but  the  final  result  must 
then  be  multiplied  by  k to  obtain  the  pressure  or  power;  or,  these  factors 
must  be  divided  by  Ac,  when  finding  the  quantity,  as  in  formulas  (49)  to  (51). 


tH 

Oi 

O 

rH 

iO 

iO 

o3  jq 

fH  O 

P*5S 

fH 

3 

t « 

fH* 

<D 

>3 

p 

55 

09 

0> 

M 

£ 

o 

I 

to* 

P. 

P 

<? 

> a 5 2 
*3  o.o3  2 

pj*  Ph’43  Pi 


380 


VENTILA  TIOX  OF  MIXES. 


Proportionate  Division. 

Primary  Splits  (only).— (1)  4 ft.  X 5 ft.,  800  ft.  long  = 3,500  cu.  ft.  (2] 
4 ft.  X 5 ft.,  1,200  ft.  long  = 6,500  cu.  ft. 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Pressure  due  to 
friction. 

13 

(f 

P X 2* 

(1)  S--"- 

(2)  IS = 2-4757,b- 

To  accomplish  this  division  of  air,  the  pressure  in  split  (1)  must  be 
increased  by  means  of  a regulator  to  make  it  equal  to  the  pressure  in  the 
free  or  open  split  (2),  and,  hence,  the  pressure  due  to  the  regulator  is 
equal  to  the  difference  between  the  natural  pressures  in  these  splits. 

Pressure  due  to 
the  regulator 
in  split  (1). 

53 

P = P-2  — Pi- 

2.4757  — .47845  = 1.99725  lb. 

Area  of  the 
opening  in 
regulator. 

37 

, _ .0004  q 
^ /—  * 
V * 

.0004  X 3,500  _ 2 259  gq  ft 
1.99725 
\ 5.2 

Secondary  Splits.— (1)  4 ft,  X 5 ft.,  800  ft.  — 3,500  cu.  ft.  (2)  4 ft.  X 5 ft., 
500  ft.  — 6,500  cu.  ft.  (3)  4 ft.  X 5 ft.,  400  ft.  — 4,000  cu.  ft.  (4)  4 ft.  X 5 ft., 
300  ft.  — 2,500  cu.  ft. 

Note— When  using  the  relative  potential,  multiply  the  result  by  k,  to 
obtain  the  pressure,  or  the  power. 

Pressure  due  to 
friction.  Free 
split-second- 
ary pressure. 

13 

*8 

11  J 

(1)  .0000000217 2 =-  -47848  lb. 

(2)  .0000000217  = 1.0314  lb. 

(3)  -0000000217 = -31248  lb- 

(4)  .0000000217 (£^)*  = .0915461b. 

V 1.2172  / 

Since  the  natural  pressure  in  (3)  is  greater  than  that  in  (4),  (3)  is  the  free 
split,  and  its  natural  pressure  is  the  pressure  for  the  secondary  splits.  The 
pressure  for  the  primary  splits  is  then  found  by  first  adding  the  pressures  in 
(2)  and  (3),  and  if  their  sum  is  greater  than  the  natural  pressure  for  (1),  it 
becomes  the  pressure  for  the  primary  splits,  or  the  mine  pressure.  If  the 
natural  pressure  for  (1)  is  the  greater,  this  is  made  the  free  split,  and  its 
natural  pressure  becomes  the  primary  or  mine  pressure.  In  this  case,  the 
secondary  pressure  must  be  increased  by  placing  a regulator  in  split  (3). 


Primary  or 
mine  pressure. 

P2+P3. 

1.0314  + .31248  = 1.34388. 

Pressure  due  to 

P3  — Pi- 

(4)  .31248  — .091546  = .220934  lb. 

the  regula-1 
tors. 

(Pa  + Pa)—Pi- 

(1)  (1.0314  + .31248)  — .47848 

= .86540  lb. 

Areas  of  open- 
ings in  the 
regulators. 

37 

i _ .0004  q 

Vi 

(4)  •0004  X 2'500  - 4.8514sa.ft. 

/.220934 

M 5.2 

(1)  '°004  X 3,500  = 3.4328  sq.  ft. 

1.8654 
\ 5.2 

METHODS  AND  APPLIANCES. 


381 


METHODS  AND  APPLIANCES  IN  THE  VENTILATION 

OF  MINES. 

Ascensional  Ventilation.— Every  mine,  as  far  as  practicable,  should  be  venti- 
lated upon  the  plan  known  as  ascensional  ventilation.  This  term  refers 
particularly  to  the  ventilation  of  inclined  seams.  The  air  should  enter  the 
mine  at  its  lowest  point,  as  nearly  as  possible,  and  from  thence  be  conducted 
through  the  mine  to  the  higher  points,  and  there  escape  by  a separate 
shaft,  if  such  an  arrangement  is  practicable.  Where  the  seam  is  dipping 
considerably  and  is  mined  through  a vertical  shaft,  the  upcast  shaft  should 
be  located  as  far  to  the  rise  of  the  downcast  shaft  as  possible.  The  intake  air 
is  then  first  conducted  to  the  lowest  point  of  the  dip  workings,  which  it 
traverses  upon  its  way  to  the  higher  workings.  In  the  case  of  a slope 
working  where  a pair  of  entries  is  driven  to  the  dip,  one  being  used  as  the 
intake  and  the  other  the  return,  there  being  cross-entries  or  levels  driven  at 
regular  intervals  along  the  slope,  the  air  should  be  conducted  at  once  to  the 
inside  workings,  from  which  point  it  returns,  ventilating  each  pair  of  cross- 
entries from  the  inside,  outwards.  Where  the  development  of  the  cross- 
entries or  levels  is  considerable,  their  circulation  is  considered  separately, 
and  a fresh  air  split  is  made  in  the  intake  at  each  pair  of  levels.  In  all 
ventilation,  the  main  point  to  be  observed  is  to  conduct  the  air-current  first 
to  the  inside  workings,  from  whence  it  is  distributed  along  the  working  face 
as  it  returns  toward  the  upcast. 

General  Arrangement  of  Mine  Plan.— Every  mine  should  be  planned  with 
respect  to  three  main  requirements,  viz.:  (a)  haulage;  ( b ) drainage;  (c) 
ventilation.  These  requirements  are  so  closely  connected  with  one  another 
that  the  consideration  of  one  of  them  necessitates  a reference  to  all.  The 
mine  should  be  planned  so  that  the  coal  and  the  water  will  gravitate  toward 
the  opening,  as  far  as  possible.  There  are  many  reasons,  in  the  consideration 
of  non-gaseous  mines,  why  the  haulage  should  be  effected  upon  the  return 
airways.  The  haulage  road  is  always  a dusty  road,  caused  by  the  traveling 
of  men  and  mules,  as  well  as  by  the  loss  of  coal  in  transit,  which  becomes 
reduced  to  fine  slack  and  powder.  If  the  haulage  is  accomplished  upon  the 
intake  entry  or  air-course,  this  dust  is  carried  continually  into  the  mine  and 
working  places,  which  should  be  avoided  whenever  possible.  When  the 
loaded  cars  move  in  the  same  direction  as  the  return  air,  the  ventilation  of 
the  mine  is  not  as  seriously  impeded.  It  is  often  the  case  that  fewer  doors  are 
required  upon  the  return  airway  than  upon  the  intake,  which  is  a feature 
favorable  to  haulage  roads.  Again,  in  this  arrangement,  the  hoisting  shaft 
is  made  the  upcast  shaft,  which  prevents  the  formation  of  ice,  and  conse- 
quent delay  in  hoisting  in  the  winter  season.  The  arrangement,  however, 
presupposes  the  use  of  the  force  fan  or  blower,  since  if  a furnace  or  exhaust 
fan  is  employed,  a door,  or  probably  double  doors,  would  have  to  be  placed 
upon  the  main  haulage  road  at  the  shaft  bottom,  which  would  be  a great 
hindrance. 

In  the  ventilation  of  gaseous  mines;  however,  other  and  more  important 
considerations  demand  attention.  The  gaseous  character  of  the  return 
current  prevents  making  the  return  airway  a haulageway.  In  such  mines, 
the  haulage  should  always  be  accomplished  upon  the  intake  air,  as  any  other 
system  would  often  result  in  serious  consequences.  In  such  gaseous  mine, 
men  and  animals  must  be  kept  off  the  return  airways  as  far  as  this  is 
possible.  . 

As  far  as  practicable,  ventilation  should  be  accomplished  m sections 
or  districts,  each  district  having  its  own  split  of  air  from  the  main  intake,  and 
its  own  return  connecting  with  the  main  return  of  the  mine.  Reference 
has  been  made  to  this  under  Distribution  of  the  Air  in  Mine  Ventilation. 
This  splitting  of  the  air-current  is  accomplished  preferably  by  means  of  an 
air  bridge,  either  an  under  crossing  or  an  over  crossing.  There  are,  in 
general,  three  systems  of  ventilation,  with  respect  to  the  ventilating  motor 
employed:  (a)  natural  ventilation;  (b)  furnace  ventilation;  (c)  mechanical 
/VC71/t'i/l/CLt'i071/ 

Natural  ventilation  means  such  ventilation  as  is  secured  by  natural  means, 
or  without  the  intervention  of  artificial  appliances,  such  as  the  furnace, 
or  any  mechanical  appliances  by  which  the  circulation  of  air  is  maintained. 
In  natural  ventilation,  the  ventilating  motor  or  air  motor  is  an  air  column 
that  exists  in  the  downcast  shaft  by  virtue  of  the  greater  weight  of  the 
downcast  air.  This  air  column  acts  to  force  the  air  through  the  airways 


382 


VENTILATION  OF  MINES. 


of  the  mine.  An  air  column  always  exists  where  the 
currents  of  air  pass  through  a certain  vertical  height,  and  Afferent 

temperatures  This  is  the  case  whether  the  opening  is  a shaft  or  a slope, 
since?  in 'either  case,  there  is  a vertical  height  which  ^ part  determines 
the  height  of  air  column.  The  other  factor  determining  the  hei§h^  of  mr 

column  is  the  difference  of  temperature  between  rfu^de^ticai 

The  calculation  of  the  ventilating  pressure  m natural  ventilation  is  identical 
with  that  of  furnace  ventilation,  which  is  described  later.  ,lirnri 

ventilation  of  Rise  and  Dio  Workings.— We  have  referred  to  the  air  column 
existing  either  in  vertical  shafts  or  slopes  as  the  motive  column  or  venti- 
Mng  motor  Such  an  air  column  will  be  readily  seen  to  exist  m any  rise 
or  din  workings  within  the  mine,  and  may  assist  or  retard  the  circulation 
of  the  air-current  through  the  mine.  It  is  this  air  column  that  renders  the 
ventilation  of  dip  workings  easy,  and  that  of  rise  workings  correspondingly 
difficult  depending,  however,  on  the  relative  temperature  of  the  intekeaim 
return  currents;  the  latter  usually  is  the  warmer  of  the  two,  i\hich  gpwes 
rise  to  the  air  column.  The  influence  of  such  air  columns  m^{.al^a*  jbe 
taken  into  account  in  the  calculation  of  any  ventilation.  This  is  often 

neglected  • • 

The  influence  of  air  columns  in  rise  or  dip  workings,  within  the  unne, 
becomes  very  manifest  where,  from  any  reason,  the  mam  intake  current  is 
increased  or  decreased.  For  example,  a mine  is  ventilated  in  two  sphts,  a 
rise  and  a dip  split;  a current  of  50,000  cu.  ft.  of  air  is  passing  m the  mam 
airwav,  30,000  cu.  ft.  passing  into  the  dip  workings,  and  20,000  mto  the  roe 
workings.  A fall  of  roof  in  the  main  intake  airway,  or  other  cause,reduces 
the  main  current  from  50,000  to  35,000  cu.  ft.  Instead,  now,  of  21 , 
going  to  the  dip  workings  and  14,000  to  the  nse  workings,  we  find  that  this 
proportion  no  longer  exists,  but  that  the  dip  workings  are  taking  more  than 
their  proportion  of  air,  and  the  rise  workings  less.  Thus  the  emulation 
being  decreased  to  35,000  cu.  ft.,  the  dip  workings  will  ^kheQ?°Vh^ 

cu.  ft.,  and  the  rise  workings  10,000  cu.  ft.  On  the  other  hand,  had  the 
intake  current  been  increased  instead  of  decreased,  the  workings ^ would 

then  take  more  than  their  proportion,  while  the  dip  workings  would  take 
less  The  reason  for  this  distribution  is  evident;  suppose,  for  example,  the 
intake  or  mine  pressure  is  3 in.  of  water  gauge,  and  m 
there  is  k in  of  water  gauge  acting  to  assist  ventilation,  whilea  like  water 
gauge  ofi  in  in  the  ri^  workings  lets  to  retard  ventilation  The  effective 
water  auge  in  the  dip  workings  is  therefore  3,  in.,  while  the  effective 
w a nue  in  the  rise  workings  is  21  in.,  or  they  are  to  each  other  as  7 . 5. 
If,  now,  the  mine  pressure  is  decreased  to,  say,  2 in.,  the^  effective  nse  and 
diD  pressures  will  be,  respectivelv,  2£  in.  and  11  in.,  or  as  o : 3.  e observe, 
before  the  decrease,  the  dip  pressure  was  h or  1.4,  times  the  i ^ P^^f e’ 
while  after  the  decrear  iok  place  m the  mine  pressure,  the  dip  pressure 
became  for 1 M times  the  rise  pressure.  The  relative  quanUtiespa^ng  m 
the  dip  split  before  and  after  the  decrease  took  placets  compared  with  the 

quantities  passing  in  the  rise  split,  will  be  as  the  V 1.4  : j/l.66,  ?bowing  an 
increase  of  proportion.  Now,  instead  of  a decrease  taking  piacemthemme 
pressure,  let  us  suppose  it  is  increased , say,  from  3 in.  to  4 m.  The  eff^tive 
pressures  in  t1  lip  and  rise  workings  will  then  be,  re^ckvel^Jj  “■ 
and  3£  in.,  or  they  will  be  to  each  other  as  9:7,  instead  of  7.  5.  Her e we 
observe  that  the  dip  pressure  is  If,  or  1.15,  times  the  nse  pr^sure,  instead 
of  1.4.  The  relative  quantities,  therefore,  passing  in  the  dip  split,  before 
and  after  the  increase  of  the  mine  pressure,  as  compared  with  the  quantities 

passing  in  the  rise  split,  will  be  in  the  ratio  of  V 1.4 : l/l.lo. 
decrease  of  proportion.  We  observe  that  any  alteration  of  the  mme 
sure  bv  which  it  is  increased  or  decreased  does  not  affect  the  inside  dip  or 
rise  columns,  and  hence  the  disproportion  obtains.  In  case  of  a dec^^  of 
the  mine  pressure,  the  dip  workings  receive  more  than  p^^rtion 
of  air,  and  in  case  of  an  increase  of  the  mine  pressure,  they  receive  less 

thai nfl uence  of^Msons^-In  any  ventilation,  air  columns  are  always  established 
in  slopes  and  shafts,  owing  to  the  relative  temperatures  of  the  outade  and 
inside1  air.  The  temperature  of  the  upcast,  or  return  column,  may  always  be 
assumed  to  be  the  same  as  that  of  the  inside  air  The  of  the 

downcast,  or  intake  column,  generally  approximates  the  tempw^^eof  the 
outside  air.  although,  in  deep  shafts  or  long  slopes,  this  temperature  imy  be 
Changed  considerably  before  the  bottom  of  the  shaft  or  slope  is  reached,  and 


METHODS  AND  APPLIANCES 


383 


consequently  the  average  temperature  of  the  downcast  or  intake,  is  often 
different  from  that  of  the  outside  air.  The  difference  of  temperatures  will 
also  vary  with  the  season  of  the  year.  In  winter  the  outside  temperature  is 
below  that  of  the  mine,  and  the  circulation  in  shafts  and  slopes  is  assisted, 
since  the  return  columns  are  warmer  and  lighter  than  the  intake  columns 
for  the  same  circulation.  In  the  summer  season,  however,  the  reverse  of 
this  is  the  case.  The  course  of  the  air-current  will  thus  often  be  changed. 
When  the  outside  temperature  approaches  the  average  temperature  of  the 
mine,  there  will  be  no  ventilation  at  all  in  such  mines,  except  such  as  is 
caused  bv  accidental  wind  pressure.  „ . . , 

In  furnace  ventilation  the  temperature  of  the  upcast  column  is  increased 
above  that  of  the  downcast  column  by  means  of  a furnace.  The  chief 
points  to  be  considered  in  furnace  ventilation  are  in  regard  arrange- 

ment and  size  of  the  furnace.  Furnace  ventilation  should  n<?t  be  applied  to 
gaseous  seams,  and  in  some  cases  is  prohibited  by  law.  It  is,  however,  in 
use  in  manv  mines  liberating  gas.  In  such  cases  the  furnace  fire  is  fed  by  a 
current  of  air  taken  directly  from  the  air-course  sufficient  to  maintain  the 
fire,  and  the  return  current  from  the  mine  is  conducted  by  means  of  a dumb 
drift,  or  an  inclined  passageway,  into  the  shaft  at  a point  from  50  to  100  ft. 
above  the  seam.  At  this  point,  the  heat  of  the  furnace  gases  is  not  sufficient 
for  the  ignition  of  the  mine  gases.  The  presence  of  carbonic-acid  gas  in  the 
furnace  gases  also  renders  the  mine  gases  inexplosive.  In  other  cases 
where  the  dumb  drift  is  not  used,  a sufficient  amount  of  fresh  air  is  allowed 
to  pass  into  the  return  current  to  insure  its  dilution  below  the  explosive 
point  before  it  reaches  the  furnace.  . _ „ 

Construction  of  a Mine  Furnace.— In  the  construction  of  a mine  furnace,  a 
sufficient  area  of  passage  must  be  maintained  over  the  fire  and  around  the 
furnace  to  allow  the  passage  of  the  air-current  circulating  in i the  mine.  The 
velocity  of  the  current  at  the  furnace  should  be  estimated  not  to  exceed 
20  ft.  per  second,  and  the  entire  area  of  passage  calculated  from  this  velocity. 
Thus  for  a current  of  50,000  cu.  ft.  of  air  per  minute,  the  area  of  passage 
through  and  around  the  furnace  should  be  not  less  than 

50,QQ-  = 41f  sq.  ft. 

60  X 20  3 H 

This  is  a safe  method  of  calculation,  notwithstanding  the  fact  that  the 
velocity  of  the  air  is  often  much  more  than  20  ft.  per  second,  yet  the  volume 
of  the  air  is  largelv  increased  owing  to  the  increase  of  temperature. 

The  length  of  the  furnace  bars  is  limited  to  the  distance  in  which  good 
firing  can  be  accomplished,  and  should  not  exceed  5 ft.  1 he  width  of  the  grate 
will  therefore  determine  the  grate  area.  The  grate  area  must,  m every  case, 
be  sufficient  for  the  heating  of  the  air  of  the  current  to  a temperature  such 
as  to  maintain  the  average  temperature  of  the  furnace  shaft  high  enough  to 
produce  the  required  air  column,  or  ventilating  pressure,  in  the  mine. 
The  area  A of  the  grate  of  the  furnace  is  best  determined  by  the  formula 

A = x H.  P.,  in  which  A = grate  area  in  square  feet;  H.  P.  = horse- 
•\[ D 

power  of  the  circulation;  and  D = depth  of  shaft  in  feet.  The  horsepower 
for  any  proposed  circulation  may  always  be  determined  by  divining  the 
quantity  of  air  (cubic  feet  per  minute)  by  the  mine  potential  Xu,  and  cubing 
and  dividing  the  result  by  33,000;  thus, 

3 1 


H.  P 


-m 


X 


33,000' 


The  furnace  should  have  proper  cooling  spaces  above  and  at  each  side; 
upon  one  side,  at  least,  should  be  a passageway  or  manway.  The  furnace 
should  be  located  at  a point  from  10  to  15  yd.  back  from  the  f90t  of  the  shafh 
at  a place  in  the  airway  where  the  roof  is  strong.  This  is  well  secured 
by  railroad  iron  immediately  over  the  furnace.  A good  foundation  is 
obtained  in  the  floor,  and  the  walls  of  the  furnace  carried  up  above  the 
level  of  the  grate  bars,  when  the  furnace  arch  is  sprung.  If  possible,  a 
full  semicircle  should  be  used  in  preference  to  a flat  arch.  The  sides  ana 
arch  of  the  furnace  should  be  carried  backwards  to  the  shaft;  this  is 
necessary  in  order  to  prevent  ignition  of  the  coal.  The  walls  and  arcn 
are  constructed  of  firebrick  a sufficient  distance  from  the  furnace,  and  after- 
wards  of  a good  quality  of  hard  brick;  the  shaft  is  also  lined  with  brick 
or  protected  by  sheet  iron  a sufficient  height  to  prevent  the  ignition  ot 
the  curbing. 


38a 


VENTILATION  OF  MINES. 


Air  Columns  in  Furnace  Ventilation.— As  previously  stated,  natural  ventilation 
and  furnace  ventilation  are  identical,  m so  far  as  in  each  the  ventilating 
motor  is  an  air  column.  This  air  column  is  an  imaginary  column  of  air 
whose  weight  is  equal  to  the  difference  between  the  weights  of  the  upcast 
and  downcast  columns.  The  upcast  and  downcast  columns  in  furnace 
ventilation  are  sometimes  referred  to  as  the  primary  and  secondary 
columns,  respectively.  The  primary  or  furnace  column  is,  in  nearly  every 
case,  a vertical  column,  and  consists  of  a single  air  column  whose  average 
temperature  is  easily  approximated.  According  to  the  manner  of  opening 
the  mine,  whether  by  shaft,  slope,  or  drift,  the  secondary  column  may  be 
a vertical  column  in  the  shaft,  an  inclined  column  in  the  slope,  or  an  outside 
air  column  in  case  of  a drift  opening.  Again,  it  is  to  be  observed  that  in 
case  of  a slope  opening  where  the  top  of  the  furnace  shaft  is  much  higher 
than  the  mouth  of  the  slope,  and  the  dip  of  the  slope  is  considerable,  the 
secondary  column  consists  of  two  columns  of  different  temperatures,  an 
outside  air  column  and  the  slope  column.  These  two  parts  of  the  secondary 
column  must  be  calculated  separately,  and  their  sum  taken  for  the  weight  of 
the  secondary  column.  The  level  of  the  top  of  the  furnace  shaft  determines 
the  top  of  both  the  primary  and  secondary  columns,  whether  these  columns 
are  in  the  outer  air  or  in  the  mine.  The  weight  of  the  upcast  or  primary 
column  is  largely  affected  by  its  gaseous  condition.  For  example,  if  the 
return  current  from  the  mine  is  laden  with  blackdamp  C02,  its  weight  will 
be  much  increased,  since  this  gas  is  practically  1£  times  as  heavy  as  air, 
while,  if  laden  with  marsh  gas,  or  firedamp  mix- 
ture, its  weight  will  be  considerably  reduced. 
These  causes  decrease  and  increase,  respectively, 
the  ventilating  pressure  in  the  mine. 

Inclined  Air  Columns.— In  a slope  opening,  the 
air  column  is  inclined;  it  is  none  the  less,  how- 
ever, an  air  column,  and  must  be  calculated  in 
the  same  manner  as  a vertical  column  whose  ver- 
tical height  corresponds  to  the  amount  of  dip  of 
the  slope.  Fig.  7 shows  a vertical  shaft  and  a 
slope,  the  air  column  in  each  of  these  being  the  same  for  the  same  tem- 
perature. The  air  column  in  all  dips  and  rises  must  be  estimated  in  like 
manner,  by  ascertaining  the  vertical  height  of  the  dip. 

Calculation  of  Ventilating  Pressure  in  Furnace  Ventilation.— The  ventilating 
pressure  in  the  mine  airways,  in  natural  or  in  furnace  ventilation,  is  caused 
by  the  difference  of  the  weights  of  the  primary  and  secondary  columns.  Air 
always  moves  from  a point  of  higher  pressure  toward  a point  of  lower 
pressure,  and  this  movement  of  the  air  is  caused  by  the  difference  between 
these  two  pressures.  In  this  calculation  each  column  is  supposed  to  have 
an  area  of  base  of  1 sq.  ft.  Hence,  if  we  multiply  the  weight  of  1 cu.  ft.  of 
air  at  a given  barometric  pressure,  and  having  a temperature  equal  to  the 
average  temperature  of  the  column,  by  the  vertical  height  D of  the  column, 
we  obtain  not  only  the  weight  of  the  column  but  the  pressure  at  its  base  due 
to  its  weight.  Now,  since  the  ventilating  pressure  per  square  foot  in  the 
airway  is  equal  to  the  difference  of  the  weights  of  the  primary  and  secondary 
columns,  we  write 

1.3253  X B 1.3253  X B 


Fig.  7. 


P=( 


X D. 


459  At  459+  T 

Example. — Find  the  ventilating  pressure  in  a mine  ventilated  by  a 
furnace,  the  temperatures  of  the  upcast  and  downcast  columns  being, 
respectively,  350°  F.  and  40°  F.,  the  depth  of  the  upcast  and  downcast  shafts 
being  each* 600  ft.,  and  the  barometer  30  in.  # 

Substituting  the  given  values  in  the  above  equation,  we  have 


p = 1.3253  X30X600  lb'  P«  ft' 

Calculation  of  Motive  Column  or  Air  Column. — It  is  often  convenient  to 
express  the  ventilating  pressure  p (lb.  per  sq.  ft.)  in  terms  of  air  column  or 
motive  column  M,  in  feet.  The  height  of  the  air  column  M is  equal  to  the 

pressure  p divided  by  the  weight  w of  1 cu.  ft.  of  air,  or  M = The  expres- 
sion for  motive  column  may  be  written  either  in  terms  of  the  upcast  air  or 
of  the  downcast  air,  the  former  giving  a higher  motive  column  than  the 
latter  for  the  same  pressure,  since  the  upcast  air  is  lighter  than  that  of  the 


MECHANICAL  VENTILATORS. 


385 


downcast.  As  the  surplus  weight  of  the  downcast  column  of  air  produces 
the  ventilating  pressure,  it  is  preferable  to  write  the  air  column  in  terms  of 
the  downcast  air,  or,  in  other  words,  to  consider  the  air  column  as  beiijg 
located  in  the  downcast  shaft,  and  pressing  the  air  downwards  and  through 
the  airways  of  the  mine.  If  we  divide  the  expression  previously  given  for  the 


which  is  the  expression  for  motive  column  in  terms  of  the  downcast  air. 

If,  on  the  other  hand,  we  divide  the  expression  for  the  ventilating 


the  upcast  air. 

Influence  of  Furnace  Stack.— To  increase  the  height  of  the  primary  or 
furnace  column,  a stack  is  often  erected  over  the  mouth  of  the  furnace  shaft. 
The  effect  of  this  is  to  increase  the  ventilating  pressure  in  the  mine  in 
proportion  to  the  increased  height  of  the  primary  column,  and  to  increase 
the  quantity  of  air  passing  in  the  mine  in  proportion  to  the  square  root  ot 
this  height.  Thus,  the  square  root  of  the  ratio  of  the  heights  of  the  primary 
column,  before  and  after  the  stack  is  erected,  is  equal  to  the  ratio  of  the 
quantities  of  air  passing  before  and  after  the  erection  of  the  stack.  Or, 
calling  these  quantities  qi  and  q2,  and  the  height  of  stack  d,  we  have 


A large  number  of  mechanical  ventilators  have  been  invented  and  applied, 
with  more  or  less  success,  to  the  ventilation  of  mines.  The  earliest  type  of 
ventilator  was  the  wind  cowl,  by  which  the  pressure  of  the  wind  at  the  sur- 
face was  brought  to  bear  effectively  upon  the  mine  airways  by  the  action  of 
a cowl  whose  mouth  could  be  turned  toward  the  wind;  this  was  naturally 
very  unreliable.  The  waterfall  was  also  extensively  applied  at  one  time,  but 
its  application  could  only  be  made  where  there  was  a reliable  source  of 
water  supply,  and  where  the  drainage  of  the  mine  could  be  effected  through 
a tunnel,  or  where  the  mine  opening  could  be  placed  in  connection  with 
such  a waterfall  outside  of  the  mine.  Where  these  conditions  are  obtained, 
as  is  the  case  in  some  mountainous  districts,  the  waterfall  is  still  in  use,  as 
it  is  an  effective  means  of  ventilation,  and  is  economical.  Its  application, 
however,  must  be  limited  to  the  ventilation  of  small  mines.  The  steam  jet 
is  another  mechanical  device  for  producing  an  air-current  in  the  mine.  The 
steam  is  allowed  to  issue  from  a jet  at  the  bottom  of  an  upcast  shaft,  and, 
by  the  force  of  its  discharge,  causes  an  upward  current  in  the  shaft.  Its  use, 
however,  is  very  limited,  and  is  practically  restricted  to  the  ventilation  of 
shafts  while  sinking.  In  this  connection  it  may  be  mentioned,  however, 
that  the  discharged  steam  from  the  mine  pumps,  where  practicable,  may  be 
conducted  into  the  upcast  shaft;  or  the  discharge  pipe  from  the  pumps  may 
be  carried  up  the  upcast  shaft,  its  heat  increasing  the  temperature  of  the 
shaft,  and  thereby  increasing  the  motive  column  and  the  ventilation. 

Fan  Ventilation.— Mechanical  motors  of  this  type  present  two  distinct 
modes  of  action  in  producing  an  air-current:  (a)  by  propulsion  of  the  air; 
and  (b)  by  establishing  a pressure  due  to  the  centrifugal  force  incident  to 
the  revolution  of  the  fan.  Fans  have  been  constructed  to  act  wholly  on 
one  or  the  other  of  these  principles,  while  others  have  been  constructed  to 
act  on  both  of  these  principles  combined. 

Disk  Fans. — The  action  of  this  type  of  fan  resembles  that  of  a windmill, 
except  that  in  the  latter  the  wind  drives  the  mill,  while  in  the  former  the 
fan  propels  the  air  or  produces  the  wind.  This  type  of  fan  consists  of  a 
number  of  vanes  radiating  from  a central  shaft,  and  inclined  to  the  plane  of 
revolution.  The  fan  is  set  up  in  the  passageway  between  the  outer  air  and 
the  mine  airways.  Power  being  applied  to  the  shaft,  the  revolution  of  the 


MECHANICAL  VENTILATORS. 


386 


VENTILATION  OF  MINES. 


vanes  propels  the  air,  and  produces  a current  in  the  airways.  The  fan  may 
force  the  air  through,  or  exhaust  the  air  from,  the  airways,  according  to  the 
direction  of  its  revolution.  This  type  of  fan  is  most  efficient  under  light 
pressures.  It  has  found  an  extensive  application  in  mining  practice,  and 
has  a large  number  of  devotees,  but  has  been  replaced  to  a large  degree 
in  the  ventilation  of  extensive  mines.  This  type  of  fan  acts  wholly  by 

PJ°(Sntrifugal  fans  include  all  fans  that  act  solely  on  the  centrifugal  principle, 
and  those  that  combine  the  centrifugal  and  propulsion  principles.  The 
action  of  the  fan,  whether  by  centrifugal  force  alone,  or  combined  with 
propulsion,  depends  on  the  form  of  the  fan  blades.  In  this  type  of  fan,  the 
blades  are  all  set  at  right  angles  to  the  plane  of  revolution,  and  not  inclined, 
as  in  the  disk  fan  just  described.  The  blades  may,  however,  be  either  radial 
blades,  sometimes  spoken  of  as  paddle  blades,  or  they  may  be  inclined  to  the 
radius  either  forward  in  the  direction  of  revolution,  or  backward.  When 
the  blades  are  radial,  the  action  of  the  fan  is  centrifugal  only.  The  inclina- 
tion of  the  blades  backward  from  the  direction  of  motion  gives  rise  to  an 
action  of  propulsion,  in  addition  to  the  centrifugal  action  of  the  fan.  Ihe 
blades  in  this  position  may  be  either  straight  blades  in  an  inclined  position^ 
as  in  the  original  Guibal  fan,  or  they  may  be  curved  backward  in  the  form 
of  a spiral,  as  in  the  Schiele  and  Waddle  fans.  - 

Centrifugal  fans  may  be  (a)  exhaust  fans  or  (b)  force  fans  of  blowers.  In 
each,  the  action  of  the  fan  is  essentially  the  same;  1.  e.,  to  create  a difference 
of  pressure  between  its  intake  or  central  opening,  and  its  discharge  at  the 
circumference.  The  centrifugal  force  developed  by  the  revolution  of  the  air  . 
between  the  blades  of  the  fan  causes  the  air  within  the  fan  to  crowd  toward 
the  circumference;  as  a result,  a depression  is  caused  at  the  center  and  a 
compression  at  the  circumference,  giving  rise  to  a difference  of  pressure 
between  the  intake  and  the  discharge  of  the  fan 

Exhaust  Fans.— If  the  intake  opening  of  the  fan  be  placed  m connection 
with  the  mine  airways,  and  the  discharge  be  open  to  the  atmosphere,  the 
fan  will  act  to  create  a depression  in  the  fan  drift  leading  to  the  mine,  which 
will  cause  a flow  of  air  through  the  mine  airways  and  into  and  through  the 
fan.  In  this  case,  the  fan  is  exhausting,  its  position  being  ahead  of  the 
current  that  it  produces  in  the  airway.  The  atmospheric  pressure  at 
the  intake  of  the  mine  forces  the  air  or  propels  the  current  toward  the 
depression  in  the  fan  drift  caused  by  the  fan’s  action.  , 

Force  Fans  and  Blowers.-If  the  discharge  opening  of  the  fan  he  placed  m 
connection  with  the  mine  airways,  a compression  will  result  m the  fan  anit 
owing  to  the  fan’s  action,  and  the  air  will  flow  from  this  point  of  compres- 
sion through  the  airways  of  the  mine,  and  be  discharged  into  the  upcast, 
and  thence  into  the  atmosphere.  The  ventilating  pressure  m the  case  ot 
either  the  exhaust  fan  or  the  force  fan  is  equal  to  the  difference  of  pressure 
created  by  the  fan’s  action.  In  the  former  case,  when  the  fan  is  exhausting, 
the  absolute  pressure  in  the  fan  drift  is  equal  to  the  atmospheric  pressure 
less  the  ventilating  pressure,  while  in  the  latter  case,  when  a fan  is  forcing, 
the  absolute  pressure  in  the  fan  drift  is  equal  to  the  atmospheric  pressure 
increased  by  the  ventilating  pressure.  This  gives  rise  to  two  distinct  systems 
of  ventilation,  known  as  (a)  vacuum  system  and  (b)  plenum  system. 

Vacuum  System  of  Ventilation.-In  this  system,  the  ventilation  of  the  mine 
is  accomplished  by  creating  a depression  m the  return  airway  of  the  rome. 
This  depression  may  be  created  by  the  action  of  an  exhaust  tan,  as  just 
described,  or  by  the  action  of  a furnace.  In  either  case,  the  absolute  pres- 
sure in  the  mine  is  below  that  of  the  atmosphere,  or,  we  may  say,  the  mine 
is  ventilated  under  a pressure  below  the  atmospheric  pressure.  This  system 
has  many  points  of  advantage  over  the  plenum  system,  and  for  years  was 
considered  by  many  the  only  practicable  system  of  ventilation.  Its  appli- 
cation, however,  is  controlled  by  conditions  in  the  mine  with  respect  to 
the  gases  liberated,  the  arrangement  of  the  haulage  system,  etc.  # 

Plenum  System  of  Ventilation.-In  this  system,  the  air-current  is 
through  the  mine  airways  by  means  of  the  compression  or  ventilating 
pressure  created  at  the  intake  opening  of  the  mine.  This  ventilating  pres- 
sure may  be  established  by  a fan,  waterfall,  wind  cowl,  or . 
mechanical  means  at  hand . In  this  system,  the  absolute  pressure  m the  mine 
is  above  that  of  the  atmosphere;  or,  as  we  say,  the  mine  is  ventilated  under 
a pressure  above  the  atmospheric  pressure.  , 

Comparison  of  Vacuum  and  Plenum  Systems.— No  hard-and-fast  rule  can  be 
made  to  apply  in  every  case,  as  each  system  has  its  particular  advantages. 


TYPES  OF  FANS. 


387 


In  case  of  a sudden  stoppage  of  the  ventilating  motor ,at  a mine,  there  is 
i-n  vapiinm  svstem  a rise  of  mine  pressure,  instead  of  a tall,  ana.  tne 
^ IJe  lack ’into  the  workings  for  a while,  while,  in  the  plenum 

Inv  stoDDaee  of  the  ventilating  motor  is  followed  at  once  by  a fall  of 
pressure  iii  the^ine,  and  mine  gases  expand  more  freely  into _the  passage - 
the  verv  moment  when  their  presence  is  most  dangerous.  This 
3 must  be  caremily  considered  in  the  ventilation  of  deep  workings  In 
shallow  workings,  the  plenum  system  is  often  advantageous,  especially  if 
there  is  a lar^e  area  of  abandoned  workings  that  have  a vent  or  opening  to 
thfatmosnhCTe^ either  Through  an  old  shift  or  through  crevices  extending 
to  the  surface  'Every  crevice  or  other  vent  becomes  a discharge  opening  by 
whfchThe  Sne  gaS  find  their  way  to  the  surface,  and  the  gases  accum.i- 
latine  in  the  old  workings  are  driven  back  into  the  workings,  and  find  their 
way'to'tte  surface  instead  of  being  drawn  into  th « ;mlne amwaj as  wotdd  be 
th please  in  an  exhaust  system.  Any  given  fall  of  the  barometer  altects  tne 
expansion1  of  mine  gases  to  a less  extent  in  the  plenum  system  than  in 
the  vacuum  system,  but  this  small  advantage  would  not  give  it  consider- 
ation^ dSerhiining  between  the  adoption  of  the  one  or  the  other  of  these 
two^vS^s^S^ard  must  be  had,  however,  to  other  conditions  more  vital 
than  this  In  the  ventilation  of  gaseous  seams,  owing  to  the  necessity  of 
making  the  intake  airway  the  haulage  road,  the  exhaust  system  has  usualiy 
been  adopted,  as  the  main  road  is  thereby  left  unobstructed  by  doors. 

TYPES  OF  CENTRIFUGAL  FANS. 

We  shall  only  mention  the  more  prominent  types  of  fans  that  have  been 
or  are  still  in  use,  giving  the 
characteristic  features,  as  nearly 
as  possible,  of  each  fan.  Many 
fans  have  been  built,  however, 
combining  many  of  the  features 
that  originally  characterized  a 
single  type  of  fan.  . 

Nasmyth  Fan. — Fig.  8 is  the 
original  type  of  fan  representing 
straight  paddle  blades  radiating 
from  the  center,  which  is  its 
characteristic  feature.  This  was 
probably  the  earliest  attempt  to 
apply  the  centrifugal  principle 
to  a mine  ventilator,  and  al- 
though not  recognized  at  the 

. • j-1-  _ DArn a AT 


‘some  of  the  most  essential  principles  in  centrifugal 

Illation  It  possessed  certain  disadvantages, 

_ — j. — /.nntvni  /Yr  intake  opening.  The  blades,  also,  were  siraigni 

throughout  their  entire  length  being  normal 
both  to  the  inner  and  outer  circles  of  the  tan. 


UOLIl  IU  LHC  lliii ci  a iici  r . - . 

and  thus  did  not  provide  for  receiving  the  air 
without  shock  at  the  throat  of  the  fan.  The 
depth  of  Nasmyth’s  blades  equaled  one-half  the 
radius  of  the  fan,  which  was,  under  ordinary 
conditions  of  mine  practice,  far  too  great,  and 
gave  the  fan  a low  efficiency. 

Biram’s  Ventilator.  - About  1850,  Biram  at- 
tempted  to  improve  upon  the  Nasmyth  ventilator 
bv  reducing  the  depth  of  blade  so  that  it  was 
but  one-tenth  of  the  radius.  The  blades  were 
straight,  as  in  Nasmyth’s  ventilator,  but  inclined 
backwards  from  the  direction  of  motion  at  a 
considerable  angle.  A large  number  of  these 
blades  were  employed.  This  fan  was  run  at  a 
considerable  speed,  but  proved  very  inefficient.  It  depended  ^o^e  on  the 
effort  of  propulsion  given  to  the  air  than  on  the 

the  depth  of  the  blade  was  as  much  too  small  as  that  of  Nasmyth  s was  too 
great.  The  intake  or  central  opening  in  this  fan  was  as  contracted  as  in 

theWad(He^ Venti?ator.—  Intis’ fan,  Fig.  10,  the  invents  attempted  to  reenforce 
the  discharge  pressure  at  the  circumference  against  the  pressure  of  the 


388 


VENTILATION  OF  MINES. 


atmosphere.  The  discharge  took  place  all  around  the  entire  circumference 
of  the  fan,  which  was  entirely  opened  to  the  atmosphere.  The  blades  were 
curved  backward  from  the  direction  of  motion  in  spiral  form.  The  width 
of  the  blade  decreased  from  the  throat  toward  the  circumference,  so  as  to 
present  an  inverse  ratio  to  fhe  length  of  radius.  Thus,  the  area  of  passage 

between  the  fan  blades  was 
maintained  constant  from 
the  throat  to  the  circumfer- 
ence of  the  fan.  The  pur- 
pose of  this  was  to  maintain 
the  velocity  of  the  air 
through  the  fan  constant, 
and  to  fortify  the  pressure 
due  to  the  fan  against  the 
atmospheric  pressure  at  the 
point  of  discharge.  The  es- 
sential features  of  the  Wad- 
dle ventilator  were,  there- 
fore, curved  blades  tapered 
toward  the  circumference, 
and  a free  discharge  into 
the  atmosphere  all  around 
the  circumference.  This 
type  is  the  best  type  of  the 
open-running  fan  having  no  peripheral  casing,  and  discharging  air  into 
the  atmosphere  all  around  the  circumference. 

Schiele  Ventilator.— This  ventilator,  Fig.  11,  was  constructed  on  the  same 
principles  as  the  Waddle  ventilator  just  described,  but  differed  from  the 
latter,  as  the  discharge  was  made  into  a spiral  chamber  surrounding  the 
fan  and  leading  to  an  expanding  or  6vase  chimney.  There  was  some  advan- 
tage in  this  feature,  as  it  protected  the  fan  against  the  direct  influence  of 
the  atmosphere,  and  reduced  the  velocity  of  discharge;  but,  in  each  of 
these  fans,  the  intake  opening  was  contracted,  and  the  depth  of  blade  was 
very  great,  yielding  a comparatively  low  efficiency. 

Guibal  Ventilator.— The  next  important  step  in  the  improvement  of  centrif- 
ugal ventilators  was  introduced  by  M.  Guibal,  who  constructed  a fan, 
Fig.  12,  embodying  the  features  of  the  Nasmyth  ventilator,  with  the  addition 
of  a casing  built  over  the  fan  to  protect  its  circumference.  This  casing  was, 
however,  a tight-fitting  casing,  and  as  such,  differed  very  materially  from  the 
Schiele  casing.  In  the  Guibal  fan  the  blades  were  arranged  upon  a series  of 
parallel  bars  passing  upon  each  side  of  the  center  and  at  some  distance  from 
it.  By  this  construction,  the  blades  were  not  radial  at  their  inner  edge  or 
the  throat  of  the  fan.  They  were  curved,  however,  as  they  approached  the 
circumference  of  the  fan,  so  as  to  be  normal  or  radial  at  the  circumference. 


The  advantage  of  this  construction  was  to  give  a strong  skeleton  or  frame- 
work to  the  revolving  parts,  and,  further,  each  blade  was  inclined  to  the 
radius  at  its  inner  extremity,  the  effect  of  which  was  to  receive  tbe  air  upon 
the  blade  with  less  shock  than  was  the  case  in  the  Nasmyth  ventilator.  The 
intake  or  central  opening,  however,  was  very  contracted,  and  the  tight-fitting 


EFFICIENCY  OF  FANS. 


389 


casing  about  the  circumference  prevented  the  effective  action  of  the  fan 
during  a considerable  portion  of  its  revolution.  The  fan  was  supplied 
with  an  6vase  chimney,  which  was  a feature  of  the  Schiele  fen,  but 
vibration  was  so  strong  that  a shutter  was  required  at  the  cut-off  below 


the  chimney,  to  prevent  it.  This  shutter  was  made  adjustable,  and  is  known 
as  the  Walker  shutter , having  been  applied  to  the  fan  later  , . , 

The  Guibal  ventilator  presents  some  important  and  valuable  features 
in  the  protecting  cover,  and  in  the  blades  meeting  the  outer  circumference 
radially,  and  in  the  air  being  received  with  less  shock  than  before.  On  the 
whole  it  has  proved  a very  efficient  ventilator,  although  much  work  is  lost 
by  reason  of  its  contracted  central  orifice  and  tight  casing,  where  the  same 

is  used.  - . _ _ , , ,, 

Murphy  Ventilator.— Fig.  13  consists  of  twin  fans  supported  on  the  same 
shaft  and  set  a few  feet  apart.  Each  fen  receives  its  air  on  one  side  only, 
the  openings  being  turned  toward  each  other.  This  ventilator  is  built  with 
a small  diameter,  and  is  run  at  a high  speed.  The  blades  are  curved  back- 
wards from  the  direction  of  motion.  The  intake  opening  is  considerably 
enlarged;  a spiral  casing  generally  surrounds  the  fan,  and  in  every  respect 
this  fan  makes  an  efficient  high-speed  motor.  It  has  received  considerable 
favor  in  the  United  States,  where  it  has  been  introduced  into  a large  number 


of  mines.  A.,  , , , 

Capell  Ventilator.— Perhaps  none  of  the  centrifugal  ventilators  have  been 
as  little  understood  in  regard  to  their  principle  of  action  as  the  Capell  fen. 
The  fan  is  constructed  along  the  lines  of  the  Schiele  ventilator,  but  diners 
from  that  ventilator  in  the  manner  of  receiving  its  intake  air  and  delivering 
the  same  into  the  main  body  of  the  fen.  Here,  and  revolving  with  it,  is  a set 
of  smaller  supernumerary  blades.  These  blades  occupy  a cylindrical  space 
within  the  main  body  of  the  fan,  and  are  inclined  to  the  plane  of  revolu- 
tion so  as  to  assist  in  deflecting  the  entering  air  through  small  ports  or 
openings  into  the  main  body  of  the  fan,  where  it  is  revolved  and  discharged 
at  the  circumference  into  a spiral  space  resembling  that  surrounding  the 

Schiele  fan.  The  larger  blades  of  this 
fan  are  curved  backwards  as  the  Schiele 
blades,  but  are  not  tapered  toward  the 
circumference.  The  fan  is  capable  of  giv- 
ing a high  water  gauge,  and  is  efficient 
as  a mine  ventilator.  The  space  surround- 
ing the  fan  is  extended  to  form  an  ex- 
panding chimney.  The  fan  may  be  used 
either  as  an  exhaust  fan  or  a blower. 
The  best  results  in  the  United  States  have 
been  obtained  by  blowers.  In  Germany, 
where  this  fen  is  in  general  use,  there  are 
no  blowers. 

The  position  of  the  fan,  whether  used  as 
an  exhaust  or  blower,  should  be  suffi- 
ciently removed  from  the  fan  shaft  to 
avoid  damage  to  the  fan  in  case  of  ex- 
plosion in  the  mine.  Even  in  non-gaseous 
mines,  the  fan  should  be  located  a short  distance  back  from  the  shaft 
mouth,  to  avoid  damage  due  to  settlement.  Connection  should  be  made 
with  the  fan  shaft  by  means  of  an  ample  drift,  which  should  be  deflected 
into  the  shaft  so  as  to  produce  as  little  shock  to  the  current  as  possible.  In 


390 


VEXTILA  TIOX  OF  MIXES. 


' — **  f 

u~~\ 

U] 

F* 

K] 

„ , 

A 

1 


case  of  gaseous  seams,  explosion  doors  should  be  provided  at  the  shaft 
mouth.  The  ventilator  at  every  large  mine  should  be  arranged  so  that & 
mav  be  converted  from  an  exhaust  to  a blow-down  fan  at  short  notice. 
This  is  managed  bv  housing  the  central  onhees  or  intake  of  the  fan  m 
such  a manner  as  to  connect  them  directly  with  the  fan  drift.  A noor 
ab.  Fig.  15,  is  arranged  at  the  foot  of  the  expanding  chimney,  the  latter 
- ^ ^ ° hwng  placed  between  the  tan 

and  the  shaft.  This  door, 
when  the  fan  is  exhausting, 
is  in  the  lower  position  a b. 
and  then  forms  a portion,  of 
the  spiral  casing  leading  to 
the  chimney.  When  the  fan 
is  blowing,  however,  the  door 
is  swung  upwards  so  as  to  oc- 
cupy the  position  ae . being 
tangent  to  the  cut-off  at  c, 
thereby  closing  the  discharge 
into  the  chimney  and  causing 
it  to  enter  the  fan  drift  behind 
the  door.  At  the  same  time, 
the  positions  of  the  two  doors, 
e d and/d,  in  the  fan  drift,  are 
changed  to  c t and  / s,  respec- 
tively, to  open  the  fan  drift 
to  the  discharge  from  the  fan, 
and  to  close  the  openings  lead- 
ing from  the  fan  drift  to  the 
housing  upon  each  side  of  the 
fan.  while  another  set  of  doors 
A A upon  each  side  of  the  fan. 
in  the  housing,  which  were 
-Prr-  u previously  cl:sed  rigidly  .are 

now  set  wide  open  to  admit 
the  outside  air  to  the  intake  openings  of  the  fan.  The  fan  is  thus  made  to 
draw  it-  air  from  the  atmosphere,  and  discharge  it  into  the  fan  drift,  instead oof 
drawing  its  air  from  th e fan  drift  and  discharging  into  the  chimnev.  as  before. 

The  manometrical  efficiency  of  a fan  is  the  ratio  between  its  effective  and 
theoretical  pressures.  It  has-been  assumed  that  the  theoretical  PJ^iredue 

to  the  fan’s  action  is  given  by  the  equation  h = — , or  i = pXlooo  » 

u hpincr  a«  before  the  tangential  speed  feet  per  second),  and  g the  force  of 
™?iP?V3AlCd:  h = head  of  air  column  in  feet:  i = water  gauge  m inches. 
~ The  term  mechanical  efficiency,  as  applied  to  the  ventilator, ^btie  ratm 
between  its  effective  and  theoretical  powers.  In  estimating  the  e^cJ^ncv  of 
a ventilator,  it  is  customary,  though  incorrect,  to  estimate  the  theoretical 
power  of  the  fan  from  an  engine  card  taken  from  the  steam 
to  en°ine  The  efficiency  of  the  steam  engine  is  thus  confused  with  the 
efficiencyof  the  ventilat6r.  Mr.  Beard  gives  the  following  formula  for 

the  theoretical  work  of  the  to  per  minute:  U = .001699^-  1 V&b 

in  which  m = ratio  between  outer  and  inner  diameters  of  {^(D  = md). 

y _ velocitv  i feet  per  minute)  of  air  m fan  drift:  R — outer  radim  of 
fan  blades  (feet)r  b = breadth  of  fan  blades  1 feet);  n ==  number  of  reyolu- 
of  fan  per  minute.  If  we  divide  the  power  upon  the  air.  as  determined 
hv^hfexprSdoTqp  bv  the  theoretical  work  given  in  the  last  eqnanon  we 
cffitaffi  thev^lue  of the ’coefficient  of  efficiency  According  to  tins  formula 
the  efficiencv  of  the  ventilator  changes  with  the  speed.  pnt 

speed  increases,  but  not  in  the  same  ratio.  An  expression  for  the^coe^ient 

of  efficiency  of  a ventilator  is  given  by  Beard  as  follows:  K = - ^ + 163>6o^ 
TbP  factor  c is  a constant  of  design  whose  value  may  vary  from  2 to  7.  but 
en^o Stfc  res^Jmw  its  e^^yforpa.^ 

the^morPa£dwith  straight  radial  blades  having  only  a forward 


FAN  CONSTRUCTION. 


391 


curve  at  the  lip  of  the  blade  to  avoid  the  shock  of  the  entry  air  against  the 
revolving  blades,  and  the  spiral  casing  starting  a short  distance  upon  the 
cut-off  and  extending  uniformly  around  the  circumference  of  the  fan, 
the  value  of  this  constant  may  be  2 or  3.  Where  none  of  these  accessories 
to  the  efficiency  of  the  fan  is  employed,  the  value  of  c may  be  as  high  as  7. 


FAN  CONSTRUCTION. 


Size  of  Central  Orifice.— The  velocity  of  the  intake  should  vary  between 
1,000  ft.  and  1,500  ft.  per  minute,  while  1,200  ft.  may  be  used  for  fan  calcula- 
tions. If  d = diameter  of  opening,  and  q = quantity  of  air  passing  per 

minute,  d = ^^0x7? 854  fOT  sinSle-intake  faIls’  and  d = V^400  X .7854 
for  double-intake  fans. 

Upon  entering  the  fan  the  air  travels  in  a radial  direction;  this  change  of 
direction  is  accompanied  by  a slight  reduction  of  the  velocity,  hence  the 
throat  area  of  the  fan  must  be  slightly  in  excess  of  the  intake  area.  The 
throat  is  the  surface  of  the  imaginary  cylinder  that  has  for  its  two  bases  the 
two  intake  openings  of  the  fan,  and  for  its  length  the  width  of  the  fan,  = 
ndb.  [The  throat  area  is  commonly  made  1.25  times  the  total  area  of  the 
intake  orifices,  which  gives  for  breadth  of  blade  b = f d for  double  intake, 
and  b = T%  d for  single  intake. — Beard.] 

Diameter  of  Fan.— Murgue  assumes  the  tangential  velocity  of  the  blade 
tips  (it)  to  create  a depression  double  that  due  to  the  velocity  as  expressed 

by  the  equation  H = — , or  if  the  manometrical  efficiency  = K , and  the* 

rfi  la  h 

effective  head  produced  = h,  h = K H = K — , or  m=  ^ If'  From  this 

equation,  the  tangential  velocity  (feet  per  second)  may  be  calculated  for 
any  given  effective  head  h.  This  effective  head  h is  the  head  of  air  column 
effective  in  producing  the  circulation  in  the  airway.  To  convert  the 
effective  head  of  air  column  into  inches  of  water  gauge  (£),  we  have 

h = ^ 2 )<°i2  Hav^118'  f°un(l  the  tangential  speed  required  in  feet  per 

second,  this  is  multiplied  by  60,  to  obtain  the  speed  in  feet  per  minute, 
and  dividing  this  result  by  the  desired  number  of  revolutions  per  minute,  or 
the  desired  speed  of  the  ventilator,  the  outer  circumference  of  the  fan 
blades  is  obtained.  No  reference  is  made  in  the  equation  to  the  quantity 
of  air  in  circulation,  which  is  determined  from  the  equivalent  orifice  of 

the  mine  and  of  the  fan  by  the  equation  V — an*  which 

V = volume  of  air  (cu.  ft.  per  sec.);  a = equivalent  orifice  of  the  mine: 
o = the  equivalent  orifice  of  the  fan.  M.  Murgue  also  uses  the  equation 


h = — — , and  suggests  that  the  value  of  K for  any  particular  type  of 

machine  should  be  first  decided,  after  which  the  tangential  speed  required 
to  produce  any  given  effective  head  of  air  column  ( h ) is  easily  calculated 


from  the  formula  u 


4 


Igh 

method 


The  breadth  of  the  blade  is  left  largely  to 


judgment,  while  this  method  of  calculation  gives  the  same  size  of  fan 
for  any  given  effective  head  desired,  regardless  of  the  quantity  of  air  to 
be  circulated,  which  is  the  same  as  saying  that  the  ventilator  will  present 
the  same  efficiency  when  a large  amount  of  air  is  crowded  through  its 
orifice  of  passage  as  when  a smaller  amount  of  air  is  necessary. 

Mr.  Beard  uses  the  following  formulas  for  determining  the  several  dimen- 
sions of  a ventilating  fan: 


m 


= a/_J 

\ nV  V ' 


c + 


163, 6002  \ 
X3  j 


Q 

n2i/  V 

385,000,000  p 
(m3  — l)n2K  V^IV 


+ i; 


D = 


e = 


m 


|/  77Z3  — 1 

i/m3  — 1 
170  m 


3,770  V p . 
n i/K*v' 
4,'X3  K*  V 


392 


VENTILATION  OF  MINES. 


in  which  m = — , which  is  the  ratio  between  the  outer  diameter  of  the  fan 
a 

blades  D and  the  inner  diameter  of  the  blade  d , which  equals  the  diameter  of 
the  intake  orifice;  b = width  of  fan  blade;  e = expansion  of  spiral  casing  at 

point  of  cut-olf.  , . , . ,.  . , 

The  other  symbols  stand  for  the  same  quantities  as  previously  indicated. 

Curvature  of  Blades.— It  was  at  one  time  supposed  that  the  curvature  of 
the  blades  should  be  such  that  the  radial  passage  of  the  air-current  would 
be  undisturbed  by  the  revolution  of  the  fan;  but  fans  constructed  on  this 
principle  gave  no  adequate  results,  and  the  theoretical  spiral  thus  developed 
was  entirely  abandoned.  A certain  curvature  of  the  blade  backward, 
however,  is  assumed  by  many  to  increase  the  efficiency  of  the  fan.  This 
has  not  been  proved  in  practice,  but  the  effect  of  the  backward  curvature 
appears  simply  to  necessitate  a higher  speed  of  revolution  in  the  fan,  in 
order  to  obtain  the  same  results  as  are  obtained  with  radial  blades. 

The  Guibal  blade,  radial  at  its  outer  extremity,  or  normal  to  the  outer 
circumference,  and  curved  forward  in  the  direction  of  motion,  atits  inner 
extremity,  so  that  the  lip  of  the  blade  approaches  tangency  to  the  throat 
circle,  seems  the  most  effective  blade  in  centrifugal  ventilation. 

Tapered  Blades.— The  object  of  the  taper  is  to  produce  a constant  area  of 
passage  from  the  throat  to  the  circumference  of  the  fan,  and  thus  prevent 
the  reduction  of  the  velocity  of  the  current  in  its  passage  through  the 
fan  This  feature  presents  an  attempt  similar  to  that  attempted  by  the 
curvature  of  the  blades,  to  hasten  the  passage  of  the  air  through  the  fan. 
It  has  not  been  proved,  however,  to  have  produced  any  beneficial  result, 
except  in  the  strengthening  of  the  discharge  pressure  against  the  atmos. 
pheric  pressure,  in  open-running  fans.  On  the  other  hand,  the  slowing  up 
of  the  air  in  its  passage  through  a covered  fan  has  by  no  means  been 
proved  a detriment,  but  is  assumed  by  many  to  be  an  advantage,  inasmuch 
as  the  air  thus  remains  longer  within  the  influence  of  the  fan  blades. 

The  number  of  blades  depends  on  the  size  of  the  fan.  An  increased  number 
strengthens  the  fan’s  action  at  the  circumference,  or  supports  the  air  at  that 
point,  and  thus  prevents  the  backlash  or  the  reentry  of  air  into  the  fan.  due 
to  the  eddies  occurring  at  the  circumference  when  the  blades  are  too  iar 
apart.  To  a certain  extent,  the  number  of  blades  is  modified  by  the  speed 
of  revolution,  high-speed  motors  requiring  a somewhat  lesser  number, 
while  low-speed  motors  require  more.  In  any  case,  the  number  of  blades 
should  not  be  so  great  as  to  abnormally  increase  the  resistance  to  the  air- 
current.  In  general,  the  distance  upon  the  outer  circumference  from  tip 
to  tip  of  the  fan  blades  should  be  from  2 to  3 times  the  depth  of  the  blade. 

The  spiral  casing  gradually  reduces  the  velocity  of  the  air  and  reduces  the 
shock  incident  to  the  discharge  of  the  air  into  the  ati^sphere.  The  spiral 
casing  should  be  so  proportioned  that  the  velocity  of  the  flow  from  the  fan 
blades  will  be  maintained  constant  around  the  entire  circumference,  and 
this  should  not  be  less  than  the  velocity  of  the  blade  tips.  The  expansion  e 
of  the  casing  at  the  cut-off  should  be  such  as  to  provide  a velocity  of  the 
air  at  this  point  equal  to  the  velocity  of  the  blade  tips,  according  to  the 

equation  e = -|-v.  in  which  T>  = diameter  of  fan;  n = number  revolu- 

1 it  Dnb 

tions  per  minute;  b = breadth  of  fan  blade.  , . . 

The  evase  chimnev  reduces  the  velocity  of  the  air,  as  it  is  discharged  into 
the  atmosphere  to  The  chimney  should  be  sufficiently  high 

to  protect  toe  fan  from  the  effect  of  high  winds,  but  should  not  extend  too 
far  above  the  fan  casing,  the  point  of  cut-off  b®i^1®1^t®ijDelow  thlS’  a 
about  the  level  of  a tangent  to  the  throat  circle  at  its  lower  side. 

High-Speed  and  Low-Speed  Motors— The  question  of  speed  of  the jrenti 
latin!  motor  is  largely  an  open  one,  inasmuch  as  the  same  work  maybe 
performed  by  a small  ventilator  running  at  a high  speed  as  is  performed  by 
a large  ventilator  running  at  a low  speed.  . 

It  is  important  to  design  a mine  ventilator  at  a speed  &™h  for*  his  teen 
its  being-  increased  in  case  of  emergency.  If  the  ventilator  has  oeen 
designed  at  a high  speed,  a demand  for  an  increase  of  speed  cannot  be  met 
as  rladily  as  whin  the  ventilator  is  designed  at  a ^^m^ 
other  words,  the  exigencies  of  mine  ventilation  demand  that  a ventilator 
shall  be  capable  of  greatly  increased  speed. 

Fan  Tests.— A large  number  of  fan  tests  have  been  made,  from  time  t 


CONDUCTING  AIR-CURRENTS. 


393 


time,  on  different  types  of  fans  and  under  different  conditions,  with  respect 
to  the  resistance  against  which  the  fan  is  operated,  and  the  quantity  of  air 
required,  and  the  speed  of  the  ventilator.  The  experiments  have  resulted, 
to  a large  extent,  in  tabulating  a mass  of  contradictory  data.  The  condi- 
tions that  affect  the  yield  of  the  centrifugal  ventilator  are  so  numerous,  and 
the  tabulation  of  the  necessary  data  has  been  so  often  neglected  m these 
experiments,  as  to  render  them  practically  useless  for  the  purpose  of 
scientific  investigation.  In  conducting  a reliable  fan  test,  the  following 
points  should  be  observed:  (1)  Take  the  velocity,  pressure,  and  temperature 
of  the  air  at  the  same  point  in  the  airway,  as  nearly  as  practicable.  This 
point  should  be  selected  near  the  foot  of  the  downcast  shaft,  or  m the  fan 
drift  at  a suitable  distance  from  the  fan,  to  avoid  oscillations  of  pressure  and 
velocity.  (2)  The  area  of  the  fan  drift  should  be  uniform  for  a suitable 
distance  in  each  direction  from  the  point  of  observation,  and  tins  area 
should  be  carefully  measured.  (3)  Take  the  anemometer  readings  at  differ- 
ent positions  in  the  airway,  so  as  to  obtain  an  average  reading  over  the  entire 
sectional  area.  Do  not  interpose  the  body  in  this  area  so  as  to  decrease  the 
sectional  area  of  the  airway.  (4)  Take  outside  temperature  of  the  air  and 
the  barometric  pressure  at  the  time  of  making  the  test.  (5)  The  intake  and 
discharge  openings  of  the  fan  should  be  protected  against  wind  pressure. 
(6)  At  least  three  observations  should  be  made,  at  as  many  different  speeds 
of  the  ventilator,  and  the  number  of  revolutions  of  the  fan  carefully  observed 
and  recorded  for  each  observation.  . 

Mr.  R.  Van  A.  Norris  (Trans.  A.  I.  M.  E.,  Yol.  XX,  page  637)  gives  the 
results  of  a large  number  of  experiments  performed  upon  different  mine 
ventilating  fans.  This  table,  like  all  other  tabulated  fan  tests,  shows  a large 
amount  of  contradictory  data.  The  conclusions  drawn  by  Mr.  Norris  from 
these  tests  are  interesting  and  would  be  given  here  excepting  that  they 
might  be  misleading  if  considered  apart  from  the  description  of  the  experi- 
ments and  the  discussion  leading  up  to  the  conclusions. 


CONDUCTING  AIR-CURRENTS. 

Doors.— A mine  door  is  used  for  the  purpose  of  deflecting  the  air-current 
from  its  course  in  one  entry  so  as  to  cause  it  to  traverse  another  entry,  at  the 
same  time  permitting  the  passage  of  mine  cars  through  the  first  entry.  The 
essential  points  in  the  construction  of  a mine  door  are  that  it  shall  be  bung 
from  a strong  door  frame  in  such  a manner  as  to  close  with  the  current.  The 
door  should  be  hung  so  as  to  have  a slight  fall.  If  necessary,  canvas  flaps 
may  be  supplied  to  prevent  leakage  around  the  door,  and  particularly  at  the 
bottom.  Double  doors  are  used  on  main  entries  at  the  shaft  bottom,  or  at 
any  point  where  the  opening  of  the  door  causes  a stoppage  of  the  entire  cir- 
culation of  the  mine.  Such  doors  should  be  placed  a sufficient  distance 
apart  to  allow  an  entire  trip  of  mine  cars  to  stand  between  them,  so  that  one 
of  the  doors  will  always  be  closed  while  the  other  is  open. 

Stoppings.— Stoppings  are  used  to  close  break-throughs  that  have  been 
made  through  two  entries,  or  rooms,  for  the  purpose  of  maintaining  the  cir- 
culation as  the  workings  advance;  also  to  close  or  seal  off  abandoned  rooms 
or  working  places.  Stoppings  must  be  air-tight  and  substantially  built.  A 
good  form  of  stopping  is  constructed  by  laying  up  a double  wall  of  slate, 
having  about  8 or  10  in.  of  space  between  the  two  walls.  This  space  is  filled, 
as  the  building  progresses,  with  dirt  taken  from  the  roadways,  or  other  fine 
material.  In  the  building  of  stoppings  to  seal  off*  mine  fires,  it  is  important 
to  begin  the  work  at  the  end  nearest  the  return  air,  and  work  toward  the 
intake  end,  which  should  be  sealed  off  last.  This  method  avoids  the  danger 
of  an  explosion  occurring  within  the  workings  that  are  being  sealed  off,  as 
the  necessary  dilution  of  the  gases  within  is  accomplished  by  the  fresh  air- 
current,  until  the  intake  is  finally  sealed.  Where  the  intake  is  sealed  first, 
an  explosion  is  almost  inevitable,  as  has  been  proved  in  many  instances. 

Air  Bridges.— An  air  bridge  is  a bridge  constructed  for  the  passage  of  air 
across  and  over  another  airway,  this  being  called  an  overcast;  or,  the  cross- 
ing may  be  made  to  pass  under  the  airway,  this  being  called  an  unaercast. 
In  almost  every  instance,  overcasts  are  preferable  to  undercasts  for  several 
reasons.  An  undercast  is  liable  to  be  filled  with  water  accumulating  from 
mine  drainage;  it  is  also  liable  to  fill  with  heavy  damps  from  the  mine,  when 
the  ventilation  is  sluggish,  and  to  offer  considerable  resistance  to  the  free 
passage  of  the  air-current.  An  undercast  can  never  be  maintained  as  air- 
tight as  an  overcast,  on  account  of  the  continual  travel  through  the 


394 


HOISTING  AND  HAULAGE. 


haulageway  or  passageway  leading  over  it.  This  continual  passing  over 
the  bridge  causes  a fine  dust  to  sift  into  the  airway  and  mingle  with  the 
air-current.  All  these  objections  are  overcome  in  the  construction  of  the 
overcast 

An  air  brattice  is  any  partition  erected  in  an  airway  for  the  purpose  of 
deflecting  the  current.  A thin  board  stopping  is  sometimes  spoken  of  as  a 
brattice;  but  the  term  applies  more  particularly  to  a thin  board  or  canvas 
partition  running  the  length  of  an  entry  or  room  and  dividing  it  into  two 
airways,  so  that  the  air  will  be  obliged  to  pass  up  one  side  of  the  partition 
and  return  on  the  other  side  of  the  partition,  thus  sweeping  the  face  of  the 
heading  or  chamber.  Such  a temporary  brattice  is  often  constructed  by 
nailing  brattice  cloth  or  heavy  duck  canvas  to  upright  posts  set  from  4 to  6 ft. 
apart  along  one  side  of  the  entry  a short  distance  from  the  rib. 

Curtains. — These  are  sometimes  called  canvas  doors.  Heavy  duck,  or 
canvas,  is  hung  from  the  roof  of  the  entry  to  divide  the  air  or  deflect  a 
portion  of  it  into  another  chamber  or  entry.  Curtains  are  thus  used  very 
often  previous  to  setting  a permanent  door  frame.  They  are  of  much  use 
in  longwall  work,  or  where  there  is  a continued  settlement  of  the  roof, 
which  would  prevent  the  construction  of  a permanent  door;  also,  in  tempo- 
rary openings  where  a door  is  not  required. 


HOISTING  AND  HAULAGE. 

HOISTING. 

There  are  two  general  systems  of  hoisting  in  use:  (a)  Hoisting  without 
attempting  to  balance  the  load.  In  this  system,  the  cage  and  its  load  are  hoisted 
by  an  engine  and  lowered  by  gravity.  (b)  Hoisting  in  balance.  In  this 
system,  the  descending  cage  or  a special  counterbalance  assists  the  engine  to 
hoist  the  loaded  ascending  cage.  Hoisting  in  balance  is  usually  effected  by 
the  use  of  (1)  double  cylindrical  drums;  (2)  flat  ropes  winding  on  reels; 
(3)  conical  drums;  (4)  the  Koepe  system;  (5)  the  Whiting  system 

1.  Double  cylindrical  drums  are  widely  used:  they  consist  essentially  of  an 

engine  coupled  directly  or  else  geared  to  the  common  axis  of  the  drums. 
The  drums  are  usually  provided  with  friction  or  positive  clutches,  and 
brakes,  so  that  they  can  be  run  singly  if  desired,  or  the  load  can  be  lowered 
by  gravity  and  the  brake.  , _ , , , 

2.  Flat  ropes  wound  on  reels  are  sometimes  used  either  for  unbalanced 
hoisting  with  a single  reel  or  for  balanced  hoisting  with  a double  reel.  With 

& the  double  reels,  the  load  on 

the  engine  is  balanced 
throughout  the  entire  hoist, 
for,  as  the  rope  is  wound  on 
the  reel,  the  diameter  of  the 
reel  is  increased,  and  the 
lever  arm  through  which 
the  power  of  the  engine  is 
applied  is  also  increased  and 
the  mechanical  efficiency  of 
the  hoisting  system  de- 
creased. Thus,  when  the 
cage  is  at  the  bottom  of  the 
shaft  and  the  entire  weight 
of  the  rope  is  out,  giving  the 
maximum  load  to  be  hoisted, 
the  drum  is  of  a minimum 
diameter  and  the  engine  has, 
therefore,  its  greatest  lever- 
age to  start  the  load.  A flat 
rope  has  the  advantage  of 
preventing  fleeting,  but  its  first  cost,  extra  weight,  wear,  and  difficulty  of 
repairing  have  prevented  its  very  general  adoption. 

3.  Conical  Drums— A conical  drum,  Fig.  1,  equalizes  the  load  on  an  engine 
just  as  a flat  rope  on  a reel  does.  On  account  of  the  fleeting  of  the  rope, 
however,  the  drum  must  be  set  at  a considerable  distance  from  the  shaft  to 
prevent  the  rope  leaving  the  head-sheave.  A tail-rope  gives  the  most 


Fig.  1. 


HOISTING. 


395 


perfect  counterbalance,  the  weight  of  the  cage  and  rope  on  each  side  being 
exactly  equal. 

4.  In  the  Koepe  system.  Fig.  2,  one  rope  runs  over  and  the  other  under 
driving  sheaves  S.  A tail-rope  R is  used,  and  the  head-sheaves  x , x'  are 
placed  vertically  and  at  such  an 

angle  to  each  other  that  their 
grooves  and  the  groove  in  the  dri- 
ving sheave  are  in  line.  As  the 
main  driving  shaft  is  short,  the  en- 
gines can  be  placed  close  together, 
thus  requiring  a smaller  foundation 
and  engine  house  than  for  a drum 
hoist.  The  objection  to  the  system 
is  the  liability  of  the  rope  to  slipping 
about  the  driving  sheave,  and  for 
this  reason  a hoisting  indicator  can- 
not be  depended  on.  The  system  is 
also  inconvenient  for  hoisting  from  different 
levels  in  the  same  shaft,  and,  in  case  of  the  rope 
breaking,  both  cages  fall  to  the  bottom. 

5.  The  Whiting  system,  Fig.  3,  uses  two  narrow- 
grooved  drums  placed  tandem  instead  of  a single- 
driving sheave  as  is  used  in  the  Koepe  system. 

The  rope  passes  from  the  cage  A over  a head-sheave, 
under  the  guide  sheave  T and  around  the  sheaves 
if,  F three  times,  then  out  to  the  fleet  sheave  C, 
back  under  another  guide  sheave,  and  up  over 
another  head-sheave  to  the  cage  B.  The  sheave  M 
is  driven  by  a motor  either  coupled  direct  to  its 
shaft,  or  geared.  The  drums  F and  M are  coupled 
together  by  a pair  of  connecting-rods,  like  the 
drivers  of  a locomotive,  and  this  arrangement 
makes  it  possible  to  utilize  all  the  friction  of  both 
drums  to  drive  the  rope.  Thus  a tail-rope  is  not  depended  on  to  produce 
more  friction,  though  one  is  generally  used  as  a balance  to  the  loads. 

It  is  best  to  incline  the  follower  sheave  F from  the  vertical  an  amount 


Fig.  2. 


Q 


n 


equal  in  its  diameter  to  the  distance  between 
the  centers  of  two  adjacent  grooves,  the  object 
being  to  eliminate  chafing  between  the  ropes 
around  the  drums  and  to  prevent  them  from 
running  off  by  enabling  the  rope  to  run  from 
each  groove  in  one  drum  straight  to  the  proper 
groove  in  the  other.  This  throws  the  shaft  and 
crankpins  out  of  parallel  with  those  of  the  main 
drum,  but  this  difficulty  is  overcome  by  the 
connections  in  the  ends  of  the  parallel  rods. 

The  fleet  sheave  C is  arranged  to  travel  back- 
wards and  forwards,  as  shown  by  the  dotted 
lines,  in  order  to  change  the  working  length  of 

the  rope,  whereby  hoisting  can  be  done  from  different  levels  in  the 
The  power  used  for  hoisting  is  generally  steam  for  the  main  hoists, 
tricity  is,  however,  coming  rapidly  into  use,  particularly  for  smaller 


shaft. 

Elec- 

hoists 


396 


HOISTING  AND  HAULAGE . 


and  local  Installations,  and  for  main  hoists  in  locations  where  fue*  in- 
expensive and  water-power  available.  Gasoline  engines  are  also  being  used 
to  an  increasing  degree,  particularly  for  smaller  hoists  and  in  local  installa- 
tions, and  they  are  said  to  give  very  satisfactory  results. 


PROBLEMS  IN  HOISTING. 

To  Balance  a Conical  Dram.— Having  given  the  diameter  of  one  end  of  a 
conical  drum,  to  determine  the  diameter  of  the  other  end  that  will  equalize 
the  load  on  the  engines.  In  Fig.  1.  call  total  load  at  bottom  A,  empty  cage 
at  top  B,  loaded  cage  at  top  C,  empty  cage  plus  rope  at  bottom!),  small 
diameter  of  dram  z,  and  large  diameter  y;  then.  Ax  — By  = Cy  — Vx. 

Example.— In  a shaft,  the  cage  weighs  2 tons,  the  empty  car  1 ton.  the 
loaded  car  3 tons,  and  the  rope  2 tons.  What  should  be  the  small  diameter  of 
a conical  drum  whose  large  diameter  is  30  ft.? 

(2  + 2 + 3)x  - (2  + 1)30  = (2  + 3)30  - (2+  2 + l)z, 
or  7 x — 90  = loO  — 5 z. 

12z  = 240, 
x = 20  ft. 

To  Find  the  Size  of  the  Hoisting  Engine.— Let  D = diameter  of  cylinder. 

P = mean  effective  steam  pressure  in  cylinders,  r = ratio  of  stroke  to  diam- 
eter of  cylinder  and  i c = work  per  revolution  required  to  be  done:  then,  by 
making  one  cylinder  capable  of  doing  the  work,  n = number  of  strokes, 
u = work  per  minute  (ft.-lb.). 

D = 1®^.  or  2)  = 

Example  —What  should  be  the  size  of  the  cylinders  of  a hoisting  engine 
that  is  to  perform  152.580  ft.-lb.  of  work  per  revolution,  if  the  mean  effective 
pressure  is  45  lb.  per  sq.  in.  and  the  stroke  of  the  piston  is  twice  its  diameter  ? 

D = = 23-5in' 

To  get  up  speed  in  a few  seconds,  more  power  than  would  be  represented 
by  the  load  to  be  lifted  is  required.  Mr.  Percy  gives  the  following  rule  for 
this  case:  In  a properly  balanced  winding  arrangement,  with  uniform  load, 
multiplv  the  weight  of  coal  in  pounds  by  the  average  speed  of  the  cage  m 
feet  per  minute:  add  one-half  to  cover  the  frictional  resistances,  and  call 
ihat  the  load.  Then  the  power  that  must  equal  this  must  be  the  average 
effective  pressure  of  steam  in  pounds  per  square  inch  on  the  piston,  multi- 
plied by  the  area  of  one  cylinder  in  square  inches,  and  multiplied  again  by 
the  average  speed  of  the  piston  in  feet  per  minute. 

Approximately,  the  average  effective  pressure  of  steam  will  be  two-thirds 
of  the  pressure  shown  on  the  gauge  near  the  engines.  A good  average  piston 
speed  is  400  ft.  per  minute.  . , „ . _ _ , , n . , c. 

To  Find  the  Actual  Horsepower  of  an  Engine  for  Hoisting  Any  Load  Out  of  a Shaft 
at  a Given  Rate  of  Speed  — To  the  weight  of  the  loaded  car  add  the  weight  of 
the  rope  and  cage.  This  will  give  the  gross  weight. 


Then,  H.  P. 


gross  weight  in  lb.  X speed  in  ft.  per  minute.  L ^ 
“ 33.000 


contingencies,  friction,  etc.  . , . , . , ^ ~ ^ 

Example. — Having  a shaft  600  ft.  deep,  gross  weight  of  load  20,000  Id.,  to 
be  hoisted  in  II  minutes,  what  horsepower  is  required? 


H.  p.  _ = 243  H.  P„  nearly . 


To  which  add  £ for  contingen- 


cies, and  we  have  324  H.  P.  . ^ _ ...  , 

In  a shaft  with  two  hoistways,  use  the  net  weight  -j-  the  weight  of  one 
rope,  instead  of  the  gross  weight.  . 

The  following  rules  regarding  winding  engines  are  given  by  Percy: 

1.  To  Find  the  Load  That  a Given  Pair  of  Direct-Acting  Engines  Will  Start. 
Multiply  the  area  of  one  cylinder  by  the  average  pressure  of  the  steam 
per  square  inch  in  the  cylinder,  and  twice  the  length  ot  the  stroke.  Divide 
this  by  the  circumference  of  the  drum,  and  deduct  i for  friction,  etc. 


HEAD-FRAMES. 


397 


Example.— Given  a pair  of  engines,  cylinders  20  in.  diameter  by  40  in. 
stroke,  the  drum  12  ft.  diameter,  and  the  pressure  at  steam  gauge  50  lb., 
steam  cut-off  at  average  pressure  of  steam  in  cylinder  48.2  lb. 

Then,  area  of  cylinder  = 314.16  sq.  in.  314.16  X 48.2  X 80  = 1,211,400.96. 

The  circumference  of  the  drum  = 452.4  in.  1,211,400.96  -4-  452.4  = 2,677. 
f of  2,677  = 1,784  lb.,  or  the  net  load. 

The  gross  load  would  include  the  weight  of  rope,  cage,  and  car,  but  as 
these  are  balanced  by  the  descending  rope,  cage,  and  car,  the  net  load  only 
is  found.  The  drum  mentioned  is  cylindrical. 

2.  Knowing  the  Load  and  the  Diameter  of  a Cylindrical  Drum,  and  the  Length  of 
Stroke,  the  Cut-ofF  and  Pressure  of  Steam  at  Steam  Gauge,  to  Find  the  Area  and 
Diameter  of  Cylinders  of  a Pair  of  Direct-Acting  Engines. — Multiply  the  load  by 
the  circumference  of  the  drum,  and  add  one-half  for  friction,  etc.  Divide 
this  by  the  mean  average  steam  pressure,  multiplied  by  twice  the  length  of 
the  stroke. 

Example. — Having  the  drum  10  ft.  in  diameter,  the  stroke  6 ft.,  the  steam 
pressure  at  gauge  60  lb.,  the  cut-off  at  £ of  stroke,  and  the  load  5 tons,  or 

11,1 Then’  11,200  X 31.416  (circumference  of  drum)  = 351,859.  351,859  + £ of 
351,859  (or  175,930)  = 527,789.  , _ 

The  mean  average  pressure  = 56.2  lb.  56.2  X (6  X 2)  = 674.4.  527,789 
-4-  674.4  = 782.6  sq.  in.,  area  of  piston. 

782.6  .7854  = 996.  V 996  — 31.56  in.,  or  diameter  of  cylinder. 

3 To  Find  the  Approximate  Period  of  Winding  on  a Cylindrical  Drum  With  a Pair 
of  Direct-Acting  Engines.— Assume  the  piston  to  travel  at  an  average  velocity  of 
400  ft.  per  minute,  and  divide  this  by  twice  the  length  of  the  stroke,  and 
multiply  by  the  circumference  of  the  drum.  This  gives  the  speed  of  cage  in 
feet  per  minute.  Divide  the  depth  of  shaft  by  this,  and  the  result  will  be  the 
period  of  winding.  , „ ^ _ . _ . , 

Example. — Drum,  31.416  ft.  circumference;  stroke,  6 ft.;  depth  of  shaft, 

1 500  ft 

’ Then,  400  -4-  12  = 33.33.  33.33  X 31.416  = 1,047.1.  1,500  -4-  1,047.1  = 1.43 

min.,  or  about  1 min.  26  sec.  . „ _A.  , _ ..  , 

4.  To  Find  the  Useful  Horsepower  During  a Winding. — Multiply  the  depth  of 
shaft  by  net  weight  raised;  divide  this  by  number  of  minutes  occupied  in 
winding,  and  divide  again  by  33,000.  . , _ . , 

Example. — Net  weight,  2 tons  = 4,4801b.;  depth,  1,500  ft.;  period  of  wmd- 

mgThen,m4^0ex  1,500  = 6,720,000.  6,720,000  -4- 1.43  = 4,699,301.  4,699,301 

-4-  33,000  = 142+  H.  P.  

HEAD-FRAMES. 

Head-frames  are  built  of  wood  or  steel,  and  some  of  the  typical  forms  are 
shown  on  pages  275  and  276.  They  vary  in 
height  from  30  to  100  ft.,  depending  on  local 
conditions.  , , „ _ . , , 

The  inclined  leg  of  a head-frame  should  be 
placed  so  as  to  take  up  the  resultant  strain  due 
to  the  load  hanging  down  the  shaft  and  the 
pull  of  an  engine.  Fig.  4 shows  the  graphical 
method  of  determining  the  direction  and  mag- 
nitude of  this  resultant  force.  Produce  the 
direction  of  the  two  portions  of  the  rope  lead- 
ing to  the  drum  and  down  the  shaft  until 
they  intersect  at  G,  measure  off  a distance  G K 
to  scale  to  represent  the  load  hanging  down  the 
shaft;  similarly,  measure  off  GH  to  the  same 
scale  to  represent  the  pull  of  the  engine,  com- 
plete the  parallelogram  GHLK;  the  direction 
of  the  line  G L represents  the  direction  of  the 
resultant  force,  and  its  length  represents  the 
amount  of  this  force.  The  inclined  leg  of 
the  head-frame  should  be  placed  as  nearly  as 
possible  parallel  to  this  resultant  line,  and 
should  be  designed  to  withstand  a compressive 
strain  equal  to  this  resultant.  _ . , .. 

Head-sheaves  are  made  of  iron,  being  sometimes  entirely  cast,  or  else  tne 


Fig.  a. 


✓ 


398 


HOISTING  AND  HAULAGE. 


rim  and  hub  are  cast  separately  and  wrought-iron  spokes  are  used.  The 
former  are  cheaper  and  quite  satisfactory,  but  the  latter  are  lighter  and 
stronger,  and  therefore  usually  better.  The  diameter  of  the  sheave  depends 
on  the  diameter  of  the  rope,  and  the  table  giving  this  will  be  found  on 
page  120.  The  groove  in  the  sheave  should  be  wood-lined,  to  reduce  wear 
on  the  rope.  Wrought-iron  spokes  should  be  staggered  in  the  hub  and  not 
placed  radially.  _ _ A A_ 

Guides  and  conductors  are  usually  of  timber  rigidly  attached  to  the  sides  of 
a shaft.  In  England  and  certain  parts  of  Europe,  wire  ropes  are  used  for  guides 
and  are  strongly  advocated,  but  they  have  never  found  favor  in  America. 
These  ropes  when  used  are  weighted  at  the  bottom,  and  Percy  gives  1 ton 
for  each  600  ft.  in  depth  for  each  wire  as  a good  weight  to  be  used.  When 
not  thus  weighted,  the  ropes  are  fastened  at  the  bottom  and  attached  to 
levers  at  the  top,  the  levers  being  weighted  to  produce  the  requisite  tension. 

Safety  catches  usually  consist  of  a pair  of  toothed  cams  placed  on  either 
side  of  the  cages  and  enclosing  the  guides.  When  the  load  is  on  the  hoisting 
rope,  these  cams  are  kept  away  from  the  guides  by  suitable  springs;  but  if 
the  rope  breaks,  the  springs  come  into  action  and  throw  the  catcnes  or 
dogs  so  that  they  grip  the  guides,  and  the  tendency  to  fall  increases  the 

^Detaching  hooks  are  devices  that  automatically  disconnect  the  rope  from 
the  cage  in  case  of  overwinding. 


HAULAGE. 

The  magnitude  of  modern  mines  and  the  practice  of  loading  or  of  treating 
the  coal  or  ore  at  a large  central  station  makes  the  underground  haulage  of 
the  material  one  of  the  most  important  problems  in  connection  with 
mining.  A good  haulage  system  is  now  essential  to  make  most  mines  a 
commercial  success.  Haulage  may  be  considered  under  the  following  heads: 

1.  Inclined  Roads—  Gravity  planes,  engine  planes.  , 

2.  Level  Roads—  Mule  haulage,  rope  haulage  (tail-rope  and  endless  rope), 
motor  haulage  (steam,  electricity,  compressed  air,  or  gasoline). 

Gravity  Planes.— The  loaded  car  or  trip  hauls  the  empty  car  up  the  grade. 
Two  ropes  are  attached  to  a drum  so  that  the  rope  attached  to  the  loaded 

car  unwinds  from  the  drum  as  the  car  de- 
- scends,  while  the  rope  attached  to  the  empty 

4^  car  is  wound  on  the  drum  and  the  car  thus 

— hauled  up  the  plane.  The  natural  slope  of 

Horizontal.  the  ground,  in  a large  measure,  determines 

Fig.  5.  the  grade  of  the  incline,  but  where  it  is  pos- 

sible to  alter  the  direction  of  the  incline, 
the  grade  may  be  lessened  by  constructing  the  incline  across  the  slope  of 
the  ground.  The  grade  of  the  incline  may  be  increased  by  carrying  the 
upper  landing  forwards  till  a point  is  reached  from  which  the  required 
grade  is  obtained.  „ A _ , 

The  following  rule  gives  suggestions  based  on  practice  that  has  been 
successful:  For  lengths  not  exceeding  500  ft.,  the  minimum  grade  for  the 
incline  should  be  5 $ when  the  weight  of  the  descending  load  is  8,000  lb.  and 
that  of  the  ascending  load  2,8001b.  Or  the  inclination  should  not  be  less 
than  5 H if  the  respective  descending  and  ascending  loads  are  one-half  of 
those  just  given.  When  the  length  of  the  plane  is  from  500  to  2,000  It.,  the 
grade  should  be  increased  from  5$  to  10$,  according  to  the  loads.  A load 
of  4,000  lb.  on  a 10$  grade  2,000  ft.  long  will  hoist  a weight  of  1,400  lb. 

The  angle  of  inertia  is  that  angle  or  inclination  at  which  a car  will  start  to 
move  down  the  slope  or  plane.  The  car,  when  it  has  once  started  on  this 

Srade,  will  continue  to  accelerate  its  speed  as  it  descends  the  plane  A B , 
ig.  5.  If  we  decrease  the  angle  of  inclination  until  the  plane  A B occupies 
the  position  A C,  such  that  the  moving  car  will  continue  to  move,  at  a 
uniform  velocity  instead  of  accelerating  its  speed,  the  angle  EGA  will  be 
the  angle  of  rolling  friction,  and  the  tangent  of  this  angle  will  be  the  coefficient 
of  rolling  friction  for  the  car.  . _ .. 

The  upper  portion  of  a plane  is  made  steeper  than  the  lower  portion  so 
that  the  trip  may  start  quickly  at  the  head  and  afterwards  maintain  a 
uniform  velocity.  With  a good  brake  to  control  the  cars,  the  uniform  grade 
of  a central  portion  of  a gravity  plane  should  not  fall  much  below  3 , which 
corresponds  practically  to  a 5£$  grade. 


HAULAGE. 


^99 


The  acceleration  f of  the  haulage  system  is  given  by  the  formula 

/ = x g X sin  a 

Pl  + P2 

where  p,  and  p,  are  the  descending  and  ascending  pulls,  respectively. 

The  length  of  steep  pitch  is  given  by  the  formula- 

i = |L, 

to  haul  the  loaded  trip  up,  is 

T = ( W + w l)  sin  a + ( W + w l)  cos  a X /*> 

where  IF  = weight  of  loaded  trip;  wl  = weight  of  rope;  a = slope  angle; 

**  "example6—1 Mndthe°possible  tension  of  a rope  used  to  lower  a loaded  trip 
nf  two  cars  upon  a plane  800  ft.  long,  having  a uniform  grade  of  5 <fo  at  a 
speed  of  20  miles  per  hour,  using  a factor  of  _10,  and l 

To  find  the  number  of  cars  that  must  run  in  a trip  on  a self-acting  incline,  use 
the  formula 


N 


(40  sin  a + cos  a)  TT3 


(40  sin  a — cos  a)  W\  — (40  sin  a + cos  a)  W2 

in  which  N = number  of  cars;  a = angle  of  inclination  of  plane; 

= weight  in  pounds  of  one  loaded  car;  W2  = weight  m pounds  of  one 
empty gcar;  W3  = weight  in  pounds  of  haulage  rope;  — coefficient  of 

^ Example  — A gravity  plane  has  an  inclination  of  8°;  it  is  2,000  ft.  ^ng,  the 
rope  weighs  4,000  lb.,  a loaded  car  weighs  3,000  lb.,  and  an  empty  car  weighs 
1 800  lb.  What  number  of  cars  must  be  m the  trip  to  start  it? 

’ Substituting  values  in  the  above  formula,  we  have 


N 


(40  X .13917  -f  .99027)4,000 


= 13.6. 


(40  X .13917  — .99027)  3,000  — (40  X .13917  + .99027)1,800 

Fnffinp  Planes  —With  an  engine  plane,  the  load  is  delivered  at  the  foot  of 
the  nlane  and  has  to  be  hoisted.  The  engine  may  be  either  at  the  top  or  the 
bottom.  The  grade  of  the  plane  is  usually  uniform  from  top  to  bottomland 
there  mav  be  a single  track,  a double  track,  or  three  rails  with  a turnout. 

S^EngmeTRequired  for  Engine-Plane  Haulage.-(a)  ^gineat  Hef  of 
Plane  Sinale  Track. — Calling  the  load  on  the  engine  or  the  tension  of  the 
rone  at  the  winding  drum  T,  the  weight  of  the  ascending  loaded  trip  TF,1 the 
weight  of  the  rope  per  lineal  foot  w,  and  the  length  of  the  plane  l,  the  ang 
of  inclination  or  the  slope  angle  being  a,  as  before,  we  have 
T=  {W +wl)  {sin  a + cos  a). 

Assume  an  approximate  value  for  w,  and  determine  T approximately. 
The  size  of  rone  required  for  this  load  is  then  obtained  from  the  table  fo 
haul&J ^ropes?and  with  this  new  value  of  w,  the  correct  load  on  the  engine 

is  ^XAMPLK— What  size  of  rope  will  be  required  to  haul  up  an  incline  a 
loaded  trip  of  10  mine  cars  weighing  1,000  lb.  each,  and  carrying  a load  of 
2,000  lb.  each,  the  inclination  of  the  plane  or  the  slope  angle  being  16  and 
its  length  500  yd.,  assuming  for  the  coefficient  of  frictmn  ^ - ■ • 500) 

jy  _ 30(000  lb.,  and  assuming w = .89  lb.,  W + wl  — 30,000  + Co;*  X 


31,335  lb.  Sin  a + 


= .27564  + -fP-  = .29967. 
40  40 


Hence,  T = 31,320  X 


.29967  = 9,394  lb.  To  provide  against  shock,  we  double  the  loa^orimllon 
the  rone  in  calculating  the  size  of  rope  required;  thus,  9,394  X 2 ^ 18,788  lb.^ 
and  uSng  a factor  of  safety  of  6,  we  have  for  the  breaking  strain  of  the  rope 

18,788  X 6 = 57  tong  In  the  table  of  wire  ropes,  a If"  plow-steel  rope 

2,000 


400 


HOISTING  AND  HAULAGE. 


presents  a breaking  strain  of  56  tons.  Since  a 1|"  rope  weighs  2 lb.  per 
lineal  foot,  we  have  IF  4-  wl  = 30.000  + (2  X 1,500)  = 33.000  lb.  Then  T = 
33,000  X .29967  = 9,889  lb.  , 

(6)  Engine  at  Head  of  Incline , Double  Track.— The  load  on  the  engine 
equals  the  difference  between  the  gravity  pulls  of  the  ascending  and 
descending  trips,  including  the  rope,  plus  the  friction  pull  of  both  the  trips 
and  one  rope,  since  there  is  only  one  rope  on  the  plane  at  any  time.  Calling 
the  weight  of  the  ascending  trip  TF,  as  before,  and  that  of  the  descending 
trip  TFi,  we  have  for  the  difference  of  the  gravity  pulls  when  the  loaded  trip 
is  at  the  foot  of  the  incline,  ( TF— TFi  + w l)  sin  a.  and  for  the  friction  pull  of 
the  entire  moving  system  ( TF  + TFi  + w l)  /x  cos  a,  and  L = ( W — W\  + w l) 
sin  a + ( TF  -f  W\  -I-  w l)  n cos  a. 

Assuming  the  same  conditions  as  given  in  the  example  of  the  preceding 
paragraph,  we  have  for  the  load  L on  the  engine,  L = [10  X 2,000  -f  2 x 

1,500]  .27564  + [10  X (3,000  + 1,000)  + 2 X 1,500]  X = 23,000  X .27564 

+ 43,000  X .02403  = 7,373  lb.  instead  of  9,394,  the  unbalanced  load  for  single 
track.  ... 

(c)  Engine  at  Foot  of  Incline.— The  load  on  the  engine  is  the  same  as  m 
(a),  except  that  the  gravity  pull  is  the  pull  due  to  the  weight  of  the  loaded 
cars  only,  the  weight  of  the  ascending  rope  being  balanced  by  the  descend- 
ing rope,  while  the  friction  pull  is  increased  by  the  friction  of  the  descend- 
ing rope.  Calling  the  load  on  the  engine  X,  as  before,  we  have,  in  this  case, 

L = TF  sina-i(lF-j-2wZ)M-  cos  a. 


Assuming  the  conditions  of  the  previous  example  and  calculating  the 
load  on  the  engine  for  this  case,  we  have  L = 30,000  X .27564  H-  [30,000  + 
2(2X1,500)].02403  = 9,1341b. 

To  Find  the  Horsepower  of  an  Engine  Required  to  Hoist  a Given  Load  Up  a Single- 
Track  Incline  in  a Given  Time.— Multiply  the  length  of  the  incline  in  feet  by  the 
natural  sine  of  the  angle  of  inclination,  which  will  give  you  the  vertical  lift. 
Divide  the  vertical  lift  by  the  given  time  in  minutes.  Multiply  this  by  the 
gross  load,  including  weight  of  rope,  and  divide  the  product  by  33,000. 

Example.— Length  of  incline,  600  ft.;  angle  of  inclination,  35°;  weight  of 
loaded  car  and  600  ft.  of  rope,  5,000  lb. ; time  of  hoisting,  2 minutes.  Required, 
the  horsepower. 

Sine  of  35°  = .573576.  .573576  X 600  = 344.1456.  344.1456  -s-  2 = 172.728. 

172.728  X 5,000  ~ 

^ooo — = h-  p- 

Add  from  25^  to  50^  for  contingencies,  friction,  etc.  In  mine  practice.  50£ 
is  not  any  too  much  to  add.  because  the  condition  of  track,  cars,  etc.,  is  not 
as  good,  as  a general  rule,  as  on  railroad  planes. 

To  Find  the  Horsepower  of  an  Engine  Required  to  Hoist  a Given  Load  Up  a Double- 
Track  Incline  in  a Given  Time.— Proceed  as  above,  using  the  net  load,  to  which 
should  be  added  the  weight  of  one  rope,  instead  of  the  gross  load. 


ROPE  HAULAGE. 

The  tail-rope  system  of  haulage  uses  two  ropes  and  a pair  of  drums  on  the 
same  shaft.  The  main  rope  passes  from  one  drum  directly  to  the  front  of  the 
loaded  trip,  and  the  tail-rope  passes  from  the  other  drum  to  the  large  sheave 
wheel  at  the  end  of  the  road  and  back  to  the  rear  of  the  loaded  trip.  While 
hauling  the  loaded  trip,  the  drum  on  which  the  tail-rope  is  wound  is  allowed 
to  turn  freelv  on  its  journal  by  throwing  its  clutch  out,  while  the  engine 
turns  the  other  drum.  When  the  empty  trip  is  being  hauled,  the  clutch  on 
the  main-rope  drum  is  thrown  out  and  the  one  on  the  tail-rope  drum  is 
thrown  in.  The  engine  then  turns  the  tail-rope  drum  and  allows  the  other 
one  to  pav  out  rope  as  the  trip  advances. 

The  tail-rope  svstem  is  suitable  for  steep,  circuitous,  and  undulating 
roads.  The  trip  can  be  kept  stretched  at  all  points,  and  thus  the  cars  will 
be  prevented  from  bumping  together  or  from  being  jerked  apart  as  the  trip  is 
passing  over  changes  in  the  grade.  It  is  undoubtedly  the  most  satisfactory 
system  of  rope  haulage  under  the  natural  conditions  of  most  haulage  roads 
in  mines,  and  especially  so  where  but  one  road  is  available  for  haulage 
purposes. 


ROPE  HA  ULAGE. 


401 


CALCULATION  OF  THE  TENSION  OF  HAULING  ROPE. 

T = tension  or  pull  upon  rope  (lb.). 

W = weight  of  loaded  trip  (lb.). 

w = weight  of  rope  per  lineal  foot  (lb.).  - . jj-w 

l = length  of  two  ropes;  equals  2 times  the  distance  from  winding 
drum  to  tail-sheave  (ft.). 
d = vertical  drop  of  rope  (ft.). 
a = slope  angle  of  maximum  grade. 

T = TF(sin  a + /u.  cos  a)+w(d-jrn  l). 

Example.— What  size  of  steel  wire  rope  will  be  required  to  haul  a trip  of 
20  mine  cars  the  weight  of  the  loaded  cars  being  3,000  lb.  each,  the  depth  of 
the  shaft  300* ft.,  and  the  distance  from  the  loot  of  the  shaft  to  the  t^^g| 
900  vd.  the  maximum  grade  in  this  haulage  being  10  , n — 4o  • Assumi  g 

^ on  IVv  ■nor  linnol  ft 


''  rope,  weighing  .89  lb.  per  lineal  ft. 
, .9848  \ 

r = 


60,000  (.17365  + 
what  over  6 tons. 


40  ) 


.89  (soo+^gr)  = sa-y 12'300  lb- or  some‘ 


^eferringTo^the  tables  for  steel  haulage  ropes  with  6 strands i of ’1 'wire: 3 
each  we  find  the  breaking  strain  of  a f"  rope,  weighing  .89  lb.  per  hneal  it., 
is  1 8 6 tons  which  will  give  a factor  of  safety  of  about  3.  We  would,  however, 
use  a or  evenal''  rope,  as  a change  of  ropes  would  then  be  required  less 
often.8  Making  the  necessary  corrections  for  1"  rope  weighing  1.58  lb.  per 

^Tliee  n dTe  s s - r o p e°s  y s t e m uses  an  endless  rope,  which  is  kept  mnning  con- 
tinuously by  a pair  of  drums  geared  together  and  set  tandem.  The  drums 
are  comparatively 
narrow  and  provided 
with  grooves  for  the 
rope  to  run  in.  Two 
drums  are  necessary 
to  get  sufficient  fric- 
tion to  drive  the  rope 
when  the  trip  is  at- 
tached to  it.  The 
rope  is  passed  around 
both  drums  a num- 
ber of  times,  depend- 
ing on  the  amount  of 
friction  desired, 
without  completely 
encircling  either.  It 
then  passes  to  a ten- 
sion wheel  at  the  rear 
of  the  drums  and 
thence  to  the  sheave 
wheel  at  the  far  end 
of  the  road  and  back 
to  the  drums.  To  be 
used  to  best  advan- 

qmres^hatthe  grade  be  in  one  direction  and  that  it  he 

from  a number  of  places  en  route.  The  cars  are  attached  to  the  rop  y 
friction  grips  in  a manner  quite  similar  to  the  way  in  which  street  cars 
are  attached  to  cable  lines.  It  is  evident,  therefore,  that  any  jerking  due 
to  the  cars  bumping  together  or  stretching  the 

injure  the  rope  where  the  grip  takes  hold.  A double  road  is  an  essential 

fCaThe  endless-rope  system  of  haulage  is  best  adapted  to  roads  Ffairlvrel^ 
fairly  uniform  grade,  particularly  when  the  trips  are  not  sp^ed  at  fairly  reg 
lar  intervals  along  the  road.  Owing  to  delays  m the  dehvery  of  the  cars  by  the 
drivers  and  to  irregularity  in  unloading  at  the  Uppte,  it 
possible  to  have  the  several  trips  regularly  spaced,  and  m 
load  on  the  engine  varies  greatly.  In  order  to  take  up  any  elongation  of  the 
rope  due  either  to  change  in  temperature  or  to  stretching  some  form  of 
balance  car  or  balance  weight  is  used  This  weight  should  be  sufecient  to 
keep  the  empty  rope  taut,  and  any  tendency  of  the  rope  to  slip  on  tne 


Fig.  6. 


402 


HOISTING  AND  HA  ULAGE. 


winding  drum  may  be  overcome  by  increasing  the  weight  in  the  bal- 
ance car. 

Fig.  6 shows  a device  for  working  a district  haulage  by  connecting  it  with 
the  main  haulage.  The  main  rope  makes  one  or  two  complete  turns  around  a 
fleet  wheel  located  at  the  mouth  of  each  district,  and  then  continues  on  its 
course.  This  fleet  wheel  d is  directly  connected  with  the  driving  sheave  m 
for  the  district  by  means  of  beveled  gears  g , h,  as  shown.  The  driving 
sheave  m is  thrown  in  or  out  of  gear  by  levers  o and  q. 

To  Determine  the  Friction  Pull  on  an  Endless-Rope  Haulage. — Let 

0 = output  (lb.  per  min.);  tcx  = weight  of  mine  car  (lb.); 

= speed  of  winding  (ft.  per  min.);  w = weight  of  rope  (lb.); 

= length  of  haulage  road  (ft.);  T = load  on  the  rope  (lb.); 

= capacity  of  mine  car  (lb.);  /u.  = coefficient  of  friction. 


v 

l 

c 

Then, 


— = weight  of  material  in  transit; 
v 

2 ^ W\  = weight  of  moving  cars,  loaded  and  empty; 
2 1 w = weight  of  rope; 


^ ^ 1 + + 2 w l = entire  moving  load. 

And  if  the  coefficient  of  friction  equals 


[t( 


] 


H.  P.  = 


til 


33,000 


[•( 


1 + 


*-?> 


+ 2w 


’] 


Example.— Find  the  horsepower  for  an  endless-rope  system  5,000  ft.  long 
for  an  output  of  1,000  tons  per  day  of  10  hours  in  a flat  seam,  the  mine  cars 
having  a capacity  of  2.000  lb.  each  and  weighing  1,200  lb.  each. 

Assuming  a speed  of  winding  of  8 miles  per  hour  or  704  ft.  per  minute,  and 
for  the  coefficient  of  friction  /m  = 

T = a[5,00°^^(1  + + 2 X 1-58  X 5,OOo]  = 1,697,  say  1,700  lb. 


H.  P.  = 


704 
5,000 


40  X 33,000 


[3,333  ( 


2 X 1,200  \ 

+ 2,000 


X 1.58  X 704 J = 36.2  H.  P.  or, 


36.2 


assuming  an  efficiency  for  the  engine  of  60^,—^  = 60  H.  P. 


Inclined  Roads.— The  calculation  of  power  for  inclined  roads  is  the  same  as 
that  just  given,  excepting  that  the  work  due  to  lifting  the  coal  through  a 
height  h must  be  added  to  that  found  by  the  previous  formulas.  If  h equals 
the  elevation  due  to  the  grade  of  the  incline,  the  additional  work  of  the 
engine  due  to  hoisting  the  load  from  this  elevation  will  be  OA  and  the 
total  work  per  minute  u will  be 

u = fi  i[o  ^1  + + 2 w v J + O h. 

Example. — Assuming  the  same  conditions  as  given  above,  and,  in  addi- 
tion, a rise  or  elevation  of  100  ft.  in  the  entire  length  of  the  haulage  way,  we 

hare  u = ^[3,333(1  +2^^°°)  + 2 X 1.58  X 70l]  + 3,333 X 100 

= 1,528,050  ft.-lb.  per  minute  = 46.3  H.  P.,  or  assuming  an  efficiency  of  60£ 

for  the  engine,  ^ = 77  H.  P. 


MOTOR  HAULAGE. 

Locomotive  Haulage. — Wire-rope  haulage  is  very  efficient  in  headings,  on 
heavy  grades,  and  against  large  loads,  but  in  crooked  passages  it  entails  great 
costs  for  renewals  and  repairs.  When  the  grades  do  not  exceed  5£  for  short 
distances  and  average  3#  against,  or  for  short  distances  84  and  54  average  in 
favor  of  loads,  locomotives  have  been  found  the  most  economical  form  ot 
haulage. 


MOTOR  HAULAGE. 


403 


M EK^'iSS®  s““m  l-omoaves  are 

K^J3^S3!»^^"y5aa 

a?r  and  electricity  of  ^ whfchTnumber  of  types  have  been  designed  in  recent 
yearf and  whTch  have  been  very  successful  and  have  shown  a marked 
efficiency  over  the  mule  . _ 194  , compressed  air  is  particularly 

auDlicable  irf  gaseolis  mines,  as  it  improves  ventilation  and  is  perfectly  safe 
under  all  conditions.  The  great  disadvantage  in  compressed-air  haulage  is 

^M^H^MyeXof^he  Baldwin  Locomotive  Works,  gives  the  following 

in  In8  oMer  th^co^pre^ed^locomotives  may  be  able  to  make  a fair 
lenffth°  of  run,  the  tanks  for  storage  purposes  must  necessarily  be  rather 
cumbersome^  and  constructed  to  carry  high-storage  pressures  lnorder  that 
theTmay  be  designed  correctly  and  get  a minimum  of  storage  for  the 
maximum  work  expected,  it  is  necessary  to  have  a complete  profile  of  the 
nrnnosed  haulage  road  and  to  make  a tabulated  statement  of  the  air  con 
Siwfon  oSTe  Various  grades,  noting  the  “ cut-off”  necessary  to  produce  the 
reamsite  tractive  effort.  By  making  a summation  of  these  varmus  amounts, 
an^addtng^O^y we  will  have  the  possible  amount  of  air  used  in  doing  cer- 

taiIMrLcesLerylfitherefore,  to  provide  storage  on  the  loepmotive  for  this 
amount  of  air  at  a much  greater  pressure  than  that  used  m the  cylinders. 
Tn  order  that  the  locomotive  may  receive  a quick  charge  at  the  stations 
specially  provided  for  the  purpose,  it  is  necessary  to  have  stationary  storage 

to  800  lb  and  to  have  the  volume  of  this  storage  at  least  double  the  tank 
capacity  of  the  locomotives  comprising  the  system.  This  allows  an  equalized 
nressure  in  the  locomotive  storage  of  approximately  600  lb.  . . 

^ The  following  formula  is  useful  in  determining  the  capacity  of  stationary 

storage:  P'  = in  which  V = volume  of  storage  on  locomotive; 

X = volume  of  stationary  storage  desired;  p = cylinder  pressure;  P = 
stationary  storage  pressure;  and  if  = locomotive  storage  Pres®^-  . , 

If  the  average  time  for  each  trip  is  30  minutes,  the  compressor  must  be 
able  to  compress  in  that  time  to  pressure  P,  the  calculated  amount  of  air 
required  for  one  trip  or  series  of  trips  for  the  various  locomotives  included 
in  the  haulage.  In  general,  it  is  customary  to  extend  extra-strong  pipeinto 
the  mine  and  of  such  length  and  diameter  as  to  bave  the  required  volume 
for  the  stationary  storage.  There  are  times  however  when  it  would  be  found 
more  economical  to  arrange  for  tank  storage  either  inside  or  putsitm  the 
mine,  but  in  general,  especially  when  the  mine  is  advancing,  it  is  the  better 
practice  to  install  pipe  storage  since  it  increases  the  range  of  the  locomotive 
as  the  workings  advance.  . ^ ^ - 

The  following  table  gives  the  various  tractive  efforts  of  different  sizes  of 
compressed-air  locomotives,  when  working  at  100  lb.  cylinder  pressure,  and 
various  cut-offs.  If  other  pressures  or  strokes  are  used,  the  tractive  efforts 
are  directly  proportionate.  This  table  is  calculated  by  means  of  the  formula, 


tractive  effort  = 


d2lxP' 

D ’ 

in  which  d = diameter  of  cylinder;  D = diameter  of  driver;  Z = length  of 
stroke;  p — working  pressure  of  the  cylinders;  and  x — variable  due  to  the 
various  cut-offs. 


404 


HOISTING  AND  HAULAGE. 


Tractive  Efforts  of  Compressed-Air  Locomotives. 


Cylinder. 

Diam- 
eter of 
Driver. 

Inches. 

Weight 

on 

Driver. 

Pounds 

Tractive  Effort  for  Each  100-Lb.  Cylinder 
Pressure  at  Various  Cut-Offs. 

Diam. 

Inches. 

Stroke. 

Inches. 

7 

e 

3 

3F 

5. 

8 

■ 1 

* 

3. 

8 

4 

1 

8 

5 

10 

24 

6,000 

1,020 

990 

920 

835 

710 

530 

325 

6 

10 

24 

8,500 

1,470 

1,425 

1,320 

1,200 

1,020 

760 

445 

7 

12 

26 

13,000 

2,200 

2,150 

1,990 

1,810 

1,540 

1,140 

700 

8 

12 

26 

18,000 

2,880 

2,750 

2,600 

2,360 

2,000 

1,510 

900 

9 

14 

26 

25,000 

4,340 

4,140 

3,840 

3,490 

2,960 

2,220 

1,350 

10 

14 

26 

32,000 

5,280 

5,150 

4,740 

4,310 

3,660 

2,630 

1,670 

11 

16 

28 

42,000 

6,770 

6,450 

5,980 

5,440 

4,620 

3,470 

2,140 

12 

16 

28 

52,000 

8,050 

7,800 

7,200 

6,550 

5,580 

4,150 

2,550 

On  account  of  certain  losses  due  to  radiation,  etc.  for  cut-off  at  full  length 
of  stroke  in  steam  practice,  x is  taken  as  .85.  While  cylinder  surface  acts  as 
a detriment  to  the  use  of  steam,  it  acts  entirely  opposite  in  the  use  of  air, 
for  the  reason  that,  in  the  expansion  of  the  air,  very  low  temperatures  are 
produced,  and,  with  a maximum  of  cylinder  surface  exposed,  we  absorb  a 
maximum  of  heat  from  the  surrounding  air,  which  virtually  adds  new 
energy  to  the  air,  thus  acting  as  a reheater.  Therefore  in  air  practice,  x is 
made  .98  for  full-stroke  cut-off,  with  the  others  proportionately  high.  If 
simple-expansion  cylinders  are  used,  the  working  pressure  should  not 
exceed  130  lb.,  while,  with  compounds,  one  can  easily  use  from  180  to 
225  lb.  with  great  economy.  Where  it  is  imperative  to  have  a minimum- 
sized locomotive  storage  with  a maximum  run,  this  can  be  accomplished 
with  compound  locomotives.  Originally,  it  was  the  custom  to  lag  the  cylin- 
ders as  in  steam  practice,  but  now  it  is  found  advantageous  to  leave  them 
bare  and  to  corrugate  both  sides  and  ends  so  as  to  present  a maximum 
surface  to  the  surrounding  atmosphere  while  running,  thus  absorbing 
new  energy. 

Example.— It  is  desired  to  haul  trips  of  60  cars,  empties  weighing  2,000  lb. 
and  loads  6,000  lb.  each,  over  a track  having  the  following  profile,  and  with 
one  charge  of  air.  All  grades  are  in  favor  of  loads.  (The  following  calcu- 
lations have  been  made  with  the  slide  rule.) 


Profile  of  Road. 


Grade. 

Distance. 

Grade. 

Distance. 

Grade. 

Distance. 

1.3# 

800  ft. 

0.30# 

700  ft. 

2.4# 

400  ft. 

2.0# 

600  ft. 

1.77# 

1,025  ft. 

3.5# 

425  ft. 

1.3# 

800  ft. 

0.90# 

300  ft. 

1.2# 

320  ft. 

The  maximum  grade  being  3.5#,  and  the  car  friction  in  this  case  being  1 #, 
the  total  resistance  when  ascending  a 3.5#  grade  due  to  cars  is,  hence, 
3.5#  -HI#  = 4.5#.  Since  it  is  desired  to  haul  60-car  trips,  and  all  grades  are 
in  favor  of  loads,  it  is  only  necessary  to  provide  a locomotive  capable  of 
hauling  60  empties  weighing  120,000  lb.  up  the  above-mentioned  grade.  The 
drawbar  pull  necessary  to  do  this  is  4.5#  of  120,000  lb.  = 5,400  lb.  In  general, 
it  will  require  a locomotive  having  a weight  on  drivers  of  5 times  the 
tractive  effort  desired  if  steel  tires  are  used,  as  is  the  practice  in  the  con- 
struction of  air  locomotives,  and  6 times  the  tractive  effort  if  cast-iron  chilled 
wheels  are  used,  as  is  the  practice  in  electric  locomotives.  We  will  there- 
fore assume  the  necessary  weight  of  the  locomotive  to  give  the  proper 
adhesion  as  32,000  lb.,  and  we  calculate  that  the  tractive  effort  necessary  to 
haul  itself  up  the  3.5#  grade  would  be  3.5#  + .5#  = 4#  (.5#  covering  the  fric- 
tion of  the  locomotive  on  the  level)  of  32,000  lb.,  or  1,2801b.,  to  which  we 
add  the  necessary  drawbar  pull  to  haul  the  desired  load,  1,280  + 5,400,  and 
have  a total  tractive  effort  of  6,680,  which  is  about  the  limit  of  a locomo 
live  on  dry  rail  with  sand. 


MOTOR  HAULAGE. 


405 


Bv  consulting  the  table  of  tractive  efforts  of  compressed-air  locomotives, 
we  see  that,  at  100  lb. working  pressure,  a 10"  X 14",  26"  driver. locomotive  has 
a maximum  tractive  effort  at  £ cut-off,  which  is  practically  full  stroke,  of 
5,280  lb.,  and  by  dividing  -5T%8<£  into  our  necessary  tractive  effort,  we  find  that 

the  necessary  working  pressure  would  be  about  130  lb.  # 

On  this  basis,  we  then  make  up  the  following  table  in  order  to  ascertain 
the  necessary  air  consumption: 


Grade. 

Distance. 

Going  in 
T.E. 

1.3 

800' 

3,375 

2.0 

600' 

4,450 

3,375 

1.3 

800' 

0.3 

700' 

1,830 

1.77 

1,025' 

4,100 

0.9 

300' 

2,750 

2.4 

400' 

5,075 

3.5 

425' 

6,760 

1.2 

320' 

2,220 

0.3 

700' 

Coming 

2,600 

Strokes. 

120 

80 

120 

105 

150 

40 

60 

65 

50 


Cut-Off. 


Cu.  In.  Air  Used. 
126,000 

176.000 

126.000 
55,125 

315.000 
42,000 

157,500 

239.000 
52,500 


110,000 


20 l additional . 


1,399,125 

279,825 


Total - 1,678,950  cu.  m. 

This  equals  975  cu.  ft.  at  130  lb.  pressure  used  in  hauling  the  required  loads 
on  a single  round  trip.  Since  we  should  return  to  the  starting  point  with 
130  lb.  in  the  locomotive  storage,  it  is  evident  that  the  volume  of the  tanks 
shall  allow  for  the  use  of  975  cu.  ft.  in  addition  to  1 volume  at  130  lb. 

Let  V = volume  of  storage  on  locomotive;  P'  = pressure  of  storage  on 
locomotive;  p — working  pressure;  V'  = volume  at  working  pressure  nec- 
essary to  do  the  work  required.  _ .,  „„„ 

Then  the  product  of  the  volume  of  the  locomotive  storage  by  its  pressure 
must  equal  the  sum  of  the  volume  necessary  to  do  the  work  required 
multiplied  by  the  working  pressure,  and  the  locomotive  storage  volume  by 
the  working  pressure,  thus, 

p’v  = pv  + pv\  or,r=  v przrp- 

130 

If  P'  = 650,  then  V = 975  X _ f3Q  = 244  cu-  ft- 

With  one  locomotive,  making  trips  every  30  minutes, we  must  arrange  for 
a compressor  capable  of  compressing  975  cu.  ft.  at  130  lb.  m this  time,  bince 
it  is  customary  to  rate  compressors  at  their  capacity  in  free  air  per  minute, 


the  above  is  equivalent  to 


975  X 130 


= 288  cu.  ft.  free  air  per  minute. 


14.7  X 30 

This  must  be  compressed  to  800  lb.  in  the  compressor,  and  stored  in 
stationary  storage.  If  X is  the  volume  of  the  stationary  storage, 

pV+PX 
VAX  * 


P'  = 


P'-P 


or  X = 244  X 


650-130 
800  — 650 


= 846  cu.  ft. 


“ r P-P" 

The  length  of  the  haulage  is  5,370  ft.,  hence  the  cross-section  of  the  pipe 

846 

necessary  to  furnish  the  requisite  storage  is  = .157  sq.  ft. 

From  the  following  table,  this  would  require  a 5£"  pipe,  but  for  practical 
purposes  it  is  possible  that  a 5"  pipe  would  be  selected. 


# Returning  with  loads,  it  is  possible  that  there  is  only  one  grade  that  the  trip  will  hare 
to  be  hauled. 


406 


HOISTING  AND  HAULAGE. 


Standard  Steam  and  Extra-Strong  Pipe  Used  for  Compressed-Air 
Haulage  Plants. 


Trade 

Diam- 

eter. 

In. 

Cu.  Ft.  in 
1 Lineal 
Ft. 

Lineal  Ft. 
Necessary 
to  Make 
1 Cu.  Ft. 

Steam. 

Extra  Strong. 

Trade 

Diam- 

eter. 

In. 

Thick- 

ness. 

Weight 
per  Ft. 

Thick- 

ness. 

Weight 
per  Ft. 

2 

.0218 

45.41 

.15 

3.61 

.22 

5.02 

2 

2i 

.0341 

29.32 

.20 

5.74 

.28 

7.67 

2£ 

3 

.0491 

20.36 

.21 

7.54 

.30 

10.20 

3 

3£ 

.0668 

15.00 

.22 

9.00 

.32 

12.50 

3£ 

4 

.0873 

11.52 

.23 

10.70 

.34 

15.00 

4 

4£ 

.1105 

9.05 

.24 

12.30 

.35 

17.60 

4£ 

5 

.1364 

7.33 

.25 

14.50 

.37 

20.50 

5 

5£ 

.1650 

6.06 

.26 

16.40 

.40 

24.50 

6 

.1963 

5.10 

.28 

18.80 

.43 

28.60 

6 

From  the  following  table  we  see  that  it  would  require  2.88  X 32.5  — 
93.6  H.  P.;  hence,  we  would  be  compelled  to  arrange  for  a boiler  capacity 
of  practically  100  H.  P.,  provided  we  used  a three-stage  compressor,  as  is  the 
general  custom. 

Horsepower  Necessary  to  Compress  100  Cu.  Ft.  of  Free  Air  to  Various 


Pressures  and  With  Two-,  Three-,  and  Four-Stage  Compressors. 


Gauge 

Pres- 

sure. 

Horsepower  Necessary. 

Gauge 

Pressure. 

Horsepower  Necessary. 

Two- 

Stage. 

Three- 

Stage. 

Four- 

Stage. 

Two- 

Stage. 

Three- 

Stage. 

Four- 

Stage. 

100 

15.7 

15.2 

14.2 

900 

36.3 

33.7 

31.0 

200 

21.2 

20.3 

18.8 

1,000 

37.8 

34.9 

31.8 

300 

24.5 

23.1 

21.8 

1,200 

39.7 

36.5 

33.4 

400 

27.7 

25.9 

24.0 

1,400 

41.3 

37.9 

34.5 

500 

29.4 

27.7 

25.9 

1,600 

43.0 

39.4 

35.6 

600 

31.6 

29.5 

27.4 

1,800 

44.5 

40.5 

36.7 

700 

33.4 

31.2 

28.9 

2,000 

45.4 

41.6 

37.8 

800 

34.9 

32.5 

30.1 

2,500 

43.0 

39.0 

Electric  Haulage.— Mr.  H.  K.  Myers  says  in  regard  to  mine  haulage  by 
electricity:  In  general,  it  costs  from  6 to  10  cents  per  ton  to  deliver  coal 
from  face  of  workings  to  shaft,  slope,  or  tipple,  where  the  haul  is  1 mile  and 
the  tracks  approximately  level;  yet  I know  three  mines  that  at  present  haul 
from  parting  with  the  trolley  system,  the  miner  delivering  from  face  of 
room,  making  an  average  round  trip  of  9,000  ft.,  at  a total  cost  of  1 cent  per 
ton.  These  mines  have  never  had  a mule  in  them,  and  it  would  be  almost 
an  impossibility  to  introduce  them,  for  the  reason  that  the  seam  is  of  such 
thickness  that  the  clearance  between  tie  and  roof  is  only  about  4 ft.  Since 
the  advent  of  the  electric-mining  locomotive,  there  has  been  a change  in 
the  mine  wagons  universally  used.  Formerly  it  was  customary  to  find  as 
much  as  60  lb.  per  ton  car  resistance  on  the  level,  while  at  present  it  is  as 
low  as  15  lb.  . _ . . , . 

In  dimensioning  mining  locomotives,  it  is  customary  to  make  the  weight 
from  6 to  8 times  the  necessary  tractive  effort,  dependent  entirely  on  the 
nature  of  the  work.  If  the  work  is  constant  and  a maximum,  then  the 
weight  will  be  only  6 times  the  torque  of  the  motors,  while  if  the  work  is 
intermittent  with  a short-time  maximum  tractive  effort,  then  the  factor 
will  be  8.  The  weight  of  an  electric  locomotive  running  at  a speed  of  6 to 


MOTOR  HAULAGE. 


407 


8 miles  per  hour  with  intermittent  load  may  also  be  mM  be 

400  lb  for  each  rated  horsepower  of  the  motor,  and  the  weight  should  be 
Himes the  rated  drawbar  pull,  regardless  of  speed.  For  continuous  work, 
these  weights  should  be  decreased  25/*. 

Drawbar  Pull  on  Various  Grades  for  Different  Sized  Locomotives. 


Horse- 

Weight. 

Grades. 

power. 

Level. 

1/* 

2 J 

3/ 

4/ 

5 J 

6/* 

10 

20 

30 

50 

70 

100 

4.000 

8.000 
12,000 
20,000 
28,000 
40,000 

500 

1,000 

1.500 

2.500 

3.500 
5,000 

460 

920 

1,380 

2,300 

3,220 

4,600 

420 

840 

1,260 

2,100 

2,940 

4,200 

380 

760 

1,140 

1,900 

2,660 

3,800 

340 

680 

1,020 

1,700 

2,380 

3,400 

300 

600 

900 

1,500 

2,100 

3,000 

260 

520 

780 

1,300 

1,820 

2,600 

In  mines  it  is  found  that  the  friction  between  wheel  and  rail  is  less  than 
on  the  surface,  due  to  dampness  and  powdered  coal  on  the  rail.  The  tractive 
efforts  with  chilled  wheels  is  usually  considered  ¥ of  the  weight,  lhe 
table  on  page  408  and  diagram  on  page  409  give  hauling  capacities  of 

locomotives  in  tons  of  2,000  lb.  . , . 

For  maximum  continuous  work,  it  is  necessary  to  have  a grade  such 
that  the  efforts  to  haul  the  same  number  of  empty  wagons  as  loaded 
are  equal.  With  the  car  resistance  considered  1/  and  the  loaded  cars  weigh- 
ing 3 times  as  much  as  the  empties,  this  is  found  to  be  * of  1/.  The  most 
critical  point  in  the  designing  of  mining  locomotives  is  to  make  the  limiting 
dimensions  a minimum.  The  demands  for  various  dimensions  are  wonder- 
ful. The  headings  in  mines  are  never  of  more  generous  proportions  than 
really  necessary,  and  all  clearances  a minimum.  The  minimum  dimen^ons 
for  mining  locomotives  are  as  small  as  2 ft.  for  wheel  base,  8 ft.  for  length 
over  all,  and  3 ft.  width.  Scarcely  two  orders  carry  the  same  dimensions, 
and  it  is  impossible  to  have  any  kind  of  a standard.  In  consequence  of  this, 
it  is  necessary  to  have  a great  variety  of  motors  suitable  for  gauges  as  nar- 
row as  18  in.  and  for  wheels  as  small  as  20  in.  m diameter.  With  such  a 
variety,  it  becomes  possible  to  construct  a locomotive  weighing  40,000  lb. 
on  3'  gauge,  having  the  width  over  all  62  in.,  height  35  in.,  and  length 
12  ft.  In  construction,  it  is  necessary  to  have  the  most  modern  form  of 
motors  and  the  most  rigid  mechanical  construction. 

The  motors  now  used  are  of  the  best  possible  construction  and  efficiency. 
They  are  of  the  slow-speed  street-car  type,  6 to  8 miles  per  hour  winding, 
and  range  in  size  from  4 to  50  H.  P.  It  is  customary  to  use  the  rheostatic 
type  of  controller  for  mining  locomotives,  on  account  of  its  small  dimensions 
and  apparent  efficiency  for  this  class  of  work,  but  it  is  doubtless  but  a short 
time  until  a very  compact  form  of  series-parallel  type  will  be  devised.  On 
account  of  the  use  of  this  rheostatic  controller,  it  becomes  necessary  to  Pro- 
vide for  large  diverter  capacity,  and  since  the  locomotive  is  designed  for  the 
maximum  tractive  effort,  it  is  hardly  ever  possible  to  run  without  resist- 
ance and,  hence,  a large  amount  of  current  must  be  dispeped  with  the 
consequent  heating.  If  the  motors  are  overloaded,  they  heat  rapidly,  this 
heating  varying  as  the  square  of  the  current.  A motor  that  has  a rating  of 
40  amperes  for  regular  work,  if  worked  for  3 minutes  at  100  amperes,  should 
not  be  subjected  to  such  a strain  oftener  than  once  in  18f  minutes,  as  shown 
by  the  following  equation: 

402  x x = 3 X 1002;  x = 18£  minutes. 

Using  the  same  problem  given  under  compressed-air  locomotives,  in 
which  the  maximum  tractive  effort  was  6,760  lb.,  we  find  from  the  table  of 
drawbar  pulls  that  a locomotive  equipped  with  two  50  H.  P.  motors  (equals 
100  H.  P.)  will  carry  the  load  with  an  overload,  these  motors  being  rated  for 
continuous  work  at  approximately  32  amperes  of  500  volts. 

Using  the  formula  = which  t — various  times  at  which 


408 


HOISTING  AND  HAULAGE. 


various  amounts  a of  current  are  used  on  the  corresponding  grades,  2 the 
summation  of  the  items  t a2  calculated  for  each  section  or  grade,  and  T = 
total  time  that  should  be  taken  for  each  trip,  we  calculate  the  following 
table: 


Grade. 

Dist. 

T.  E. 

Time. 

Minutes. 

Amperes. 

to? 

1.30 

800 

3,375 

1.5 

114 

Empties. 

19,600 

2.00 

600 

4,450 

1.1 

134 

19,900 

1.30 

800 

3,375 

1.5 

114 

19,600 

.30 

700 

1,830 

1.3 

74 

7,100 

1.77 

1,025 

4,100 

2.0 

128 

32,800 

.90 

300 

2,750 

.6 

100 

6,000 

2.40 

400 

5,075 

.8 

148 

17,300 

3.50 

425 

6,760 

.8 

182 

26,500 

1.20 

320 

2,220 

.6 

86 

4,400 

.30 

700 

2,600 

1.3 

96 

Loads. 

13,900 

167,100  = 2 t a2 

^Jl6U00  = 64;  4 096  T = 167100;  T = 4a 

By  this  means  we  can  make  60-car  trips  every  40  minutes  without  injury 
to  the  motors,  based  upon  a speed  of  6 miles  per  hour.  (See  also  page  215.) 

Speed  of  haulage  depends  on  the  system  of  haulage  used  and  on  the  con- 
dition of  the  haulage  road.  The  law  in  Pennsylvania  provides  for  a speed  of 
haulage  not  over  6 miles  per  hour,  and  this  is  the  speed  at  which  electric  and 

Hauling  Capacity  of  Electric  Locomotives. 


Horsepower. 

Weight. 

Drawbar  Pull 
on  Level. 

Frictional  Car 
Resistance  per 
Ton  on  Level. 

Grades. 

Level. 

1 Jo 

W 

2{ 

m 

3 jo 

3 if 

4 f 

5 f 

6 i 

10 

4,000 

500 

20 

23 

15 

10 

8 

6.3 

5.2 

4.2 

3.5 

3.0 

2.2 

1.6 

30 

15 

11 

8.4 

6.7 

5.4 

4.5 

3.8 

3.2 

2.7 

2.0 

1.5 

40 

12 

9 

7 

5.7 

4.7 

4.0 

3.4 

3.0 

2.5 

1.8 

1.4 

20 

8,000 

1,000 

20 

46 

29 

21 

16 

13 

10.3 

8.4 

7.1 

6.0 

4.3 

3.1 

30 

31 

22 

17 

13 

11 

9 

7.5 

6.4 

5.4 

4.0 

3.0 

40 

23 

18 

14 

11 

9.5 

8 

6.8 

5.9 

5.0 

3.7 

2.8 

30 

12,000 

1,500 

20 

69 

44 

32 

24 

19 

15 

13 

10.7 

9.0 

6.5 

4.7 

30 

43 

33 

25 

20 

16 

13 

11 

9.6 

8.2 

6.0 

4.4 

40 

34 

26 

21 

17 

14 

12 

10 

8.8 

7.5 

5.6 

4.1 

50 

20,000 

2,500 

20 

115 

73 

52 

40 

32 

26 

21 

18 

15 

11 

7.9 

30 

77 

55 

42 

33 

27 

22 

19 

16 

14 

10 

7.3 

40 

58 

44 

35 

29 

24 

20 

17 

15 

13 

9.3 

6.8 

70 

28,000 

3,500 

20 

161 

103 

74 

56 

44 

36 

30 

25 

21 

15 

11 

30 

107 

77 

59 

47 

38 

31 

26 

22 

19 

14 

10 

40 

81 

61 

50 

40 

33 

28 

24 

20 

18 

13 

9.6 

100 

40,000 

5,000 

20 

230 

147 

105 

80 

63 

52 

42 

36 

30 

22 

16 

30 

153 

110 

84 

67 

54 

45 

38 

32 

27 

20 

15 

40 

115 

88 

70 

57 

47 

40 

34 

29 

25 

19 

14 

MOTOR  HAULAGE. 


409 


compressed-air  haulages  are  usually  calculated  and  at  which  loaded  trips 
are  usually  run.  Empty  trips  are  usually  run  at  a slightly  higher  speed. 

The  speed  for  tail-rope  haulage  is  given  by  three  prominent  makers  of 
such  plants,  as  follows:  (a)  600  to  700  ft.  per  minute;  (6)  8 to  10  miles  per 
hour;  (c)  6 to  8 miles  per  hour. 

The  speed  for  endless-rope  haulage  is  given  by  the  same  makers  as  (a) 
140  to  150  ft.  per  minute;  (5)  1 to  2 miles  per  hour;  (c)  150  to  200  ft.  per 
minute.  A slow  speed  for  endless  rope  is  to  be  preferred  as  being  much 
more  economical  in  the  wear  of  the  rope  and  cars,  and  many  prefer  a single- 
car system  to  a trip  system,  thus  doing  away  with  the  trip  rider  By  han- 
dling: the  cars  singly  or  even  in  trains  of  two  and  at  a slow  speed,  the  load 
can  be  picked  up  without  any  slippage  of  the  rope  through  the  grips;  while 
if  trains  of  from  12  to  25  cars  are  used,  with  the  rope  traveling  3 to  3*  miles 
per  hour,  it  is  impossible  to  pick  up  the  load  without  having  the  rope  slip 


through  the  grip,  thus  heating  the  rope  and  cutting  it.  The  slow-speed, 
single-car  or  small-train,  system  requires  more  cars,  but  this  is  counterbal- 
anced by  the  life  of  the  cars  and  rope.  Those  that  have  tried  both  systems 
prefer  the  slow-speed  small  trip  to  the  high-speed  large  trip. 

It  has  been  found  in  general  practice  that  the  maximum  pulling  power 
of  a mule  as  well  as  a locomotive  is,  approximately,  one-fifth  its  weight,  or, 
in  other  words,  a locomotive  will  pull  as  much  as  the  same  weight  of  mules 
will  pull,  and  at  a speed  about  three  times  as  great.  ...... 

Cost  of  Haulage.— So  much  depends  on  local  considerations  that  it  is 
difficult  to  give  costs  of  haulage  that  will  be  of  service.  Mule  haulage 
has  been  given  as  costing,  under  different  conditions,  5.74  cents  and  7.92 
cents  per  ton-mile,  and  in  other  locations  2.35  cents,  2.95  cents,  and  7.15  cents 
per  ton  of  coal  hauled.  „ . ... 

The  Berwind-White  Coal  Mining  Co.,  at  Windber,  Pa.,  uses 30  electric  loco- 
motives at  various  mines,  which  average,  approximately,  400  tons  per  day  ol 
9 hours,  per  locomotive,  over  an  average  haul  of  2 miles  for  the  round  trip. 
The  approximate  cost  for  operating  one  of  these  locomotives,  including  the 
wages  of  motorman,  trip  rider,  and  proportion  of  power-house  expense,  is 
about  $6.00  ner  day,  or  cents  per  ton  of  coal  haul  per  mile.  If  the  total 
load,  including  weight  of  cars,  is  considered,  it  figures  f of  1 cent  per  ton  per 
mile.  These  figures  do  not,  however,  include  grades,  which  is  an  important 
factor  in  equating  costs  per  ton  per  mile.  In  these  mines  there  are  no  mules 


410 


HOISTING  AND  HAULAGE. 


whatever,  the  locomotives  distributing  the  empty  cars  to  room  partings,  for 
the  men  to  push  to  the  face.  If  the  haul  is  done  between  side  tracks  and 
under  similar  grade  conditions,  the  same  locomotives  could  easily  handle 
1,000  to  1,200  cars  per  day.  . , , 

Mr.  F.  J.  Platt,  of  Scranton,  Pa.,  gives  the  following  comparative  costs  of 
electric  and  mule  haulage  per  ton  of  coal  hauled  and  under  approximately 
the  same  conditions  in  the  same  mine: 


Name  of  Mine. 

Mule  Haulage. 
Cents. 

Electric  Haulage. 
„ Cents. 

Green  Ridge  Colliery 

New  York  & Scranton  Coal  Co 

New  York  & Scranton  Coal  Co 

Mt.  Pleasant  Colliery 

Hillside  Coal  & Iron  Co 

Hillside  Coal  & Iron  Co 

7.15 

6.58 

2.35 

2.95 

10.77 

9.10 

2.76 

2.62 

1.07 

1.27 

4.56 

4.65 

The  following  costs  of  electric  haulage,  per  ton  of  material  hauled,  are 
given  in  the  catalogue  of  the  General  Electric  Co.: 

Name  of  Mine. 

Mule  Haulage. 
Cents. 

Electric  Haulage. 
Cents. 

Wythe  Lead  & Zinc  Co 

Blossburg  Coal  Co. 

Cleveland-Cliffs  Iron  Co.  (’94,  ’95,  ’96) 

10 

2.56 

7.9 

3.9,  4.5,  4.8 

At  Carbondale,  Pa.,  compressed-air  locomotives  have  hauled  coal  for 
1 5 cents  per  ton-mile,  at  Mill  Creek,  Pa.,  for  3.77  cents  per  ton-mile,  and 
at  Glen  Lyon,  Pa.,  for  1.89  to  1.93  cents  per  ton-mile. 


THIRD-RAIL  MINE  LOCOMOTIVES. 

By  W.  L.  Affelder* 

Traction  locomotives  have  overcome  practically  every  obstacle  that  has 
appeared  in  their  path  except  that  of  grade.  No  conservative  manufacturer 
will  recommend  a traction  locomotive  for  a haulage  in  which  the  grade 
against  the  loaded  trips  exceeds  5 per  cent.,  and  the  more  conservative 
Diace  4 ner  cent,  as- the  practical  limit.  A traction  locomotive  will  work 
successfully  on  considerably  steeper  grades  when  the  grades  are  short  and 
all  of  a large  trip  will  not  be  on  the  grade  at  the  same  time,  but  where  a 
grade  of  over  4 per  cent,  is  continuous  over  a considerable  distance,  some 
other  svstem  of  mechanical  haulage  should  be  adopted.  This  fact  led 
several  companies  into  experimenting  on  electric  haulage  m which  tractive 
force  due  to  the  weight  of  the  locomotive  would  not  be  a factor,  and  in 
which  friction  and  gravity  alone  would  have  to  be  overcome. 

In  1899,  the  Morgan  Electric  Machine  Co.  placed  their  first  third- 
and-traction-rail  locomotive,  or  so-called  ‘‘sprocket  locomoUve,  in  the  Star 
City  Ind.,  mine  of  the  Harder  & Hafer  Co.,  of  Chicago.  This  system,  as 
developed,  combines  the  flexibility  of  the  trolley-traction  system  and  the 
advantages  of  the  wire-rope  systems  in  surmounting  grades  Ihe  ihndiaA 
is  generally  placed  5 inches  to  the  right  of  the  center  of  the  track.  There 


are  three  sizes  of  third  rail— standard,  heavy,  and  special,  and  the  compo- 
nent  parts  of  < 

spike^to^he*  tie's,  which  are  first  trimmed,  if  necessary,  to  receive  it.  On 
this  stringer  are  spiked,  at  intervals  of  about  18  inches,  pme  blocks  E of 


nent  parts  of  each  are  made  in  16-foot  lengths.  The  standard  size  will 
be  described.  A 6*"xH"  white:pine  bottom  _stnnger^  r securely 


*See 


‘Mines  and  Minerals,”  March,  1904. 


THIRD-RAIL  MINE  LOCOMOTIVES. 


410a 


sufficient  thickness  to  bring  the  height  of  the  completed  fluid  rail  4 inches 
above  the  height  of  the  steel  rails.  Two  tongitudinal  pme  strips  D,  each 
in.  X 1£  in.,  are  spiked  to  the  blocks,  leaving  a H-m.  slot  between  them. 
They  are  trimmed  on  top  in  such  a way  as  to  allow  the  iron  track  C , which 
is  4 in.  wide  and  1-in.  thick,  to  be  partially  countersunk.  This  track  con- 
sists of  a flat  bar  of  iron  with  lf-in.  square  holes  punched  through  it  at 
intervals  of  the  same  distance.  It  is  made  continuous  by  means  of  perforated 
fish  plates  J that  are  securely  bolted  to  the  ends  of  the  two  bars  at _ a joint. 
Two  pine  strips  DD,  which  are  similar  to  strips  I)  except  that  they  are 
trimmed  on  the  lower  side  to  cover  the  iron  rail,  are  laid  on  the  strips  I) 
and  fastened  to  them  with  4-in.  spikes.  By  means  of  an  insulated  c0PPer 
cable,  which  is  connected  with  the  iron  bar,  the  positive  electric  current  is 


introduced  into  the  third  rail.  The  wooden  portion  of  the  rail  acts  both  as 
a carrier  of  the  iron  bar  or  rack  and  as  a medium  for  insulating  it.  The 
negative  current  is  carried  by  the  bonded  steel  rails. 

The  locomotives  are  made  in  two  standard  sizes:  one  having  an  oU-id.r. 
motor  and  the  other  two  motors  of  the  same  kind. 

On  each  of  the  two  axles  B are  two  track  wheels  H and  one  steel  sprocket 
A with  its  accompanying  gear.  The  track  wheels  are  tight  on  the  axles,  but 
the  sprocket  and  gear  are  loose,  the  sprocket  being  insulated  both  from  the 
axle  and  from  the  gear  by  means  of  maple  blocks,  shown  m solid  black  m the 
figure.  The  teeth  of  the  two  sprocket  wheels,  which  are  geared  to  run  in 
unison,  run  in  the  slot  between  the  two  wooden  strips  D D and  D of  the 


410b 


HOISTING  AND  HAULAGE. 


third  rail  and  engage  the  iron  rail  C.  In  coming  in  contact  with  the  charged 
iron  rail,  they  take  up  the  current,  and  through  the  agency  of  copper  con- 
tact springs  that  rub  against  them,  impart  the  current  to  the  motor  or 
motors.  In  revolving,  the  motor  drives  the  sprockets,  and  as  the  construc- 
tion of  the  third  rail  is  such  as  to  make  it  absolutely  rigid,  the  movement  of 
the  sprockets  in  the  perforated  iron  track  produces  motion  of  the  locomo- 
tive. As  all  transmission  of  power  is  through  the  cut-steel  gear-wheels,  loss 
of  power  is  entirely  eliminated. 

The  following  advantages  are  claimed  for  this  system:  The  full  power  of 
the  third-rail  locomotive — weighing  only  6.000  lb.— is  available  at  all  times 
regardless  of  the  grades,  within  limits,  or  slippery  character  of  the  track  sur- 
face. The  third  rail  can  be  extended  easily  and  cheaply  by  the  track  layers 
as  the  regular  track  is  extended.  There  is  little  liability  of  explosions  being 
caused  by  the  electric  current,  as  the  conductor  is  close  to  the  floor;  and 
from  this*  same  line  power  can  be  taken  off  at  any  point  to  light  the  mine 
and  to  run  machinery.  No  sand,  trolley  pole,  or  trolley  wire  are  required: 
and  men  and  animals  are  safe,  as  it  is  practically  impossible  for  them  to 
accidentally  come  in  contact  with  the  electric  current.  Also,  heavy  fells  of 
roof  will  not  injure  the  third  rail.  Moreover,  in  this  system,  only  a com- 
paratively small  weight  has  to  be  moved,  thus  saving  in  power  and  wear. 

A modification  of  the  above-described  system  is  manufactured  by  the 
Morgan  Electric  Machine  Co.,  consisting  of  a combination  of  a complete 
trolley  traction  locomotive  with  the  third-rail  feature  for  use  on  grades. 

Gathering  locomotives  are  used  to  take  the  cars  from  the  rooms.  They  are 
similar  in  their  general  construction  to  the  ordinary  traction  locomotive  bnt 
are  shorter  and  lower.  In  traveling  along  the  entries  the  locomotive  obtains 
its  power  by  means  of  a regular  trolley  attachment,  but  when  leaving  an 
entrv  to  go  into  a room  the  trolley  pole  is  fastened  down  and  a flexible 
insulated  cable  is  hooked  npon  the  trolley  wire  and  upon  the  track.  The 
current  returns  through  the  bonded  rails  in  rooms  where  steel  rails  are  used, 
and  when  wooden  rails  are  used  in  the  rooms  a double  cable  like  that  on  a 
mining  machine  is  used,  one  cable  being  attached  to  the  trolley  wire  upon 
the  entrv  and  the  other  to  the  ground  wire  or  entry  rail.  The  reel  upon 
which  the  cable  winds  acts  automatically  to  keep  the  cable  taut  in  winding 
and  unwinding.  It  is  operated  by  chains  and  sprocket  wheels  or  by  friction 
plates.  Several  makes  of  gathering  locomotives  are  now  being  operated 
successfully,  both  in  anthracite  and  bituminous  mines. 


MINE  ROADS  AND  TRACKS. 

Underground  or  mine-ear  tracks  should  be  solidly  laid  on  good  sills,  rest- 
ing on  the  solid  floor  of  the  mine.  They  should  be  well  ballasted,  and 
should  have  good  clean  gutters  on  the  lower  side  of  the  entry,  so  that  the 
rails  mav  be  protected  as  much  as  possible  from  the  action  .of  the  mine 
water.  Much  of  the  following  data,  on  mine  roads  is  based  on  an  article  on 
Mine  Roads.’’  by  Mr.  H.  L.  Auchnmty.  “Mines  and  Minerals."  March. 
1900. 

" Grade.— The  trades  depend  entirely  on  oirotimstanees.  V.::.  when  possible, 
the  grade  should  be  in  favor  of  the  load,  and  should  be  at  least  5 in.  in  100  ft. 
to  insure  flow  in  the  gutters  alongside  the  track.  On  main  roads,  where 
wagons  having  a capaeitv  of  15  to  2.5  tons  are  hauled  by  animal  power,  the 
grades  should  not  exceed  14  to  24  in  flavor  of  the  loaded  wagon.  Such  a rate 
of  grade  provides  for  an  easy  return  haul  of  the  empty  trip  without  wearing 
out  the  stock,  and  likewise  insures  good  drainage.  With  grades  under  14, 
unless  the  ditches  are  kept  perfectly  clean,  the  drainage  is  apt  to  be  sluggish, 
and  then,  in  low  places,  we  are  sure  to  find  a wet  and  muddy  track,  which 
is  a great  source  of  waste  energy.  . 

Where  banting  is  done  by  locomotives,  whether  by  compressed  air  or 
steam,  the  adverse  grades  should  not  be  over  1.54  to  2.54  if  it  can  possibly  be 
avoided.  When  gradients  are  heavy,  too  great  a percentage  of  the  tractive 
power  of  the  locomotive  is  consumed  in  drawing  itself  up  the  grade. 

Ties  should  be  spaced  about  2 ft.  apart,  center  to  center,  making  15  to  a 
30'  rail.  The  rail  should  be  well  spiked  to  the  ties  with  four  spikes  to  each 
tie.  the  joint  between  two  rails  on  one  side  of  the  track  being  located  about 
midway  between  two  joints  on  the  opposite  rail.  Care  should  be  taken  in 
locating  the  spikes  that  they  are  not  all  in  the  center  of  the  tie.  thereby 


MINE  ROADS  AND  TRACKS. 


411 


causing  a tendency  to  split  the  same.  It  is  best  to  place  them  each  side  of 
the  center  with  two  spikes  between  the  rails,  on  one  side,  and  the  two  spikes 
on  the  outside  of  the  rail  on  the  other  side  of  the  center  of  the  tie.  With  tne 

spikes  so  located,  there  is  no  tendency  totototo pp^oVtlfe  tif  Tte” 
outside  and  inside  spike  are  on  the  same  side  of  the  center  oi  tne  lie.  lies 
having  a 5 in.  face  and  4 in.  deep  hy  5£  ft.  in  length  should  be 
ordinary  sizes  of  rail,  i.  e.,  16  lb.  to  20  lb.,  and,  m general,  the  thickness 
should  be  sufficiently  great  that  the  spike  does  not  pass  e^re^^|^?racks 
tie  as  then  its  holding  power  is  greatly  diminished.  On  haulage  tracks 
where  35-lb.  to  40-lb.  rail  is  used,  the  ties  should  be  at  least  5 in.  deep 
have  a face  of  6 in.,  the  ties  ordinarily  used  for  lighter  sizes  of  rails  being 
entirely  too  thin  for  rails  of  this  weight,  as  a larger  spike  than  the  ordinary 
3 in.  X I in.  is  required  to  securely  hold  the  vails  to  place.  The  ends  of  the 
ties  should  be  lined  up  along  one  side  of  the  track,  so  that  they  are  all  the 
same  (Stancl  from  the  rail  and,  with  each  tie  placed  at  right  angles  to 
the  rail  as  it  should  be,  we  have  a well-spaced,  neat-looking  track,  which, 
when  we!l  tamped  with  the  ballast,  is  perfectly  solid.  On  curves,  the  ties 
should  be  laid  so  as  to  form  radii  of  the  curves  of  the  track.  , 

Rails.— The  weight  of  rail  to  be  chosen  in  any  individual  case  depends 
entirely  on  the  weight  of  wagons  used,  and  the  motive  power.  For  wagons 
whose ^Lpacity  is  alout  1.5  tons,  the  weight  of  rail,  when  the  motxve power  is 
live  stock  should  not  be  less  than  16  lb.  per  yd.,  while  for  wagons  having  a 
capacity  of  2 tons  or  over,  a 20-lb.  rail  should  be  used.  There  is  no  economy 
inPusing  a very  light  rail,  as  the  base  is  gradually  eaten  away  by  the  mine 
water  when  it  comes  in  contact  with  the  metal,  and  m the  case  of  a heav} 
section  of  rail  it  will  be  much  longer  before  the  rail  becomes  weakened. 

On  main  roads,  where  haulage  machinery  of  one  kind  or  another  is  used, 
the  weight  of  rail  for  2-ton  wagons  should  be  from  25  lb.  to  35  lb.  per  yd., 
and  on  steep  slopes  as  high  as  40  lb.  per  yd.  . ~ 

In  the  case  of  locomotive  haulage,  authorities  claim  that  the  weighty 
should  be  regulated  by  allowing  1 ton  for  each  driver  for  each  10  lb.  weight 
of  rail  per  yd . 

Gaupe  —The  gauge  of  the  track  in  coal  mines  should  not  be  less  than  30  in. 
nor  more  than  48  in.  A mean  between  these  two,  or  a gauge 
42  in.  is  desirable,  because  it  combines,  to  a certain  extent,  advantages 
claimed  for  the  extremes.  The  advocates  of  broad  gauges  believe  that  the 
greater  stability  of  the  track  and  the  consequent  reduction  ^ ^ulage  expen- 
ses, the  increased  capacity  of  the  broad-gauged  mine  cars»  the  reduction  m 
the  outlay  for  rolling  stock,  and  for  repairs  to  the  same,  more  than  equal 
the  disadvantages  of  broad  as  compared  to  the  narrow  gauges. 

Advocates  of  the  narrow  gauges  think  that  the  ease  of  hauling  around 
sharp  curves,  the  reduction  in  cost  of  construction,  and  the  use  of  mine  cars 
with  inside  wheels,  are  advantages  greater  than  those  advanced  bythe 
advocates  of  the  broad  gauges.  An  allowance  about  im  should  alwaysbe 
made  between  the  wheel  gauge  and  the  track  gauge.  By  so  < *°iug,  tne : resist 
ance  to  hauling  is  greatly  overcome,  and  there  is  no  binding  of  the  wagons 
on  the  track,  hence  a less  likelihood  of  having  derailed  wagons.  With  an 
average  running  wagon,  there  is  a resistance  of  15  to  20  lb.  per  ton  tractive 
force  on  a level  track,  which  would  be  equal  to  the  resistance  occasioned  by 
a gmde  of  .75^  to  H,  and  with  wagons  that  bind  on  the  track,  this  resistance 
is  greatly  increased.  . f 

Curves  should  be  of  as  large  a radius  as  possible,  and  never  if  possible,  of 
less  radius  than  25  ft.  The  resistance  of  curves  is  very  considerable.  - The 
less  the  radius  of  the  curve,  and  the  greater  the  length  of  thee  urvedtrack 
occupied  bythe  trip,  or  train,  the  greater  the  resistance.  The  length  of 
wheel  bases  of  the  cars,  the  condition  of  rolling  stock  and  of  the  track  and 
the  rate  of  speed,  all  influence  the  resistance,  and  there  is  no  formula 
that  will  apply  to  all  cases.  In  practice  on  surface  railroads,  engineers 
compensate  for  curves  on  grades  at  the  rate  of  ijh*  ft.  in  each  hundred  feet 
for  each  degree  of  curvature,  the  grade  being  stated  in  feet  per  hundred. 
In  mine  work,  this  compensation  is  not  made,  as  the  gam  will  not  pay  for 
the  labor  that  must  necessarily  be  employed  to  do  work  m a thoroughly 
scientific  manner.  , 

Sharper  curves  can  be  used  on  narrow-gauge  roads  than  on  broad-gauge 
roads,  because  the  difference  in  length  of  the  inner  and  ^terrailsoncurves 
on  the  same  degree  is  not  quite  so  great,  and  also  because  the  wheel  bases 
of  cars  are  less.  The  track  should  be  spread  about  * in.  on  easy  curves,  and 


412 


HOISTIXG  AND  HAULAGE. 


on  very  short  curves  about  1 in.,  or  as  much  as  the  tread  of  the  wheels  will 
permit’.  A good  rule  is  to  widen  the  track  ^ in.  for  each  2£°  of  curvature. 
Short  and  irregular  curves  are  to  be  avoided  whenever  possible,  as  they 
increase  the  load  and  are  destructive  to  rails  and  rolling  stock.  When  a sharp 
curve  is  necessary,  the  rail  should  be  bent  to  the  right  curvature  by  a 
portable  rail  bender,  or  by  a jack  and  clamps. 

To  Bend  Rails  to  Proper  Arc  for  Any  Radius.— Rails  are  usually  30  ft.  long,  and 
the  most  convenient  chord  to  use  in  bending  mine  rails  is  10  ft. 

Then,  having  the  radius  and  chord,  we  find  the  rise  of  middle  ordinate  by 
squaring  the  radius,  and  from  it  take  the  square  of  £ the  chord.  Extract  the 
square  root  of  the  remainder  and  subtract  it  from  the  radius;  the  result  will 
be  the  rise  of  the  middle  ordinate.  Thus,  having  a radius  of  30  ft.  and  a 
chord  of  10  ft.,  the  middle  ordinate  will  be 

30  — y'&E  — 5-,  or  0.42  ft. 

Rail  Elevation.— In  elevating  rails  on  curves,  consider  whether  the  hauling 
is  to  be  done  bv  a rope,  or  by  a locomotive,  or  electric  motor.  For  either  of 
the  latter,  elevate  the  rail  on  the  outside  of  the  curve;  but  for  the  first, 
elevate  the  inner  rail,  since  as  the  power  is  applied  by  a long  flexible  rope, 
there  is  alwavs  a tendency  for  both  rope  and  wagons  to  take  the  long  chord 
of  the  curve  as  soon  as  the  point  of  curve  is  reached.  On  slope  haulages, 
operated  bv  a single  rope,  when  the  weight  of  the  wagons  traveling  on  the 
grade  of  the  slope  is  sufficient  to  draw  the  rope  off  the  hoisting  drum,  the 
rails  on  curves  should  be  elevated  on  the  outside,  the  effect  then  being 
similar  to  that  of  a locomotive,  i.  e..  the  centrifugal  force  tends  to  throw  the 
wagon  to  the  outside  of  the  track.  In  such  cases,  the  elevation  should  be 
moderate  so  as  not  to  interfere  with  the  trip  when  drawn  out  again  by  the 
rope—the  opposite  effect  being  then  experienced.  On  an  18°  curve  (319  ft. 
radius  1.  an  elevation  of  2 in.  or  3 in.  in  the  outer  rail,  where  the  haulage  was 
by  slope  rope,  has  never  given  any  trouble  in  operating.  In  general,  the 
elevation  of  rail  necessary  for  different  degrees  of  curvature  for  a 42"  track 
gauge  should  be  made  in  accordance  with  the  following  table: 

Table  of  Elevations. 


For  outer  rail  of  curves  for  a speed  of  10  to  15  miles  per  hour  and  a gauge 
of  track  of  42  in.  for  locomotives;  or  for  slope  haulages  where  cars  run  down 
grade  by  gravity. 


Degree 

of 

Curve. 

Radius 

of 

Curve  (Ft.). 

Elevation 
of  Outer 
Rail  (In.). 

Degree 

of 

Curve. 

Radius 

of 

Curve  (Ft.). 

Elevation 
of  Outer 
Rail  (In.). 

1 

5,729.6 

i 

I 

10.0 

573.7 

H 

2 

2.864.9 

12.0 

478.3 

3 

1,910.1 

5 

T6 

TS 

15.0 

383.1 

if 

4 

1,432.7 

18.0 

319.6 

in 

5 

1.146.3 

T6 

20.0 

287.9 

6 

955.4 

H 

57.3 

100.0 

7 

819.0 

a 

95.5 

60.0 

4£ 

8 

9 

716.8 

637.3 

_ 

e 

l 

114.6 

50.0 

4£ 

I 

No  elevation  should  be  over  4£  in.,  which  would  be  equivalent  to  an 
elevation  of  6 in.  for  standard  track  gauge  of  4 ft.  9 in.,  the  latter  being  con- 
sidered as  the  maximum  for  standard  gauge.  A ^ 

Rollers.— The  rollers  on  level  tracks  should  not  be  more  than  about  20  ft. 
apart  to  properly  carry  the  rope,  and  on  gravity  slopes  where  the  lower  end 
of  the  slope  gradually  flattens  off.  the  distance  between  rollers  should  not 
be  more  than  12  to  15* ft.,  as  this  spacing  allows  the  trip  of  wagons  to  run 
much  farther,  by  keeping  the  rope  well  off  the  ties,  than  if  they  are  farther 
apart,  thereby  not  supporting  the  rope,  and  causing  a great  amount  of 
friction  between  the  rope  and  the  ties.  With  tracks  in  fair  shape  and  rollers 
12  to  15  ft.  apart,  the  resistance,  due  to  the  rope  in  running  empty  wagons 
down  grades  varying  from  3.8*  to  6.2*,  varied  from  6*  to  15*  of  the  weight  of 
ropes  by  actual  trial. 


MINE  ROADS  AND  TRACKS. 


413 


Switches.— The  switch,  or  latch , most  commonly  used  in  mines  is  shown 
in  Fig.  7.  When  the  branch  or  siding  is  in  constant  use,  an  ordmar\  railway 
lrog  is  substituted  for  the  bar  b.  The  latches  a,  a : are  wedge-shapeS .bars  of 
iron  (made  as  high  as  the  rail)  withan^  “nne^ldtoletoW^/a  rod 


Fig.  7. 


attached  to  a lever  so  that  they  may 
both  be  moved  at  once  from  the  side  of 
the  track,  or  by  a person  situated  some 
distance  away.  This  switch  is  made  self- 
closing or  automatic  whenever  it  is 
necessary  to  run  all  the  cars  off  at  the 
branch  (the  switch  then  being  used 
only  to  admit  cars  to  the  main  track) 
by  attaching  the  latches  through  a bar 
or  lever  to  a metallic  spring,  a stick  of 
some  elastic  wood,  or  a counter  weight, 
to  pull  them  back  into  a certain  position 
whenever  they  have  been  pushed  to  one 
side  or  the  other  by  the  passage  of  a car 

-I  ^ ^ n -t-i-tVl i oofi rtn  c nf 


on  the  main  track.  Figs.  10, 11, 12,  and  13  show  some  of  the  applications  of 

these  spring  latches  or  automatic  switches.  , 

A modification  of  this  switch  is  shown  m Fig.  8,  which  represents  a form 
of  double  switch.  These  latches  are  set  by  the  drivers,  who  kick  them  over 
and  drop  a small  square  of  plate  iron  between  them  to  hold  them  m place 
This  switch  costs  more  than  the  other  style  and  is  better  adapted  to  outside 

r0aThe^ordinary  movable  rail  switch  in  common  use  on  all  surface  railways 
is  sometimes  used  in  mine  roads.  It  is  commonly  used  m slopes  arranged  as  • 
shown  by  Fig.  12,  to  replace  latches  set  by  the 
car,  and  is  also  largely  used  in  outside  roads. 

For  crossings,  ordinary  railway  frogs  and 
grade  crossings  are  sometimes  used,  as  is  also 
a small  turntable,  which  then  answers  two 
purposes.  More  frequently  the  plan  shown 
in  Fig.  9,  in  which  four  movable  bars  are 
thrown  across  the  main  track  whenever  the 
other  road  is  to  be  used,  is  adopted. 

The  subordinate  road  is  built  from  li  to  2 
in.  higher  than  the  main  road,  to  allow  the 

bars  to  clear  the  main-track  rails.  . . , . 

Turnouts.— On  gangways  or  headings  used  as  mam  haulage  roads,  turnouts 
should  be  constructed  at  convenient  intervals  to  allow  the  loaded  and 
emptv  trips  to  pass.  These  turnouts  should  be  long  enough  to  accommodate 
from  5 or  6 up  to  15  or  20  cars.  The  switches  at  each  end  may  be  made  seli- 
acting  so  that  the  empty  trip,  coming  in,  is  thrown  on  the  turnout,  and  in 
running  out  on  the  main  track  at  the  otner  end,  the  loaded  cars  open  the 
switch,  which  immediately  closes. 

As  there  is  constant  trouble  with  self-setting  switches,  either  from  small 

fragments  of  coal  or  slate  clogging  them 
up,  or  from  insufficient  power  of  the  spring 
to  move  them,  they  are  viewed  with  dis- 
favor by  many  mine  managers,  who  do 
not  care  to  use  them  under  any  conditions. 

Slope  Bottoms.— At  the  foot  of  a slope, 
or  at  the  landing  on  any  lift,  the  gang- 
way is  widened  out  to  accommodate  at 
least  two  tracks— one  for  the  empty  and 
one  for  the  loaded  cars.  The  empty  track 
should  be  on  the  upper  side  of  the  gang- 
way, or  that  side  nearer  the  floor  of  the 
seam,  and  the  loaded  track  on  that  side 
of  the  gangway  nearer  the  roof  of  the  seam. 

An  arrangement  of  tracks  often  used 
is  shown  in  Fig.  10.  At  a distance  of  40 


IS  SIlOWll  111  -Tig.  -L V.  Al/  Cl  uioiauuv 

or  50  ft.  above  the  gangway,  the  slope  is  widened  out  to  accommodate  the 
branch  leading  into  the  gangway  loaded  track.  This  branch  descends 
with  a gradually  lessening  inclination  until  nearly  at  the  level  of  the  gang- 
way it  turns  into  the  main  loaded  track.  A short  distance  abov e the  gangway , 


414 


HOISTING  AND  HAULAGE. 


a bridge  or  door  is  placed,  which,  when  closed,  forms  a latch  by  which  the 
empty  cars  are  taken  off  the  slope.  The  empty  track  is  about  6 ft.  higher 
than  the  loaded  track,  and  is  carried  over  it  on  a trestle.  The  illustration  in 
Fig.  10  shows  the  plan  as  arranged  for  a single  slope,  or  one  side  only  of  a 

slope  taking  the  coal  from  both  directions. 
When  coal  is  being  raised  from  this  lift, 
the  bridge  is  closed;  the  empty  car  comes 
down  and  is  run  off  over  the  bridge;  the 
car  is  unhooked  from  the  rope,  and  the 
chain  and  hook  attached  to  the  rope  are 
thrown  down  to  the  branch  below  on 
which  a loaded  car  is  standing;  the  loaded 
car  is  attached,  the  signal  given,  the  car 
ascends  to  the  main  track  on  the  slope, 
opening  the  switch— or  the  switch  may  be 
set  each  time  by  the  bottom  men,  by  a lever 
at  the  bottom  of  the  branch.  This  plan  can 
only  be  economically  applied  in  thick 
seams,  as  the  height  necessary  to  allow  one 
track  to  cross  the  other  on  a trestle  cannot 
be  obtained  in  seams  of  moderate  thick- 
ness without  taking  down  a large  amount 
of  top. 

A more  simple  plan,  which  dispenses 
with  the  bridge,  is  often  used.  The  branch 
is  laid  off,  as  shown  by  Fig.  10,  but,  near 
the  point  where  it  enters  the  gangway,  a switch  opening  into  the  empty 
track  is  placed.  By  this  arrangement,  the.  tracks  cannot  be  as  well  arranged 
for  handling  the  cars  by  gravity  as  in  the  former  plan,  in  which  the  empty 
cars  when  detached  from  the  rope  run  by 
gravity  into  the  empty  siding,  and  the  loaded 
cars  descend  by  gravity  around  the  curve  to 
the  foot  of  the  branch,  where  they  lie  ready  to 
be  attached  to  the  rope. 

When  the  pitch  of  the  slope  is  so  steep  that 
the  coal  or  ore  falls  out  of  the  cars,  during 
hoisting  a gunboat  is  used  or  the  cars  are 
raised  on  a slope  carriage — in  either  case,  the 
arrangement  of  the  tracks  ^at  lift  landings  is 
entirely  different.  With  either  a gunboat  or 
a slope  carriage,  the  arrangement  of  tracks 
on  the  slope  is  the  same;  but,  in  the  former 
case,  a connection  between  the  slope  and 
gangway  tracks  is  often  advisable.  When  a , . , ™ 

gunboat  is  used,  the  gangway  tracks  run  direct  to  the  slope,  and  a tipple,  or 
dump,  is  placed  on  each  side  to  dump  the  mine  cars  f 
but  when  the  cars  are  raised  on  a slope  carriage,  the  gangway  tracks 
run  direct  (at  right  angles)  to  the  slope,  to  carry 
the  car  to  the  cage  or  carriage.  The  fl9or  of  the 
cage  is  horizontal,  and  has  a track  on  it  that  tits 
on  the  end  of  the  gangway  track  when  the  car- 
riage is  at  the  bottom,  and  this  track  is  arranged 
with  stops  similar  to  those  on  cages  used  in  shafts. 

Another  common  arrangement  of  tracks  at 
the  bottom  of  a slope  is  shown  in  Fig.  11.  A 
branch  is  made  by  widening  the  slope  out  near 
the  bottom,  and  this,  being  a few  feet  higher  than 
the  main  track,  is  used  to  run  off  the  empties  by 
gravity.  The  loaded  cars  run  in  by  gravity 
around  the  curve  to  the  foot  of  the  slope  in 
position  to  be  attached  to  the  rope. 

In  ascending,  the  loaded  car  forces  its  way 
Fig.  12.  through  the  switch,  or  the  switch  may  be  set  by  a 

lever  located  at  the  foot  of  the  slope.  When  the 
empty  car  descends,  it  runs  in  on  the  branch,  where  the  chain  is  unhooked 
and  thrown  over  in  front  of  the  loaded  car,  and  runs  around  the  curve  into 

ll^olSSved  that  in  this  plan  the  loaded  car  (and  consequently  the 


Fig.  11. 


the 


MINE  ROADS  AND  TRACKS. 


415 


bottom  men)  stands  on  the  track  in  line  with  the  slope,  and  is  in  danger  from 
any  objects  falling  down  the  slope,  or  from  the  breakage  of  the  rope  or  coup- 
lings; but  this  can  be  obviated  by  making  the  bottom  on  the  curve.  The 
illustration  in  Fig.  11  shows  only  one  side  of  the  slope;  the  other  side  is,  of 
course,  similar. 

All  these  plans  necessitate  the  location  of  that  part  of  the  gangway  near 
the  slope,  in  the  upper  benches  of  the  coal  or  near  the  top  rock.  The  gang- 
way is  then  curved  gently  around  toward  the  floor,  so  that,  when  it  has  been 
driven  far  enough  to  leave  a sufficiently  thick  pillar,  the  bottom  bench  is 
reached  and  the  gangway  is  then  driven  along  the  bottom  rock. 

A very  different  bottom  arrangement  is  shown  by  Fig.  12,  which  also 
represents  a plan  frequently  adopted  on  surface  planes.  The  two  slope 
tracks  are  merged  into  one  a short  distance  from  the  bottom  of  the  slope,  and 
on  the  opposite  sides  of  the  bottom  two  tracks  curve  around  into  the  gang- 
way on  opposite  sides  of  the  slope.  As  these  branches  curve  into  the  main 
gangway  tracks,  a switch  sends  off  a side  track  for  the  empty  cars.  The 
switch  on  the  slope  is  either  set  by  the  car— and  this  can  be  done  because 
the  next  loaded  goes  up  on  the  same  side  on  which  the  last  empty  descended 
—or  by  a lever  located  at  the  bottom.  . . 

It  will  at  once  be  seen  that  in  this  plan  no  opportunity  is  afforded  oi 
handling  the  cars  by  gravity.  The  curved  branches  are  made  nearly  level, 
and  the  momentum  of  the  descending  car,  if  quickly  detached,  is  often 
sufficient  to  carry  it  partly  or  wholly  around  the  curve,  even  against  a slight 


adverse  grade.  The  disadvantage  above  noted  of  having  the  bottom  in 
direct  line  with  the  slope  (where  there  is  danger  from  breakage  and  falling 
material)  also  obtains  in  this  plan. 

In  the  plan  shown  by  Fig.  13,  the  grades  may  be  so  arranged  that  the  cars 
can  be  entirely  handled  by  gravity.  The  latches  on  the  main-slope  track 
may  be  closed  automatically  by  a spring  or  weight,  the  loaded  car  running 
through  them  in  its  ascent  on  the  slope,  or  both  sets  may  be  operated  by  a 
single  lever  at  the  bottom.  The  switch  at  the  upper  end  of  the  central  track 
(loaded)  is  set  by  a hand  lever.  All  three  sets  may  be  linked  together,  so 
that  they  can  all  be  properly  set  by  a single  lever.  Reference  to  Fig.  11  will 
show  that  this  is  only  a modification  of  that  method.  It  requires  space  at 
the  bottom  for  only  three  tracks,  while  Fig.  13  requires  width  to  accom- 
modate four  tracks,  and  is  objectionable  because  it  is  more  complicated. 
The  extra  set  of  latches  at  the  top  of  the  central  track,  and  the  curvature  of 
both  main  tracks  into  this  central  one,  must  inevitably  cause  much  trouble 
and  delay  from  cars  jumping  the  track  at  this  point. 

The  plan  shown  in  Fig.  14  is  open  to  many  of  the  objections  pertaining  to 
some  of  those  already  described,  and  which  need  not  be  reiterated  here.  It 
can  only  be  employed  in  thick  seams,  or  in  seams  of  moderate  thickness 
lving  at  a slight  angle  or  dip. 

In  planning  the  arrangement  of  tracks  on  a slope,  it  is  advisable  to  place 
as  few  switches  as  possible  on  the  slope  itself,  to  keep  the  main  track 


Fig.  13. 


Fig.  14. 


416 


HOISTING  AND  HAULAGE. 


'ESEzZEBa 

LOADED*—: 


unbroken,  to  make  the  tracks  as  straight  as  possible,  to  have  nothing  stand- 
ing at  the  bottom  in  direct  line  with  the  slope  tracks,  and  to  arrange  the 
tracks  so  that  cars  are  handled  by  gravity.  . , 

The  arrangement  of  tracks  near  the  top  of  the  slope,  and  on  the  surface, 
is  often  very  similar  to  the  bottom  arrangements,  as  already  described;  but 
as  all  loaded  cars  (except  rock  and  slate  cars,  which  are  run  off  on  a separate 
switch)  are  to  be  sent  off  on  one  track,  and  all  the  empties  come  in  on  the 
same  track  to  the  head  of  the  slope,  and  as  there  is  usually  abundance  of 
room  for  tracks  and  sidings,  these  top  arrangements  are,  in  a measure,  much 
more  easily  designed.  In  some  instances,  the  two  mam-slope  tracks  run 
into  a single  track  near  the  head  of  the  slope— a plan  somewhat  similar  to 
the  bottom  arrangement  shown  by  Fig.  12— and  the  cars  are  then  brought  to 
the  surface  on  one  track,  which,  after  passing  the  knuckle,  bifurcates  into  a 
loaded  and  empty  track.  A similar  arrangement  is  frequently  adopted  at 
slopes  on  which  a carriage  or  gunboat  is  used.  When  the  two  mam-slope 
tracks  are  continued  up  over  the  knuckle  to  the  surface— the  most  common 
and  best  plan— the  arrangement  of  tracks  and  switches  may  be  planned 
entirely  with  a view  to  the  quickest  and  most  economical  method  of 
handling  the  cars.  „ , _ . 

Vertical  Curves.— The  vertical  curves  at  the  knuckle  and  bottom  of  a slope 
or  plane  should  have  a sufficiently  large  radius,  so  that  when  passing  over 
them  the  car  will  rest  on  the  rail  with  both  front  and  back  wheels.  The 
wheel  base  of  the  car  must  be  considered  in  adopting  the  radius  for  these 
curves,  for  if  the  curve  is  of  too  short  a radius,  there  is  danger  of  the  car 
jumping  the  track  every  time  it  passes  over  the  curve. 

Tracks  for  Bottom  of  Shaft.— Fig.  15  shows  the  arrangement  of  tracks  at  the 
foot  of  a shaft,  with  one  of  the  cages  at  surface.  The  grades  should  be  so 
arranged  that  from  the  inside  latches  of  the  crossings  the  empty  track 
should  have  a slight  down  grade  from 
the  shaft,  and  the  loaded  track  a slight 
down  grade  toward  the  shaft.  The  cross-  __y__ 
ings  and  the  short  straight  piece  of  road 
close  to  the  shaft  should  be  level.  “=* 

As  it  is  often  desired  to  move  empty  Fig.  15. 

cars  from  one  side  of  the  shaft  to  the 

other,  without  stopping  the  hoisting,  a narrow  branch  road  should  be  cut 
through  the  shaft  pillar,  and  used  for  this  purpose.  Where  the  pitch  of  the 
seam  prevents  this,  a road  should  be  laid  alongside  the  shaft,  room  to 
accommodate  it  being  cut  out  of  the  rock  on  the  side  most  desirable.  (See 
also  Shaft  Bottom,  page  276.)  _ _ „ , 

In  arranging  tracks  for  shaft  bottoms,  at  tops  and  bottoms  of  slopes,  on 
coal  bins,  for  mechanical-haulage  landings,  at  foot  of  slopes  or  shafts,  or  m 
the  body  of  the  mine,  it  is  customary  to  provide  double  tracks  of  sufficient 
length  to  hold  the  requisite  number  of  wagons  for  economically  operating 
the  plant  and  with  sufficient  distance  from  center  to  center  of  tracks,  and 
from  centers  of  tracks  to  sides  of  entries,  to  easily  pass  around  the  wagons 
where  it  may  be  necessary,  either  in  handling  them,  or  in  lubricating  the 
wheels.  For  wagons  with  a capacity  of  from  1£  to  2 tons,  it  generally 
requires  an  entry  to  be  about  15  to  17  ft.  wide  in  the  clear  for  ordinary  land- 
ings in  the  body ’of  the  mine,  while  at  shaft  bottoms  the  necessary  width 
may  attain  17  to  18  ft.  in  the  clear,  owing  largely  to  location  and  local 
requirements.  The  curved  crossovers  connecting  the  tracks  at  shaft  bot- 
toms should  be  designed  with  radii  of  as  great  length  as  can  be  introduced, 
thereby  giving  an  easy  running  track.  They  should  not  be  less  than  from 
20  to  50  ft.  on  center  lines  for  ordinary  gauge  of  tracks,  i.  e.,  36  to  44  in. 

On  landings  constructed  in  the  body  of  the  mine  for  the  reception  ot 
empty  and  full  wagons  handled  by  mechanical  haulage  from  shaft  or  slope, 
and  from  this  point  transported  by  animal  power  to  the  various  working 
places  in  the  mine,  a grade  of  about  1 f>  in  favor  of  the  loaded  wagons  to  be 
handled  by  the  stock  will  be  found  quite  an  assistance  in  delivering  the 
wagons  to  the  haulage.  The  frogs  and  switches  for  these  landings,  as  well 
as  those  required  at  the  shaft  or  slope,  should  be  formed  of  regular  track 
rails,  and  can  generally  be  arranged  to  be  thrown  by  a spring  or  a con- 
veniently located  hand  lever,  as  has  been  described,  instead  of  being  kicked 
to  position,  as  was  the  custom  at  one  time. 

Besides  these  usual  arrangements  of  shaft-bottom  landings,  at  many 
plants  the  natural  grades  of  the  entries  can  be  taken  advantage  of  in 
designing  convenient  and  economical  methods  for  handling  the  mine  cars. 


MINE  ROADS  AND  TRACKS. 


417 


For  instance,  where  the  coal  is  to  be  hauled  from  the  dip  workings  of  a 
mine  by  some  form  of  mechanical  haulage,  and  a summit  can  conveniently 
be  arranged  for  in  the  track  on  the  same  side  of  the  hoisting  shaft,  at  the 
proper  distance  therefrom,  to  accommodate  the  requisite  number  of  loaded 
wagons  to  be  hauled,  thus  allowing  them  to  run  by  gravity  over,  say,  a 
1 <f0  grade  to  the  shaft,  several  varieties  of  empty-track  arrangements  can  be 
made.  The  most  simple  form  is  to  have  the  empty  wagon  descend  a short 
grade  of  from  ApJo  to  5$  when  pushed  from  the  cage  by  the  succeeding  full 
one.  The  momentum  thus  secured  is  quite  sufficient  to  carry  the  car  up  an 
opposing  grade  of  about  1.5 Jo.  It  again  descends  on  the  same  track,  and 
passing  through  an  automatic  switch,  continues  to  the  empty-car  siding. 
From  this  latter  point  it  is  handled  by  the  regular  haulage  machinery,  and 
in  its  route  passes  around  the  shaft  through  an  entry  especially  prepared  for 
this  arrangement.  A shaft  bottom  so  constructed  is  very  economical  to 
operate,  requiring  but  few  men  to  handle  the  wagons. 

Occasionally,  it  becomes  more  expedient  to  have  a separate  short  haulage 
to  draw 'the  empty  wagons  to  the  main  haulage  when  it  cannot  be  easily 
arranged  to  construct  a complete  gravity  landing.  Several  other  modifica- 
tions of  such  a general  design  can  be  made.  All  the  different  devices, 
however,  depend  largely  on  the  local  requirements  of  the  particular  mine 
under  consideration.  , . . „ ^ , , , . 

When  endless-rope  haulage  is  employed,  it  is  generally  found  to  be  most 
convenient  to  have  the  landings  for  full  and  empty  wagons,  m the  body  of 
the  mine,  reached  by  switches  off  of  the  main-haulage  track,  the  cars 
coming  on  and  leaving  the  main  track  at  slight  knuckles  introduced  in  the 
track,  in  order  to  allow  a place  for  the  passing  of  the  rope,  which  then 
moves  along  through  a short  cut  or  channel  through  the  switch  rails. 
The  flanges  of  the  wagons  pass  over  the  rope  in  this  manner  without  any 
injury  to  it.  • 

Surface  Tracks  for  Slopes  and  Shafts. — The  arrangement  of  the  tracks  on  the 
surface  naturally  differs  at  every  mine,  owing  to  the  different  existing 
conditions.  All  surface  roads  should  be  so  arranged  that  the  loaded  cars  can 
be  moved  with  the  least  possible  power,  always  looking  out  for  the  return  of 
the  empties  with  as  little  expenditure  of  power  as  possible.  To  secure  the 
running  of  the  loaded  cars  from  the  mouth  of  the  shaft  or  slope  by  gravity , a 
slight  grade  is  necessary,  the  amount  of  which  depends  on  the  friction  of 
the  cars,  which  varies  greatly.  Care  should  be  take  that  an  excessive  grade 
is  not  constructed,  or  there  will  be  trouble  in  returning  the  empties  from  the 
dump  to  the  head  of  the  shaft  or  slope.  . , 

The  tracks  connecting  the  top  of  the  shaft  and  the  tipple  may  be  very 
short,  or  of  considerable  length,  depending  on  the  conditions  at  each  mine. 
Usually  from  20  to  60  ft.  will  be  sufficient,  although  no  definite  rule  can  be 
given  for  this.  . , ’ x,  , _ . , 

There  are  two  general  arrangements  of  tracks  about  the  head  of  a shait: 
First,  where  the  loaded  cars  are  removed  from  the  cage  and  the  empty  cars 
placed  upon  it  from  the  same  side  of  the  shaft;  second,  where  the  loaded 
cars  are  removed  from  one  side  of  the  shaft  and  the  empty  cars  returned  to 
the  cages  from  the  opposite  side  of  the  shaft. 

In  either  case  there  are  usually  several  empty  cars  on  the  platform  ready 
to  be  put  on  the  cages  when  the  loaded  cars  have  been  removed. 

Where  the  conditions  are  such  that  the  loaded  cars  can  be  run  by  gravity 
to  the  dump,  a good  plan  is  to  have  a short  incline,  equipped  with  an  endless 
chain,  in  the  empty  track.  The  empty  cars  can  be  run  to  the  foot  of  this, 
hoisted  by  machinery  to  the  top,  and  thus  gain  height  enough  to  run  them 
back  to  the  shaft  or  slope  by  gravity. 

At  the  Philadelphia  & Reading  Coal  & Iron  Co.’s  Ellango wan  colliery, 
where  the  tipple  at  the  head  of  the  breaker  is  above  the  level  of  the  head 
of  the  shaft,  the  following  plan  is  used:  The  loaded  cars  are  taken  off 
the  east  side  of  the  cages,  and  run  by  gravity  to  the  foot  of  an  incline, 
where  the  axles  of  the  car  are  grasped  by  hooks  on  an  endless  chain 
and  the  car  pulled  up  to  the  tipple.  After  being  dumped,  the  car  is  run 
back  from  the  tipple  to  the  head  of  the  incline,  and  is  carried  to  the 
foot  of  the  empty  track  of  the  incline  by  an  endless  chain.  The  foot  of 
the  empty  track  is  several  feet  higher  than  that  of  the  loaded  track,  and  the 
cars  are  run  by  gravity  around  to  the  west  side  of  the  cages,  and  are  put  on 
from  that  side.  The  empty  cars,  as  they  run  on  the  cage,  have  momentum 
enough  to  start  the  loaded  car  off  the  cage  and  on  toward  the  foot  of  the 
incline.  There  are  a number  of  hooks  attached  to  both  the  empty  ana 


418 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


loaded  chain  on  the  incline,  and  there  are  often  several  loaded  and  several 
empty  cars  on  different  parts  of  the  plane  at  once.  This  arrangement 
permits  of  the  hoisting  of  from  700  to  800  cars  per  day  out  of  a shaft  110  yd. 
deep,  with  single-deck  cages.  # * 

Another  excellent  arrangement  for  handling  coal  on  the  surface  is  the 
invention  of  Mr.  Robert  Ramsey,  and  has  been  adopted  by  the  H.  C.  Frick 
Coke  Co.  and  a number  of  other  prominent  operators.  A description  of 
this  arrangement  as  applied  at  the  H.  C.  Frick  Coke  Co.’s  Standard  Shaft 
is  as  follows:  The  landing  of  the  shaft  is  made  slightly  higher  than  the  level 
of  the  tipple,  which  is  north  of  the  shaft.  South  of  the  shaft  is  located  a 
double  steam  ram,  one  ram  being  directly  in  line  with  the  track  on  each 
cage.  Directly  in  front  of  the  rams  is  a transfer  truck,  worked  east  and 
west  by  wire  rope.  The  loaded  car  on  the  cage  is  run  by  gravity  to  the 
tipple,  where  it  is  dumped  by  means  of  a nicely  balanced  dumping  arrange- 
ment. As  soon  as  it  is  empty  it  rights  itself  and  runs  by  gravity  alongside 
the  shaft  to  the  transfer  truck,  which  carries  it  up  a grade  to  a point  directly 
in  line  with  the  cage  that  is  at  the  landing,  and  one  of  the  steam  rams 
pushes  it  on  the  cage,  and  at  the  same  time  starts  the  loaded  car  off  toward 
the  tipple.  This  second  loaded  car  is  then  returned  by  the  same  means  to 
the  opposite  cage.  The  whole  mechanism  is  operated  by  one  man,  by  means 
of  conveniently  arranged  levers,  each  of  which  is  automatically  locked, 
except  when  the  proper  time  to  use  it  arrives.  It  is  therefore  impossible 
for  the  topman  to  work  the  wrong  lever  and  put  an  empty  car  into  the 
wrong  compartment  of  the  shaft.  Besides  the  one  man  at  the  levers,  there 
is  but  one  other  man  employed  at  the  tipple,  and  his  work  is  solely  to  look 
after  the  cars  when  dumping.  All  switches  are  worked  automatically,  and 
the  average  hoisting  at  this  shaft  is  at  the  rate  of  3 wagons  per  minute.  The 
shaft  is  about  250  ft.  deep,  and  single-deck  cages  are  used. 

The  Lehigh  & Wilkes-Barre  Coal  Co.  has  a system  in  use  at  a number  of 
collieries  that  has  also  proven  very  effective.  In  this  system  the  loaded  cars 
are  run  by  gravity  from  the  cage  to  the  dump,  and  the  empties  are  hauled 
from  the  dump  back  to  a transfer  truck  by  a system  of  endless-rope  haulage. 
The  transfer  truck  carries  the  car  to  a point  opposite  the  back  of  the 
cage.  The  empty  car  runs  by  gravity  to  the  cage,  and  its  momentum  starts 
the  loaded  car  on  the  cage  on  its  way  to  the  dump.  This  system  necessi- 
tates the  employment  of  more  topmen,  but  is  a very  good  one.  At  the  Not- 
tingham shaft,  which  is  470  ft.  from  landing  to  landing,  from  140  to  150  cars 
per  hour  are  hoisted  on  single-deck  cages. 


ORE  DRESSING  AND  THE  PREPARATION 

OF  COAL. 


CRUSHING  MACHINERY. 

The  object  of  crushing  ore  or  coal  is:  first,  to  free  the  mineral  or  other 
valuable  constituents  from  the  gangue,  slate,  pyrites  (sulphur),  or  other 
worthless  or  objectionable  constituents  so  that  they  can  be  subsequently 
separated;  or,  second,  simply  to  reduce  the  size  of  the  individual  pieces  and 
so  get  the  material  into  a more  salable  or  convenient  condition  for  use. 

Selection  of  a Crusher.— The  style  of  crusher  employed  is  influenced  by  the 
following  conditions:  (a)  The  amount  of  material  to  be  crushed  in  a given 
time,  (b)  The  size  of  the  material  as  it  goes  to  the  crusher,  (c)  The 
physical  characteristics  of  the  material  to  be  crushed;  that  is,  whether  it  is 
hard  or  soft,  tough  or  brittle,  clayey  or  sticky.  ( d ) The  object  of  the  crush- 
ing; that  is,  whether  it  is  to  free  the  mineral  constituents  or  simply  to  reduce 
the  size  of  the  individual  pieces,  (e)  The  character  of  the  product  desired; 
that  is,  whether  an  approximately  sized  product  is  desirable  and  whether 
dust  or  fine  material  is  objectionable. 

All  crushing  machinery  may  be  divided  into  the  following  classes:  Jaw 
crushers,  gyratory  crushers,  cracking  rolls,  disintegrating  rolls,  crushing 
rolls,  roller  mills,  ball  mills,  stamp  mills,  hammers,  and  miscellaneous 
forms  of  crushers. 


CRUSHING  MACHINERY. 


419 


JAW  CRUSHERS. 

With  iaw  crushers,  the  material  is  crushed  between  two  jaws,  one  or 
both  being  movable.  All  jaw  crushers  have  the  common  detect  of  imparting 
a considerable  amount  of  vibration  or  shake  to  the  framework  of  the  build- 
ins  containing  them,  owing  to  the  reciprocating 

ing  parts.  There  are  three 
styles  of  jaw  crushers  in 
common  use. 

The  Blake  crusher  is 
shown  in  Fig.  1,  a being  a 
fixed  jaw  and  b a movable 
jaw  that  is  operated  by  a 
toggle  joint  and  the  pitman 
d from  a suitable  crank- 
shaft. The  jaw  b is  hung 
or  pivoted  at  the  top.  The 
advantages  of  this  style  are 
as  follows:  The  large  pieces 
of  rock  to  be  crushed  are 
received  between  the 
upper  part  of  the  jaws, 
where  the  motion  is  least 
and  the  purchase  or  lever- 
age greatest,  so  that  they 
are  broken  with  the  small- 
est possible  expenditure  of 


Fig.  1. 


energy.  The  movement  of  the  jaws  is  greatest  at  the  discharge  opening, 
thus8 affording  a free  and  rapid  discharge  of  the  material  crushed,  and 
insuring  a large  capacity  for  the  machine.  The  principal  disadvantage  is 
that  the  great  variation  in  the  discharge  opening  results  m a considerable 
range  in  the  size  of  the  material  delivered.  , . . 

This  style  of  crusher  has  found  a wide  field  for  breaking  down  material 

Table  of  Blake  Crushers. 


Size  of  Re- 
ceiving Ca- 
pacity. 

Approximate  Prod- 
uct per  Hour, 
Cubic  Yards,  to 
2 Inches. 

Weight  of 
Heaviest 
Piece. 

■s 

•pH 

> 

> 

. O 

H 

Inches. 

Lb. 

Lb. 

3X  li 

Laboratory 

40 

100 

6 X 2 

One 

560 

1,200 

10  X 4 

Three 

1,800 

4,900 

10  X 7 

Five  

3,800 

8,000 

15  X 9 

Eight 

7,400 

15,500 

15X10 

Nine  

7,800 

16,000 

20  X 6 

Ten 

5,300 

11,200 

20  X 10 

Ten 

8,100 

18,300 

12X30 

Sixteen 

14,200 

33,000 

15X30 

Twenty 

14,200 

35,000 

Extreme  Dimensions. 


Length.  Breadth. 


Ft.  In. 


1 

10 

0 

1 

6 

6 

3 

10 

10 

10 


Height. 


Ft.  In.  Ft.  In. 


6 

1 

3 
9 
0 
5 

11 

9 

4 
4 


0 10 
2 3 


9 

5 

11 

11 

6 
11 

4 

4 


250 

250 

250 

250 

250 

250 

250 

250 

250 

250 


s-<  . 

^ <X> 

ft  0 
a> 

g © 

H 


4 

6 

8 

15 

15 

15 

20 

30 

30 


and  preparing  it  for  other  crushers,  or  for  breaking  large  quantities  of  any 
material  where  an  approximate  sizing  is  not  essential. 

The  Dodge  crusher,  Fig.  2,  has  a fixed  jaw  a and  a movable  jaw  b,  operated 
by  a cam  on  the  shaft  g.  The  movable  jaw  is  pivoted  at  the  bottom,  so  that 
the  minimum  movement  between  the  jaws  is  at  the  discharge  opening.  The 
advantage  of  this  is  that  the  least  movement  occurs  at  the  discharge  opening, 


420 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


and  hence  the  product  is  of  a fairly  uniform  size,  so  that  the  crusher  may 
be  used  as  a rough  sizing  apparatus.  The  disadvantages  are  that  the  large 
pieces  of  rock  have  to  be  crushed 
in  the  upper  part  of  the  space  ^ 
between  the  jaws,  where  the 
motion  is  greatest  and  the  pur- 
chase or  leverage  least,  thus  re- 
quiring an  excessive  amount  of 
power,  especially  when  dealing 
with  hard  material.  The  move- 
ment of  the  jaw  at  the  discharge 
opening  is  so  much  less  than 
that  above  that  there  is  danger 
of  clogging  or  blocking  the  ma- 
chine, especially  when  working 
upon  tough  or  sticky  material. 

The  capacity  of  the  Dodge  style  , , , 

of  machine  is  less  than  that  of  the  Blake.  It  is  used  largely  as  a secondary 
crusher,  or  for  crushing  comparatively  small  amounts  of  material  where  an 
approximately  sized  product  is  desired. 


Fig.  2. 


The  Dodge  Crusher. 


No. 

Size  of  Jaw 
Opening. 

Diameter  of 
Pulleys. 

Width  of  Belt 
Used. 

Horsepower 

Required. 

No.  Tons  per 
Hour, Nut  Size. 

Revolutions  per 
Minute. 

Weight  Complete. 

Inches. 

Inches. 

Inches. 

• 

1 

4 X 6 

20 

4 

2 to  4 

i to  1 

275 

1,200 

2 

7 X 9 

24 

5 

4 to  8 

1 to  3 

235 

4,300 

3 

8X12 

30 

6 

8 to  12 

2 to  5 

220 

5,600 

4 

10X16 

36 

8 

12  to  18 

5 to  8 

200 

12,000 

Roll* Jaw  Crushers.— Fig.  3 is  a sectional  view  of  a Sturtevant  roll-jaw 
crusher.  The  rolling  motion  of  the  jaw  subjects  the  material  to  a rolling 
and  squeezing  action,  instead  of  a direct  squeeze.  The  product  of  this 

crusher  is  approximately  sized  and 
there  is  no  greater  producer  of  sized 
output.  The  adjustment  of  the 
machine  for  fine  crushing  neces- 
sarily contracts  the  space  for  dis- 
charge, and  thereby  lessens  its 
capacity.  When  set  wide,  or  for 
material  from  1 to  H inches  in  size, 
the  discharge  is  very  free  and  the 
capacity  is  claimed  to  be  greater 
than  that  of  any  other  jaw  and 
toggle  machine. 

Gyratory  Crushers.— These  crush- 
ers, Fig.  4,  are  all  large  capacity,  con- 
tinuous-action crushers,  a is  a ring 
or  hopper  against  which  the  material 
is  crushed  by  a conical  head  c,  which 
Fig.  3.  fits  on  a shaft  g,  the  bottom  of  which 

is  placed  in  an  eccentric  bearing 
so  that  the  amount  of  space  between  a and  c varies  as  the  head  rotates. 
The  material  to  be  crushed  is  dumped  into  the  receiving  hopper  h,  and  the 
machine  is  thus  automatically  fed. 


ROLLS. 


421 


The  advantages  of  this  style  are  that  the  large  pieces  of  material  are 
received  at  the  top  of  the  jaws,  where  the  motion  is  least  and  the  leverage 
or  purchase  greatest,  thus  reducing  the  work  necessary  m this  heavy 
y preliminary  crushing.  The  relative  move- 

ment between  the  crushing  members  is  a 
maximum  at  the  discharge  opening,  but 
the  amount  of  this  movement  is  so  small 
that  the  product  is  approximately  sized. 
The  fact  that  the  maximum  movement  is 
at  the  point  of  discharge  assures  a free 
discharge.  There  is  practically  no  shaking 
imparted  to  the  building  by  gyratory 
crushers.  Their  capacity  is  very  great,  and 
with  a large  size,  material  may  be  dumped 
into  the  hopper  h directly  from  the  cars. 
For  small  capacity  a gyratory  crusher  is 
more  expensive  than  a jaw  crusher. 

Frequently,  where  very  great  amounts 
of  material  are  to  be  crushed,  large  gyra- 
tory crushers  are  used  as  secondary  crush- 
ers after  jaw  crushers  of  the  Blake  pattern, 
the  discharge  from  the  jaw  crushers  ran- 
ging from  6"  to  12"  cubes,  and  that  from  the 
gyratory  crushers  from  1£"  to  2£"  cubes. 
(See  table  on  page  422). 

ROLLS. 

Cracking  Rolls.— This  is  a general  name 
applied  to  rolls  having  teeth,  which  are 
usually  made  separate  and  inserted. 
These  rolls,  Fig.  5,  are  employed  for 
Fig  4 breaking  coal,  phosphate  rock,  etc.,  the 

object  being  to  break  the  material  into 
angular  pieces  with  the  smallest  possible  production  of  very  fine  material. 
The  principal  field  for  cracking  rolls  is  in  the  preparation  of  anthracite 
coal,  and  the  exact  style  or  design  of  the  roll  depends  largely  on  the 
physical  condition  of  the  coal  under  treatment.  In  most  cases,  the  rolls 
are  constructed  with  an  iron  cylinder  having  steel  teeth  inserted,  the 
size,  spacing,  and  form  of  the 
teeth  depending  on  the  size 
and  physical  condition  of 
the  material  to  be  broken. 

Cracking  rolls  vary  from  12 
to  48  in.  in  diameter  and 
from  24  to  36  in.  in  face 
width.  The  teeth  of  the 
larger  sizes  are  from  3 to  3| 
in.  high,  and  of  the  smaller 
1 in.  or  less. 

The  average  practice  in 
the  anthracite  regions  of 
Pennsylvania  is  to  give  the 
points  of  the  teeth  a speed  of 
about  1,000  ft.  per  minute, 
though  the  speed  in  different 
cases  varies  from  750  to  1,200 
ft.  per  minute.  One  of  the 
largest  anthracite  companies 
has  a standard  roll  speed  of 
97.5  R.  P.  M.  for  the  main 
rolls  and  124.5  R.  P.  M.  for 
the  pony  rolls.  The  harder 
the  coal,  the  faster  the  rolls  , 

can  be  run.  If  run  slow  and  overcrowded,  the  rolls  will  make  more  culm 
than  when  driven  at  a proper  speed.  One  advantage  of  comparatively 
fast  driven  rolls  is  that  the  higher  speed  has  a tendency  to  free  the  rolls 
by  throwing  out,  by  centrifugal  force,  any  material  lodged  between  the 


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422 


ORE  DRESSING  AND  PREPARATION  OF  COAL . 


teeth.  In  one  test 
it  was  found  that 
less  fine  coal  was 
produced  at  800  ft. 
per  minute,  but 
that  the  rolls 
blocked  at  this 
speed  and  hence 
had  to  be  driven 
1,000  ft.  per  minute. 

In  one  case  a 
pair  of  main  rolls 
24  in.  in  diameter, 
30  in.  face,  running 
at  1,000  ft.  per  min- 
ute, handled  2,500 
tons  of  coal  in  24 
hours.  A pair  of 
19"  X 24''  main 
rolls  run  at  1,000  ft. 
per  minute  handled 
300  tons  mine  run 
in  10  hours. 

A well-known 
maker  of  rolls  for 
crushing  bitumi- 
nous coal  gives  a 
speed  of  100  to  150 
li.  P.  M.,  according 
to  the  output  re- 
quired, for  rolls  24 
in.  in  diameter  and 
33  in.  long.  As  a 
rule,  cracking  rolls 
are  never  run  up  to 
their  full  capacity, 
as  is  the  case  with 
crushing  rolls. 

The  form  of  the 
teeth  varies  greatly, 
but,  as  a rule,  the 
larger  rolls  have 
straight  pointed 
teeth  of  the  spar- 
row-bill or  s o m e 
similar  form,  Fig.  6 
a.  The  old  curved, 
or  hawk-billed, 
teeth,  Fig.  6 b,  have 
now  gone  almost 
wholly  out  of  use. 

On*  small  sized 
rolls,  rectangular 
teeth  with  a height 
equal  to  one  side  of 
the  square  base  are 
frequently  em- 
ployed, and  these 
may  be  cast  in  seg- 
ments of  manga- 
nese or  chrome 
steel. 

Corrugated  rolls 

have  teeth  or  cor- 
rugations extend- 
ing their  entire 
length.  They  were 
first  introduced  by 


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423 


Fig 


Mr  E.  B.  Coxe,  at  Drifton,  PaM  but  they  have  not  come  into  general  use 
owing  to  the  fact  that,  while  they  break  some  coal  fairly  well,  in  most 
cases  it  has  been  found  that  a continuous  edge  causes  too  much  disinte- 
gration along  its  length,  while  a point  splits  the  coal  into  three  or  four 
pieces  only,  all  the  cracks  radiating  from  the  place  where  the  point  strikes, 
thus  producing  very  much  less  culm.  Another  advantage  possessed  by  the 
toothed  rolls  is  that  if  anything  hard  passes  through  the  corrugated  roll 
and  breaks  out  a piece  of  the  corrugation,  the  entire  roll 
is  ruined,  while,  in  the  case  of  the  toothed  rolls,  any  one 
of  the  teeth  may  be  replaced. 

Disintegrating  rolls  and  pulverizers  are  sometimes  used  to 
reduce  coking  coal  to  the  size  of  corn  or  rice  before  intro- 
ducing it  into  the  ovens.  One  roll  is  driven  at  double  the 
speed  of  the  other,  the  slower  roll  acting  as  a feed-roll,  and 
the  other  as  a disintegrator.  The  slower  roll  is  commonly 
driven  at  from  1,800  to  2,000  ft.  per  minute  peripheral 
speed,  and  the  faster  roll  at  from  3,600  to  4,000  ft.  per  mi- 
nute. The  teeth  are  always  fine,  rarely  being  over  f m. 
high.  In  some  cases,  the  inner  roll  is  provided  with  a 
series  of  saw  teeth  from  £ in.  to  | in.  high  and  having 
about  f in.  pitch,  the  individual  teeth  being  set  so  as  to 
form  a slight  spiral  about  the  body  of  the  roll.  The  other 
roll  is  provided  with  teeth  having  their  greatest  dimension 
in  the  direction  of  rotation,  so  that  they  tend  to  cross  the  teeth  on  the  opposite 
roll.  These  teeth  are  also  set  so  as  to  form  a slight  spiral,  and  thus  prevent 
blocking.  In  other  cases,  the  teeth  on  both  rolls  are  set  in  the  form  of 
quite  a steep  spiral.  , _ . , , 

Hammers— For  the  reduction  of  coal,  crushers  employing  hammers  have 
been  used,  Fig.  7.  The  crushing  chamber  is  usually  of  a circular  or  barrel  form, 
and  the  crushing  is  done  by  means  of  hammers  pivoted  about  a central  shaft. 
These  swing  out  by  centrifugal  force  and  strike  blows  upon  the  coal  to  be 
broken.  When  it  is  reduced  sufficiently  fine,  it  is  discharged  through  bars 
or  gratings  at  the  lower  portion  of  the  machine.  This  style  of  machinery  is 
usually  employed  in  preparing  coal  for  coke  ovens,  thus  occupying  the  same 
J field  as  the  disintegrating 

rolls.  A No.  3 pulverizer  of 
this  type  will  crush  50  to  75 
tons  per  hour  run  of  mine, 
down  to  £ in.,  or  it  will  crush 
100  tons  per  hour  of  slack. 
Such  a machine  occupies 
about  8 sq.  ft.  of  floor  space 
and  requires  25  to  30  H.  P.  to 
run  it. 

Crushing  Rolls.— The  prin- 
cipal representative  of  this 
type  of  machine  is  the  ordi- 
nary Cornish  roll  having  a 
fairly  wide  face  and  rather 
small  diameter.  The  diam- 
eter of  these  rolls  was  kept 
down  for  a great  many  years 
on  account  of  the  fact  that 
the  chilled  cast-iron  shells 
could  not  be  obtained  in 

large  sizes  and  were  expen- 

sive and  hard  to  handle. 
With  the  advent  of  the  rolled- 
steel  shells,  it  became  possible  to  employ  larger  diameters  and  higher 
speeds.  Rolls  of  the  Cornish  type  vary  from  4"  face  and  9"  diameter  to 

16"  face  and  42"  diameter.  The  distinctive  feature  of  the  Cornish  roll 

is  a comparatively  wide  face  compared  with  the  diameter,  and  a 
rather  slow  peripheral  speed.  Many  of  the  modern  Cornish  rolls  are 
provided  with  rolled-steel  shells,  especially  when  employed  for  very  fine 
crushing,  owing  to  the  fact  that  these  shells  are  of  a more  uniform 
texture,  work  more  evenly,  can  be  worn  much  thinner  before  being 
discarded,  and  can  be  trued  up  with  less  difficulty  than  is  the  case 
when  chilled  iron  is  employed.  To  guard  against  the  bending  of  the  rou 


Fig.  7. 


424 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


shaft  or  breaking  of  the  machine  in  case  any  hard  material  (such  as  a pick 
or  hammer)  gets  between  the  rolls,  one  roll  is  mounted  in  a movable 
bearing  and  kept  in  place  by  a compressed  spring  washer.  This  washer  is 
composed  of  two  plates  between  which  are  placed  one  or  more  steel  springs. 
The  plates  are  kept  together  by  several  small  bolts,  which  are  screwed 
up  so  as  to  compress  the  springs  to  a certain  degree.  Then  the  entire 
arrangement  is  employed  as  a washer  on  the  rod  that  keeps  the  rolls 
together.  Should  the  pressure  exerted  on  the  rolls  exceed  that  already 
exerted  in  the  spring,  the  plates  would  be  brought  nearer  together  and  the 
roll  allowed  to  move  back  and  pass  the  hard  substance,  but  at  any  pressure 
below  this,  the  roll  acts  as  if  placed  in  a fixed  bearing. 

Cracking,  corrugated,  and  disintegrating  rolls  are  usually  provided  with 
breaking  pieces  back  of  one  of  the  rolls,  so  that  in  case  any  extra  hard  piece 
passes  through  the  rolls,  the  breaking  piece  will  give  way,  allowing  the 
rolls  to  move  back  and  thus  prevent  the  bending  of  the  shaft  or  breaking 
of  the  machine  itself.  Compressed  spring  washers  have  never  come  into 
general  use  in  connection  with  this  style  of  machinery. 

Amount  Crushed.— The  amount  of  material  that 
can  pass  between  any  pair  of  rolls  is  proportionate 
to  the  number  of  square  feet  of  roll  surface  passing 
per  minute;  hence,  the  capacity  may  be  increased 
by  keeping  the  face  width  the  same  and  in- 
creasing the  speed,  or  the  same  capacity  may 
be  obtained  by  reducing  the  face  and  increasing 
the  speed. 

According  to  Stutz  (A.  I.  M.  E.  IX,  page  464), 
if  the  distance  between  the  contact  points  of 
the  material  with  the  rolls  be  t,  Fig.  8,  the  dis- 
tance between  the  crushing  face  of  the  rolls  w, 
the  angle  a,  as  shown  in  the  figure,  and  R the  radius  of  the  roll,  then 
22  _ t — w _ t — w 
~ 2 vers,  sin  a ~~  2(1  — cos  a)’ 

According  to  Pernolet,  the  amount  of  material  that  may  be  crushed 
by  a pair  of  rolls  in  a given  time  is  equal  to  one-fourth  or  one-fifth  of  a 
band  or  layer  whose  length  is  the  circumference  of  the  roll  multiplied 
by  the  number  of  revolutions;  whose  width  is  the  length  of  the  rolls, 
and  whose  thickness  is  equal  to  the  space  or  distance  between  the  rolls. 


1 

1 \ 

Fig.  8. 


Or,  Q = 


dnnlw 


, where  d = diameter  of  rolls;  ir  = 3.14;  n = number  of  revo- 


lutions in  the  given  time:  l = length  of  rolls;  w = space  between  rolls; 
and  £ = coefficient,  to  allow  for  the  irregular  feeding  of  the  material  and 
the  space  between  the  pieces.  . _ _ 

The  Denver  Engineering  Works  gives  the  following  formulas  for  the 
capacity  of  crushing  rolls: 

T = tons  per  hour;  R = rev.  per  min.;  S = mesh  (inches). 

For  14"  X 27"  rolls,  T = 7.725  R S. 

For  16"  X 36"  rolls,  T = 11.775  RS. 

For  12"  X 20"  rolls,  T = 4.9  R S. 

Speeds. — The  pressure  on  the  bearings  necessary  to  crush  ore  depends 
directly  on  the  face  width,  and  hence  if  the  capacity  can  be  kept  the  same 
and  the  face  width  decreased,  it  is  evident  that  there  will  be  less  pressure 
on  the  bearings  and  less  loss  in  friction.  The  difficulty  of  keeping  the 
bearings  cool  when  crushing  hard  rock  with  the  old  Cornish  rolls  has  led 
to  the  adoption  of  high-speed,  narrow-faced  rolls  for  certain  classes  of  work. 
One  objection  to  running  the  small  diameter  rolls  fast  is  that  the  larger 
pieces  of  ore  have  a tendency  to  dance  on  the  face  of  the  rolls  rather  than 
to  be  crushed,  while  the  bite  is  better  when  the  speed  is  slower. 

The  advantages  of  high-speed,  narrow-faced  rolls  are:  greater  capacity 
for  a given  bearing  pressure;  less  loss  of  power  from  friction;  less  dancing 
of  the  ore  on  the  roll  face,  owing  to  the  fact  that  the  angle  of  approach 
between  the  surfaces  of  large  rolls  is  more  acute  than  with  rolls  of  a small 
diameter.  High-speed,  large-diameter  rolls  will  handle  C9arser  material  and 
hence  make  a greater  range  of  reduction  than  small-diameter  rolls.  The 
disadvantage  of  high-speed  rolls  is  that  they  tend  to  hammer  and  pulverize 
the  ore,  so  that  with  verv  brittle  minerals  a high  speed  may  be  detrimental. 
In  general,  it  may  be  stated  that  for  crushing  to  any  definite  size  with  the 
lowest  possible  production  of  very  fine  material,  rolls  are  the  best  form  of 


ROLLS. 


425 


machinery  on  the  market.  For  fine  crushing  of  brittle  material,  quite  slow 
speeds  may  give  the  best  results.  . , . ,.  ,, 

The  accompanying  table  gives  some  facts  m regard  to  the  crushing-roll 
practice  of  several  manufacturers,  the  data  having  been  taken  from  their 
catalogues  or  other  information  furnished  by  them. 


Crushing  Rolls. 


Name. 

Size. 

Inches. 

Peripheral 
Speed  in 
Ft.  per  Min. 

Spring  Pres- 
sure in  Lb.  per 
In.  of  Face 
Width. 

Character  of 
Rolls. 

Frazer  & Chalmers... 

24X8 

36X16 

600-1,500 

4,000  for  hard 
quartz. 

Cornish. 

Frazer  & Chalmers,.. 

44X5 

56X8 

2,200-2,300 

Narrow  face, 
high  speed. 

Earle  C.  Bacon 

1,000 

Cornish. 

Sturtevant  Mill  Co. 

16X3 

27X5 

3,000 

• 

Special  cen- 
trifugal. 

E.  P.  Allis  Co 

20X12 

26X14 

30X14 

36X14 

i 

800 

Cornish. 

E.  P.  Allis  Co 

1,885 

Narrow  face, 
high  speed. 

Colorado  Ironworks 

20X12 
27X14 
36  X 16 
40X16 

600 

4,000  for  hard 
rock. 

4,800  for  very 
hard  rock. 

Cornish. 

Colorado  Iron  Works 

36X6 

42X6 

54X8 

2,100-2,800 

Narrow  face, 
high  speed. 

Denver  Engineering 
Works  Co 

20  X 12 
to 

36X16 

350-100 

3,500-4,500 

Cornish. 

Gates  Iron  Works  ... 

9X4 
26X15 
36  X 15 

470-850 

2,266-3,333 

Cornish. 

The  Gates  Iron  Works  has  furnished  the  following  formulas  relating  to 
crushing  rolls,  in  which  D = diameter  of  roll  m inches;  N ==  number  of 
R.  P.  M.;  S = maximum  size  of  ore  cube  in  inches  fed  to  the  rolls, 
S'  = maximum  size  of  cube  for  a given  diameter  of  roll. 


oqo  s 

N = fxisd-  s'  = M76XZ>- 

It  will  be  seen  from  the  first  of  these  formulas  than  N is  an  inverse 
function  of  S,  which  agrees  with  the  results  shown  in  the  previous  diagram. 
As  a rule,  it  is  best  not  to  try  to  run  rolls  up  to  the  maximum  size  that  they 

will  crush,  but  to  feed  smaller  material  to  them.  . ... 

The  Denver  Engineering  Works  Company  has  furnished  the  diagram, 
Fig.  9,  and  formulas  relating  to  rolls.  This  diagram  serves  very  well  to 
illustrate  the  fact  that  small  rolls  do  not  grip  or  crush  large  pieces  as  well 
when  running  at  comparatively  high  peripherial  speeds  as  when  running 
at  slow  speeds.  In  the  case  of  the  10"  X 16"  roll,  a difference  of  from 
1"  to  cube  size  made  a difference  of  20  R.  P.  M.  in  order  to  obtain  the 


426 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


most  effective  crushing  speed,  and  the  difference  between  £"  and  £"  cube 
sizes  made  a difference  almost  as  great.  It  will  also  be  noticed  that  the 
larger  diameters,  as,  for  instance,  the  42"  roll,  are  not  so  greatly  affected  by 
this  cause,  owing  to  the  fact  that  the  effective  or  crushing  angle  between  the 
rolls  is  much  more  acute  than  in  the  case  of  the  smaller  diameters. 


CRUSHING  MILLS. 

Radial  Roller  Mills.— In  this  type  of  mill,  the  crushing  is  performed  on  a 
ring  or  die  by  a series  of  heavy  rolls  pressing  on  it  by  gravity.  In  some 
cases,  the  rolls  travel  around  on  the  die  and  in  others  the  die  travels  in 
relation  to  the  rolls.  Fig.  10  represents  one  form  of  Chilian  mill  that  is  the 
leading  type  of  this  class.  , , ,,,  . ,,  . .. 

The  peculiarity  of  the  grinding  action  of  the  radial  rolling  mills  is  that  it 
is  not  a pure  crushing  action,  but  a triturating  or  grinding  action  as  well, 
owing  to  the  fact  that  while  the  different  portions  the  face  of  the  roll  are 
all  traveling  at  the  same  speed,  the  outer  portions  have  to  travel  over 
a greater  length  of  ring  than  the  inner  po  tions,  so  that  there  is  only  one 
line  along  which  true  crushing  action  occurs.  Some  manufacturers  have 
made  the  crushing  ring  and  the  rollers  both  with  coning  faces,  the  vertices 
of  both  cones  meeting  at  a common  point.  This  has  resulted  in  a true 
crushing  action,  but  for  so'me  classes  of  work  the  triturating  action  is  to  be 
preferred,  as,  for  instance,  in  the  grinding  of  silver  ores  for  the  patio  process 
of  amalgamation.  , . 

Centrifugal  Roller  Mills.— In  centrifugal  roller  nulls  the  crushing  is  accom- 
plished between  rapidlv  moving  rolls  and  the  inside  of  a stationary  die  or 
ring.  The  Huntington ‘mill.  Fig.  11,  is  one  of  the  principal  representatives 
of  this  class  of  machinery.  The  rollers  c are  supported  from  bearings  e and 
are  carried  rapidly  around  by  means  of  the  frame  a and  the  ^Ihe 

ore  is  crushed  against  the  ring  d.  In  order  to  prevent  the  accumulation 


CRUSHING  MILLS. 


427 


Fig.  10. 


of  ore  below  the  rollers,  and  to  throw  it  out  for  crushing,  scrapers  / are  pro- 
vided. The  crushed  ore  discharges  through  screens,  as  shown  in  the  illus- 
tration. There  are  many  styles  of  this  class  of  machinery  having  different 
numbers  of  rollers,  varying  from  1 up,  and  some  machines  have  been  intro- 
duced combining  a portion 
of  the  action  of  radjal  and 
centrifugal  machines,  the 
faces  of  the  die  or  ring  being 
at  an  angle  and  the  rollers 
being  mounted  in  inclined 
bearings  so  that  they  tend  to 
crowd  out  and  down  upon 
the  ring.  Centrifugal  roller 
mills  have  found  two  espe- 
cial fields  in  concentration 
works,  one  for  crushing  clay 
or  soft  ores  containing  free 
gold,  and  the  other  for  re- 
grinding middlings  for  fur- 
ther concentration.  Rolls  of 
this  type  are  also  extensively 
employed  in  grinding  cement 
and  phosphate  rocks. 

Ball  Mills.— There  are  two 
types  of  ball  mills:  (1)  those 
in  which  the  crushing  is  per- 
formed by  balls  traveling  in 
a fixed  path,  and  (2)  those 
in  which  the  crushing  is  per- 
formed by  a large  mass  of  balls  of  various  sizes  rolling  over  one  another. 
In  the  first  type  the  balls  travel  in  a fixed  path,  track,  or  race  that 
may  be  either  vertical  or  horizontal.  Where  it  is  vertical,  the  balls 
must  be  driven  at  such  a rapid  rate  that  their  centrifugal  force  will 
keep  them  in  contact  with  the  crushing  ring  or  track.  This  form  may  be 
likened  to  a bicycle  ball  bearing  on  a large  scale,  the  crushing  being 
accomplished  between  the  balls  and  the  race  or  track.  The  serious  objec- 
tion to  this  class  of  ball  mills  is  found  in  the  uneven  wear  of  both  the  balls 
and  the  race,  so  that  the  work  soon  becomes  unevenly  distributed,  and  also 
in  the  fact  that  the  balls  cannot  be  used  after  they  have  been  worn  to  a 
slight  extent.  , . 

In  the  second  class  of  machines  the  balls  are  introduced  into  a large 
barrel  or  chamber,  where  they  roll  over  one  another,  the  ore  being  crushed 

between  the  different  balls  and 
between  the  balls  and  the  lin- 
ing of  the  chamber.  In  this 
style  of  machine  the  crushed 
material  may  be  discharged 
through  openings  in  the  per- 
iphery or  through  openings  in 
one  end  of  the  barrel.  One 
great  advantage  with  this  style 
of  mill  is  that  the  balls  can  be 
entirely  worn  out  and  it  is 
only  necessary  to  charge  a 
sufficient  number  of  new  balls 
with  the  ore  each  day  to  make 
up  for  the  wear  of  those  in 
the  mill. 


STAMPS. 

Gravity  stamps  are  especially 
well  suited  for  material  the 
Fig.  11.  valuable  portion  of  which  does 

not  have  a tendency  to  slime. 
The  fact  that  these  stamps  are  very  simple  in  construction,  easy  to  transport 
and  erect,  as  well  as  to  operate,  gives  them  a decided  advantage  over  other 
forms  of  crushers.  Fig.  12  illustrates  a 10-stamp  battery  of  the  gravity  type. 


428 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


Fie  13  is  a detail  of  the  mortar  stamp  heads  and  dies.  The  mortar  a is  placed 
on  a suitable  foundation  of  timbers  b and  the  ore  crushed  on  dies  £ by  the 
stamps  s,  which  are  secured  by  means  of  tapered  joints  to  the  he^s  or  bosses 
h The  stems  e are  attached  to  the  heads  h and  the  whole  lifted  by  the  cams 
(shown  in  detail  in  Fig.  12).  The  cams  operate  under  tappets  on  the  stems 
as  shown  in  Fig.  12.  As  the  cam  operates  under  the  -edge  of  the  tappet,  it 
not  only  lifts  the  stamp,  but  gives  a partial  rotation,  thus  equalizing  the  wear 
on  both  the  stamp  and  die.  The  ore  is  fed  in  at  the  back  of  the  mortar  and 
the  crushed  material  discharged  through  the  screen,  as  shown  in  Figs.  12  and 
13  Usually  a single  screen  at  the  front  is  employed,  but  sometimes  two  or 
more  upon  different  sides  of  the  mortar  may  be  introduced.  For  treating 
free-milling  gold  ores  in  which  the  gold  occurs  in  rather  large  grains  free 
from  iron  pyrites,  the  California  style  of  battery  was  developed,  the  charac- 
teristics of  Which  are  a small  drop  (4  in.  to  6 in.),  low  discharge  ^m.U 
heavy  stamp  (750  to  1,000  lb.),  and  a high  speed  or  number  of  drops  permin- 
ute  (90  to  105).  The  advantage  of  this  style  is  rapid  crushing,  but  the 
majority  of  the  gold  had  to  be  saved  on  apron  plates  outside  the  mortar. 

For  working  ores  that  contain  large  quantities  of  iron  pyrites  with  the 
g-old  values  occurring  in  the  cleavage  planes  of  the  pyrites,  the  Gilpin 
County . Colo.,  style  of  battery  was  developed.  This  is  characterized  by  a 
Loumy,  y high  drQp  (lg  tQ  20  in  v a high  discharge 

(14  in.),  a light  stamp  (550  to  600  lb.),  and 
a comparatively  slow  rate  of  drop  (30  per 
minute) . With  this  style  of  battery,  most 
of  the  gold  was  obtained  on  amalgamated 
plates  in  the  battery,  but  its  use  was 
accompanied  by  excessive  sliming  on 


Fig.  12. 


Fig.  13. 


account  of  the  fact  that  the  high  discharge  kept  the  material  m the  mortar 
for  a long  time,  and  subjected  it  to  repeated  treatment.  w 

Modern  practice  tends  toward  the  use  of  rather  heavy 
1 000  lb  ) quick  drop  (90  to  105  per  minute),  and  low  discharge  (4  to  6 m.). 
The  advantages  arePtU  the  capacity  of  the  hatte^ 

sliming-  reduced  to  a minimum.  If  the  ore  contains  sulphides  carrying  go  , 

they  afe  separated  by  concentration  upon  manners  or  1 amon  nlates  do 
subsea  uentlv  treated  by  chlorination  or  smelting.  If  the  apron  plates  ao 
not  catch  the  major  portion  of  the  values,  the  tailings  may  treated  by  t e 
cyanfdfproceT  This  last  method  is  that  employed  at  many  large  gold 
mines,  especially  those  of  the  Transvaal  in  South  Africa.  T.  . 

Order  of  Drop.— There  is  much  diversity  of  practice  m this  respert.  . It  is 
desirable  to  drop  the  stamps  in  such  rotation  as  to  insure  an  even  disti ^b 
tion  of  the  pulp  on  the  several  dies.  Adjacent  stamps  should  not  drop  co  ^ 
secutivelv,  as  this  occasions  accumulation  of  the  pulp  at  one  end  of 
mortar  in  conseauence  of  which  the  efficiency  of  the  stamps  at  that  end  is 
reduced  by  having  a decreased  height  of  drop  and  a cu shion 
pulverization  of  the  ore.  The  stamps  at  the  other  themortarhave 

too  little  work,  and  are  liable  to  “ pound  iron.”  The  order  of  drop  1,  4,  2,  5,  3 


STAMPS. 


429 


seems  to  best  fulfil  the  requirements.  It  gives  a good 

but  the  two  just 

m6?ni  large  &^lfs ^lie  stendanl^rop  is  gtven  as  1 7,  3,  9,  5,  2,  8,  A 1CK 
1 s,  4, 10,2,  7,  5,  9,  3,  6 as  a close  favorite;  while  1,  5,  9,  7,  3,  2,  6,  10,  8,  4 and 

1,6SDee3d  of 'SUmps— Heav^stainps  and  stamps  having  high  drops  should 

KKrS.7S|6doKr 

dislodged!  and  breakage  is  imminent.  A fast  drop  produces  a good  splash, 
which  is  very  desirable  for  battery  amalgamation. 

Shoes  and  Dies. — Shoes  and  dies  are  either  of  iron  or  steel.  In  most  mills, 
remote  from  foundries  where  transportation  is  an  important  item  m the  cost 
nf^hops  and  dies  steel  shoes  and  dies  have  replaced  those  of  iron.  Chrome 
°tfpS( shot? and ^ dies  have  been  introduced  and  have  proved  superior.  In 
feme  SS,  steel  shoesVd  iron  dies ; are  used L The  ^ £SS 

evenly  with  steel  shoes  than  the  steel  dies  do.  The  life  is  about  2.  to  3 times 
that  of  iron  shoes  and  dies,  and  the  cost  about  twice  as  great  as  those  of  iron. 
The  mixture  of  steel  ( from  the  old  chrome  steel  shoes  and  dies)  with  iron 
nrodS  Xes  and  dVes  Sat  wear  considerably  longer  than  those  of  pure 
Son* and  may be  advantageously introduced l where 

r»n<?«iiblp  for  the  old  steel,  because  of  want  of  local  facilities  ior  me 
utilization  of  this  residue.  In  many  districts,  the  old  iron  shoes  and  dies  are 
sold  to  local  foundries  for  from  1£  to  2 cents  per  lb.  • of  the 

The  weights  of  the  shoes  bear  a certain  relation  to  the  weights  of  tne 
tnoopts  stems  and  bosses.  Chrome  steel  shoes  made  for  stamps  of  850  to 
9%Plb  weiSi ’from  150  to  155  lb.,  and  measure  about  9 in.  m diameter  by 
71  to  8 in  long.  The  neck  is  from  4£  to  5 in.  long,  with  a taper  to  correspond 
to  the  socketof  the  boss  or  stamp  head.  Iron  shoes  are  usually  from  15  to 
20  lb.  lighter  than  the  above  weights.  The  chrome  steel  dies  weigh  from 
110  to  125  lb.,  and  measure  (where  shoes  of  the  above  dimensions  are  used ) 

Q in  in  diameter  bv  4 to  41  in.  in  height,  with  a rectangular  foot-plate  10, »in. 
by  91  in.  by  i in.  thick.  Iron  shoes  usually  weigh  from  20  to  25  lb.  less  than 

^eLif?°ofe  the^l^oes^and  Dies. — There  are  many  conditions  that  affect  the 
durability  of  shoes  and  dies  as,  for  instance,  the  hardness  of  the  rock  the 
wPiXt  sneed  and  height  of  drop  of  the  stamp,  the  manner  of  feeding 
the  ore’  etc  Iron  shoes  of  good  quality  last  from  30  to  47  days.  Old  shoes 
wea?  usualiv  down  to  U in.  or  1 in.  in  thickness,  and  weigh  about  25  or  40  lb. 
Old  dies  usually  wear  down  to  about  11  in.  in  thickness,  and  weigh  from 
20  to  50  lb.  The  consumption  of  iron  or  steel  in  shoes  and  dies  depends  < on 
the  character  of  the  ore  crushed.  Other  conditions  being  the  same,  it  will 
depeM  onlhe  coarseness  of  the  stamjang  and  the  heigh t of  discharge 
Dies  wear  less  rapidly  than  the  shoes,  as  they  are  Protected 
and  the  pulp,  which  covers  them  to  the  depth  of  from .1*  to  3 in.  BUt  while 
the  actual  wear  of  dies  is  less  than  that  of  the  shoes,  the  life  of  the  dies 
is  shorter  than  that  of  the  shoes,  owing  to  the  fact  that  tbe  shoes  have 
several  inches  greater  length  of  wearing  part  than  the  dies.  The  con 
sumption  of  iron  for  shoes  and  dies  per  ton  of  ore  crushed  &hfornia, 
froni  H to  3 lb.  To  obtain  the  maximum  crushing  capacity  of  the 
battery  the  dies  must  be  kept  as  high  (with  reference  to  the  lower  edge 
of  the7 screens)  as  is  compatible  with  the  safety  of  the  sheens 
successful  amalgamation  in  the  battery.  To  prevent  the  JPO^nding  of  iron, 
it  is  necessary  to  preserve  more  or  less  uniformity  m the  level  of  the  dies. 
Should  one  die  in  the  battery  project  much  above  the  others,  little  or  no 
pulp  would  remain  upon  it,  and  the  shoe  would  consequently  drop  upon 

^^am^Stamo  Heads  and  Stems.— Cams  and  stamp  heads  ought  to  last 
several  years. P They  are  usually  broken  through  carelessness,  The  stems 
break  at  the  socket  of  the  stamp  head.  Stems  are  reversible; wh^i  ^roken, 
they  may  be  swedged  or  planed  down  and  additional  lengths  welde 

WhTappets.— When  there  is  much  grease  on  the  tappet  or  cam  or  when  the 


430 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


tappets  have  so  worn  that  the  face  of  the  cam  strikes  a grooved  instead  of  a 
level  face  on  a tappet,  the  rotary  motion  is  greatly  impaired.  Tappets  last 
for  several  years,  from  4 to  5 years  being  their  usual  life.  Sometimes  they 
are  broken  by  being  too  tightly  keyed.  When  their  faces  are  worn,  they 
are  planed  down.  They  are  reversible,  so  that  when  one  face  has  been 
worn  as  far  as  possible,  the  other  face  is  placed  downwards.  They  are 
usually  of  steel,  and  weigh  about  112  lb.  when  900-lb.,  stamps  are  used. 

Battery  Water. — The  amount  of  water  fed  to  the  battery  depends  on  the 
character  of  the  ore  and  the  size  of  the  screen.  Clayey  arid  highly  sulphu- 
reted  ores  require  the  maximum  amount  of  water.  The  amount  of  water 
used  per  ton  of  ore  stamped  varies  from  1,000  to  2,400  gallons.  The  mean 
amount  used  per  ton  of  ore  stamped  is  about  1,800  gallons.  From  I to  14 
miner’s  inches  per  battery  should  be  provided.  Tn  winter,  when  the  battery 
water  is  chilly,  it  should,  when  possible,  be  heated  to  tepidity,  as  this  pro- 
motes amalgamation.  A high  temperature  should  be  avoided,  as  it  renders 
the  quicksilver  too  lively. 

Duty  of  Stamps.— The  capacity  of  gravity  stamps  varies  from  a little  over 
1 ton  per  stamp  for  24  hours  to  as  high  as  4 tons  per  stamp  for  24  hours, 
depending  on  the  quality  of  the  ore.  Usually,  an  average  of  from  1.7  to  2 
tons  per  stamp  for  24  hours  in  a combination  mill  would  be  good  practice, 
while  where  the  ore  is  crushed  to  a rather  coarse  screen  and  the  tailings 
treated  with  the  cyanide  process,  a larger  capacity  is  usually  obtained. 

The  number  of  tons  of  ore  crushed  per  stamp  depends  chiefly  on  the 
weight  of  the  stamp,  the  number  of  drops  per  minute,  the  height  of  drop, 
the  height  of  discharge,  the  size  of  the  screens,  the  width  of  the  mortar,  and 
chiefly  on  the  character  of  the  ore.  Hard  ores  and  ores  of  a clayey  nature 
(from  the  difficulty  experienced  in  discharging  the  clayey  pulp)  decrease 
the  duty  of  the  stamps.  About  2£  tons  per  stamp  in  24  hours  is  the  average 
duty  of  the  stamp  in  California.  The  discharging  capacity  of  a mortar 
depends  on  the  height  and  size  of  the  discharge  opening,  the  character  of 
the  screen,  and  the  width  of  the  mortar  discharge,  as  will  be  illustrated 
from  two  well-known  mills. 

The  Homestake  Mill  uses  an  850-lb.  stamp  dropped  9 in.,  85  times  per 
minute,  developing  78,030,000  ft.-lb.  in  24  hours,  and  crushing  44  tons  of  rock, 
or  1 ton  for  every  17,340,000  ft.-lb.  developed. 

The  Caledonia  Mill  uses  an  850-lb.  stamp,  dropping  12  in.,  74  times  per 
minute,  crushing  3.3  tons,  of  rock  and  developing  90,576,000  ft.-lb.  in  24 
hours,  or  1 ton  to  every  24,447,272  ft.-lb.  developed.  Although  developing 
more  foot-pounds  in  24  hours,  and  therefore  seemingly  more  efficient,  yet  it 
crushes  less  rock  than  the  former.  The  reasons  for  this  are  (1)  that  the  rock 
is  harder  than  that  of  the  Homestake;  (2)  the  width  of  mortar  is  16  in. 
against  134  in.;  and  (3)  the  2"  recess  for  the  8"  copper  plate  below  the  feed. 
On  the  other  hand,  the  Caledonia  has  a lower  discharge  from  the  mortar, 
using  6 in.  against  10  in.  in  the  Homestake;  but  this  advantage  is  again 
neutralized  by  a smaller  screen,  the  Caledonia  using  258  sq.  in.  against 
376  sq.  in.  of  the  Homestake. 

Horsepower  of  Stamps.— The  H.  P.  of  a stamp  battery  = 
No.ofstampsXwgt.ofeach  stamp  X No.  of  drops  per  min.  X drop  of  each  in  in. 

12  X 33,000 

The  weight  of  each  stamp  is  equal  to  the  sum  of  the  weights  of  the  stem, 
tappet,  stamp  head,  and  shoe.  To  the  nominal  H.  P.  add  25$  for  friction  of 
machinery  in  calculating  driving  H.  P. 

Cost  of  Stamping.— The  cost  of  stamping  varies  from  a little  over  $1.00 
per  ton  up.  The  Montana  Co.,  Limited,  operating  a 60-stamp  combination 
mill,  in  1888  treated  40,530  tons  of  ore  at  $1.13  per  ton.  In  Australia,  stamp- 
mill  costs  have  been  reported  varying  from  $1.30  to  $2.50  per  ton  where 
fairly  favorable  conditions  for  working  could  be  obtained.  Figures  from 
other  districts  compare  favorably  with  these,  but  it  would  be  impossible  to 
give  any  absolute  rule  by  means  of  which  the  cost  can  be  determined  in 
advance,  without  an  intimate  knowledge  of  the  character  of  the  ore  and 
the  local  conditions. 

Pneumatic  Stamps.— This  is  a name  given  to  a form  of  large  capacity 
power  stamp,  the  head  of  which  is  connected  to  a piston  in  an  air  cylinder. 
The  cylinder  is  raised  and  lowered  by  power,  the  air  forming  an  elastic 
connection  by  means  of  which  the  stamp  is  operated.  They  are  quite 
extensively  employed  in  crushing  tin  ore,  but  have  never  come  into  general 
use  for  other  purposes.  The  capacity  is  as  high  as  30  tons  per  24  hours. 


SIZING  AND  CLASSIFYING  APPARATUS. 


431 


Power  Stamps  —Various  forms  of  stamps  have  been  brought  out  at  differ- 
pnt  times  intended  to  operate  by  power  like  a trip  hammer,  or  in  which 
the  stamp's  were  connected  directly  to  the  cranks  operating  them  by  means 
MS  Neariy  all  of  these  forms  have  failed  on  account  of  exces- 
2? ve  wear  small  capacity  and  the  large  amount  of  power  consumed  . 

lt«T’st^D3.-The Targe  capacity  steam  stamp,  which  was  evolved  in 
connection  with  the  concentration  of  the  Lake  SuPeJ™r  copper  “es,  °on- 
sists  of  a steam  cylinder  in  which  °Perates  ^.Piston,  to  the  stem  of  which  the 
otomn  head  is  directly  connected.  Machines  of  this  style  are  usually 
made  very  large  and  heavy,  frequently  extending  throug  wo  or  ree 
stories  of  the  mill,  and  having  a capacity  eqmvaient  to  from  60  to  100  ordi 
nary  gravity  stamps.  In  most  forms,  live  steam  is  admitted  on  top  of  the 
piston  during  the  (lescent  of  the  stamp,  thus  increasing  the  force  of  the 
blow  For  lifting  the  stamp,  the  steam  is  throttled  so  that  a lower  pressure 
is  employed.  The  discharge  is  usually  through  a coarso  screen,  * to  8 
mesh  not  being  uncommon.  One  interesting  fact  connected  with  the  large 
steam  stamps  is  that  their  heavy  blows  do  not  cause  as  excessive  sliming  as 
th^Ughte?  gravity  Stamps,  and  on  this  account  this  form  of  stamp  has  been 
introduced  m some  cases  for  crushing  free-milling  gold  ores. 

For  prospecting  work,  for  testing  properties,  or  foroperatmgsmall  prop- 
erties a number  of  forms  of  portable  or  semiportable  steam  stamps  have 
come ’ out*1 during  ?he  last  few  years.  One  of  these  (the  Tremam)  is  illus- 
trated  in  Fig.  14.  In  this  form,  two  pistons  work  m cylin- 
ders side  by  side  and  strike  alternate  blows  in  a common 
mortar.  The  steam  is  introduced  at  full  boiler  pressure  on 
the  lower  side  of  the  cylinder,  which,  owing  to  the  large 
diameter  of  the  piston  rod,  has  a small  area.  This  high  pres- 
sure steam  is  then  allowed  to  expand  on  to  the  top  ot  the 
piston,  thus  urging  it  down  with  greater  force  than  its  own 
weight  would.  These  steam  stamps  can  be  run  at  a much 
higher  speed  than  gravity  stamps,  and  hence  have  a greater 
capacity.  In  the  figure  shown,  three  screens  are  employed, 
one  in  front  and  one  at  each  end  of  the  mortar.  There  are 
several  other  forms  of  portable  steam  stamps  manufactured. 

They  all  have  the  advantage  that  for  a small  property  they 
can  be  installed  with  much  less  trouble  than  any  other  form 
of  crusher,  owing  to  the  fact  that  no  steam  engine  is  required 
and  the  steam  necessary  to  drive  them  can  usually  be 
obtained  from  the  boiler  operating  the  hoisting  engine, 

^Mfscetlaneous  Forms  of  Crushers.-Most  crushers  can  be 
classed  under  one  of  the  previous  heads,  but  there  are  spme  . 
forms  that  depend  on  the  material  itself  to  do  the  crushing:  £or  mstance, 
in  the  preparation  of  coal  for  coke  ovens,  there  has  been  a combined  crusner 
and  separator  invented  that  may  be  described  as  follows:  A Jarge  h^izontal 
drum  or  cylinder,  provided  with  screen  openings  around 
mounted  in  a horizontal  position  The  coal  to  be  separated  is  fed  into  one 
end  and  is  caught  by  shelves  or  plates  projecting  radially  into  the  cylinder. 
These  lift  the  material  to  the  upper  side,  from  which  it  falls  by  gravity  and 
strikes  the  bottom,  thus  crushing  the  softer  parts  The  sulphur 
being  harder  than  the  coal,  are  not  crushed  by  the  same  height ; of fall,  and 
hence,  by  a proper  adjustment  of  the  diameter  of  the  cylinder, the  °oal  may 
be  crushed  and  discharged  through  the  screen  while  the  slate  and  sulphur 
will  pass  out  at  the  opposite  end  of  the  cylinder. 

SIZING  AND  CLASSIFYING  APPARATUS. 

Stationary  Screens,  Grizzlies,  Head-Bars,  or  Platform  Bars.—' These {*F® 
various  names  given  to  an  inclined  screen  employed  for  removing  tne 
fine  material  from  the  run  of  mine  so  that  only  the  coarse  portion  will  be 
passed  to  the  crushers.  At  concentrating  works,  the  term 
employed,  and  a common  form  is  shown  in  Fig .15  This  is  composed  of  flat 
bars  held  apart  by  cast-iron  washers  through  which  the  bar  bolts  are passed 
to  hold  the  entire  frame  together.  Grizzlies  are  usually  Placed  at  an  angle 
of  from  45°  to  55°,  and  ordinarily,  for  the  head  of  a large  concentrating 
works,  they  are  from  3 to  6 ft.  wide  and  from  8 to  12  ft.  long,  the  amount 
of  space  between  the  bars  depending  on  the  size  of  the  run-of-mme  material 
and  on  its  subsequent  treatment. 


Fig 


432 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


In  the  anthracite  coal  breakers,  the  terms  platform  bars  or  head-bars  are 
usually  employed,  and  these  bars  are  made  of  1£"  to  2"  round  iron  placed  at 
an  inclination  of  5 in.  to  1 ft.,  the  spacing  depending  on  the  size  of  coal  it  is 
desired  to  make  in  the  breaker. 

At  the  present  time,  in  accordance  with  an  agreement  between  the  oper- 
ators and  the  miners’  officials,  the  standard  size  for  a bituminous  lump 

screen  (the  bars  are  called  a screen)  for  Ohio, 
_ _ Pennsylvania,  Indiana,  and  Illinois  is  12  ft. 

long  and  6 ft.  wide  over  the  screen  surface.  The 
screen  consists  of  6 bearing  bars  4 in.  by  $ in. 
of  soft  steel  and  39  steel  screen  bars,  Fig.  16, 
with  li  in.  clear  space  between  bars.  . In  Iowa, 
the  same  sized  bar  is  used,  but  the  space  be- 
tween the  bars  is  If  in.  In  the  other  Western 
and  Southern  States  there  is  at  present  no 
standard. 

The  standard  nut-coal  screen  for  Pennsyl- 
vania and  Ohio  is  £ in.  space,  but  f in.  is 
Fig.  15.  sometimes  used  and  the  nut  screen  is  often 

varied  to  suit  the  special  trade.  At  present 
very  few  pea  screens  are  used,  but  if  placed  under  a nut  screen,  the 
space  is  from  f in.  to  f in.  In  the  Pittsburg  region  of  Pennsylvania,  all 
coal  passing  through  f"  screen  is  called  slack , while,  on  the  Monongaheuo 
River,  coal  passing  through  11"  screen  is  called  slack  and  is  used  in  stokers. 
Many  companies  are  at  present  crushing  their  run-of-mine  coal  to  make 
slack  suitable  for  stokers. 

It  is  difficult  to  classify  bituminous  coal  by  sizes,  but  as  nearly  as  possible 
the  following  seem  to  be  the  standard:  Lump , all  coal  passing  over  11"  screen; 
nut,  all  coal  passing  through  11"  openings  and  over  openings;  slack,  all 
coal  passing  through  %"  screen.  If  a pea-coal  screen  is  used,  all  coal  passing 
over  1",  1",  and  f"  would  be  pea  coal,  and  that  passing  through  |",  1",  or  f" 
would  be  slack. 

Adjustable  Bars.- The  top  of  the  bar  is  cylindrical  and  projects  beyond  the 
web  which  supports  it,  so  that  any  lump  which  passes  through  the  upper 
part  will  fall  freely  without  jamming.  The  two  ends  of  the  bar  are  V shaped 
and  fit  into  similarly  shaped  grooves,  so  that  the  bars  can  be  set  at  distances 
from  each  other  varying  with  the  sum  of  the  width  of  the  bases  of  the 
triangles,  the  usual  opening  being  about  4 in.  These  bars  are  generally 
4 ft.  long,  but  they  can  be  of  any  size. 

Finger  bars  are  screen  bars  that  are  fixed  at  one  end  only,  and  the  bars 
are  narrower  at  the  lower  end  than  at  the  top,  so  that  the  spaces  between 
them  are  wider  at  the  bottom  than  at  the  top,  thus  giving  less  tendency  for 
pieces  of  material  to  become  wedged  between  the  bars. 

Movable  or  oscillating  bars  are  screen  bars  that  are  attached  to  eccentrics 
at  their  lower  ends,  the  eccentrics  of  adjoining  bars  being 
placed  180°  apart.  This  movement  throws  the  material  for- 
wards and  the  bars  do  not  therefore  require  nearly  the  same 
inclination  as  fixed  bars. 

Shaking  screens  have  an  advantage  in  that  the  entire  area 
of  the  screen  is  available  for  sizing,  and  hence  a greater 
capacity  can  be  obtained  from  a given  area  of  screening 
surface.  They  also  occupy  less  vertical  height  than  a revolv- 
ing screen.  In  coal  breakers  they  are  particularly  applicable 
where  the  coal  is  wet  and  has  a tendency  to  stick  together. 

The  principal  disadvantage  of  the  shaking  screen  is  that 
the  reciprocating  motion  imparts  a vibration  to  the  framing 
of  the  building.  For  anthracite  coal,  the  screens  usually 
have  an  angle  or  pitch  of  from  £ in.  to  2 in.  per  foot,  the 
average  being  about  £ in.  per  foot.  These  screens  are  run  at 
from  90  to  280  shakes  per  minute,  the  average  being  about  200 
shakes  per  minute,  or  100  revolutions  per  minute  for  the 
cam-shaft.  The  throw  of  the  eccentric  or  cam  varies  from 
2 in.  to  5 in.  Fig.  16. 

Similar  screens  are  employed  for  sizing  salt,  but  are  usually 
placed  at  a much  steeper  incline  and  are  frequently  so  hung  that  they  have  a 
combined  rocking  and  swinging  motion.  Shaking  screens  are  rarely  employed 
in  concentrating  works  on  account  of  the  fact  that  revolving  screens  can 
be  hung  in  the  upper  part  of  the  mill  where  they  will  not  interfere  with 


Screens. 


433 


oyecti?nablT^ilea^e^doC&e\izmgasatisfactorilyawirBout°imparting  jar 

fOIFor  brokena n’d  egg  coal,  i sq.  ft.  per  ton  for  lOhoura. 

For  stove  and  chestnut  coal,  T sq.  ftft  PFr^“hf“  “ h 
For  pea  and  buckwheat  coal,  * sq.  ft.  for  10  hours 

fi^on^tSt  lasttag6? hcmrs^/OW)  tons  of  coal  were  passed  over  screens  having 

nerforated  plates  of  the  following  dimensions: 
perioraxea  ^ ^ perforations  for  making  slack. 

56  sq.  ft.  with  1£"  perforations  for  making  pea  coal. 

28  sq  ft.  with  2 i"  perforations  for  making  nut  coal. 

28  sa  ft  with  4i"  perforations  for  making  egg  coal. 

SliiSHSSSS 

Mesh  for  Shaking  Screens. 


Kind  of  Coal. 


Steamboat... 

Lump  

Broken  

Egg  

Stove  

Chestnut  ... 

Pea  

Buckwrheat 
Rice 


Lehigh  Valley 
Coal  Co. 

Phila.  & Reading 
Coal  & Iron  Co. 

Round. 

Round. 

Square. 

5f" 

5" 

4i" 

4i" 

4" 

3i" 

3i" 

24" 

2tV' 

21" 

2" 

^*16 

It" 

if 

1" 

li" 

7// 

V 

H" 

4" 

i rr 

3 

H" 

*" 

c 

16 

i // 

4 

\tf 

e 

Kind  of  Coal. 


Steamboat. 
Large  broken. 
Small  broken. 
Egg. 

Stove. 

Chestnut. 

P6£l 

Buckwheat. 

Rice. 


s^ssi5fia.'S 

many1  mills  ‘where^h^^achi^ry ^mu^of  necessity  be  crowded  into  a 
minimum  space  and  be  hard  to  get  at.  number  of  flat  sides, 

or  dashed  against  the  screen  surfaces  to  break  it  or  to  loosen  aanering  cmy 


434 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


or  dirt.  The  shaft  is  sometimes  hollow,  and  streams  of  water  from  this 
hollow  shaft  wash  the  material  as  it  is  being  screened. 

Revolving  screens  are  frequently  jacketed,  that  is,  two  or  more  screens 
are  placed  concentrically  about  the  same  shaft,  the  inmost  one  being  the 
coarsest,  and  each  succeeding  screen  serving  to  make  additional  separations. 
This  method  reduces  the  space  necessary  for  a given  amount  of  sizing 
machinery.  In  other  cases,  a long  cylindrical  screen  has  a coarse  mesh  near 
its  discharge  end  and  finer  mesh  near  the  entrance  end,  thus  making  two  or 
more  through  products  as  well  as  the  overproduct.  The  disadvantage  of 
jacketed  screens  is  that  the  necessarily  slow  speed  of  the  inmost  screen 
reduces  the  capacity  of  the  entire  combination,  so  that  if  rapid  work  is 
essential,  it  is  better  to  use  fairly  large-diameter  screens  placed  one  after  the 
other  in  place  of  jacketed  screens.  Another  disadvantage  is  that,  to  renew 
the  inner  jackets,  it  is  often  necessary  to  remove  the  outer  ones. 

The  disadvantages  of  having  two  or  more  sizes  of  wire  cloth  on  one  screen 
are  that  the  fine-meshed  screen  near  the  head  is  worn  out  rapidly,  as  all  the 
material  both  coarse  and  fine  passes  over  it,  while,  when  separate  screens 
are  employed,  each  screen  has  to  deal  only  with  its  through  or  oversized 
product,  all  coarser  material  having  been  removed. 

Speed. — The  periphery  of  a revolving  screen  should  travel  about  200  ft. 
per  minute.  In  the  case  of  very  fine  material,  screens  are  sometimes  run 
faster  than  this. 

The  following  have  been  adopted  as  standard  speeds  for  screens  by  one 
of  the  largest  anthracite  coal  companies: 

Speed  of  Screens. 


Rev.  per  Minute.  Rev.  per  Minute. 

Mud  screens 8.87  Big  screens 8.52 

Counter  mud  screens 15.49  Pony  screens 10.87 

Cast-iron  screens 11.25  Buckwheat  screens 15.30 

Duty  of  Anthracite  Screens.— The  following  table  gives  the  number  of 
square  feet  of  screen  surface  required  for  a given  duty  in  the  case  of 
revolving  screens  working  upon  anthracite  coal: 

Egg  coal,  1 ton  per  1 sq.  ft.  per  10  hours. 

Stove  coal,  1 ton  per  1£  sq.  ft.  per  10  hours. 

Chestnut  coal,  1 ton  per  If  sq.  ft.  per  10  hours. 

Pea  coal,  1 ton  per  2 sq.  ft.  per  10  hours. 

Buckwheat  coal,  1 ton  per  2f  sq.  ft.  per  10  hours. 

Rice  coal,  1 ton  per  3f  sq.  ft.  per  10  hours. 

Culm,  1 ton  per  5 sq.  ft.  per  10  hour:,. 

These  figures  may  be  reduced  from  20$  to  30$  for  very  dry  or  wash  coal. 
Revolving  Screen  Mesh  for  Anthracite.— A standard  mesh  for  revolving 
screens  for  sizing  anthracite  coal  was  adopted  some  years  ago,  but  it  is  only 
approximately  adhered  to  and  a considerable  variation  from  the  standard  is 
found  throughout  the  anthracite  region. 

The  following  are  probably  as  nearly  standard  meshes  for  revolving 
screens  for  sizing  anthracite  coal  as  can  be  given: 


Mesh  for  Sizing  Coal. 

passes  through  3y'  mesh, 
passes  over  mesh,  and  through  mesh, 
passes  over  £"  mesh,  and  through  £"  mesh, 
passes  over  mesh,  and  through  f"  mesh, 
passes  over  f"  mesh,  and  through  If"  mesh, 
passes  over  If"  mesh,  and  through  2"  mesh, 
passes  over  2"  mesh,  and  through  2f"  mesh, 
passes  over  2f"  mesh,  and  out  end  of  screen, 
over  3"  mesh,  and  out  end  of  screen. 


Culm 
Birdseye 
Buckwheat 
Pea 

Chestnut 
Stove 
Egg 

* Grate 

* Special  grate 

* Special  steamboat  passes  over  3"  bars,  and  through  6"  bars. 


Hydraulic  Classifiers.— The  separation  of  materials  by  this  class  of 
machinery  depends  upon  the  law  of  equally  falling  bodies,  which  may  be 
stated  as  follows:  Bodies  falling  free  in  a fluid , fall  at  a speed  proportional 
to  their  weight  divided  by  the  resistance.  From  this  it  will  be  seen  that  small 
masses  of  a heavy  mineral  will  fall  as  rapidly  as  large  masses  of  a light 
mineral,  owing  to  the  fact  that  the  weight  increases  as  the  volume  and  the 


* These  sizes  and  “lump”  size  are  seldom  made,  and  there  is  no  uniformity  whatever  in  the 
sizes  called  by  these  names. 


HYDRA  XJLIC  CLASSIFIERS. 


435 


resistance  only  as  the  area,  so  that  if  a quantity  of  galena  and  quartz  of 
various  sizes  were  introduced  into  water,  it  would  settle  into  approximate 
layers,  each  composed  of  relatively  large  pieces  of  quartz  and  relatively 
small  pieces  of  galena.  This  same  action  would  be  true  in  the  case  ot  any 


minerals  differing  in  specific  gravity.  The  principal  representatives  of  the 
hydraulic  classifying  machines  are  the  Spitzkasten  and  Spitzlutten.  . 

The  Spitzkasten  consists  of  a series  of  pyramidal  boxes,  one  of  which  is 
shown  in  Fig.  17.  The  material  enters  the  box  at  a , passes  down  under  the 
diving  board  b , and  discharges  into  the  next  box  through  the  trough  c.  At 
the  bottom  of  the  box,  water  is  introduced  through  the  pipe  d from  the 
launder  g in  such  quantity  as  to  more  than  supply  the  opening  or  spigot  e. 
The  heavy  particles  of  mineral  settle  against  this  rising  stream  of  water  into 
the  elbow/,  from  which  they  are  washed  out  through  e.  Each  succeeding 
box  is  made  larger  than  the  preceding,  and  the  rising  current  is  so  regulated 
that  a different  product  will  settle  out  in  each. 

The  Spitzlutten  is  a V-shaped  box,  inside  of  which  is  set  another  V having 
the  same  slope,  the  material  flowing  down  between  the  two  V’s  on  one  side 
and  up  and  out  on  the  other.  The  distance  between  the  V’s  can  be  regulated, 
as  can  also  the  rising  current  of  water,  thus  obtaining  the  separation  desired. 

Many  other  forms  of  separators,  all  depending  on  this  same  principle, 
have  been  brought  out,  some  having  a conical  form,  some  being  arranged  in 
the  form  of  troughs,  and  others  as  boxes  of  various  shapes. 

The  Calumet  classifier,  Fig.  18,  consists  of  a series  of  boxes  or  pockets  in  the 
bottom  of  a gradually  widening 
trough.  Wash  water  enters 
through  a pipe  a and  discharges 
directly  against  the  discharge 
spigot  d , which  is  however  not 
large  enough  to  carry  all  the 
water  off  directly,  hence  it  twirls 
and  eddies  in  the  bottom  of  the 
box  so  that  only  the  heaviest 
particles  having  weight  enough 
to  settle  in  this  disturbed  water 
pass  out  through  the  spigot.  A 
shield  c reflects  upward  currents 
and  confines  the  agitation  to  the 
bottom.  The  pr1-  -- 

the  direction  of 


s. 

. . .r* — 

■ M 

s 

HrH* 

k 

flowing  in 
e arrows  is 
downwards  by  the 


Fig.  18. 


deflected 

boards  s.  . 

The  settling  boxes  employed  for  mills  are  really  a form  of  hydraulic  classi- 
fier. They  are  usually  very  large  V-shaped  boxes  provided  with  a diving 
board  similar  to  that  shown  at  b in  Fig.  17,  but  no  current  of  water  is 


436 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


introduced.  In  some  cases  a small  stream  of  the  heavy  muds  or  concen- 
trates is  kept  continually  flowing  from  the  bottom,  while  in  others  they 
are  drawn  off  inteimittentlv.  One  very  important  point  to  be  observed 
in  settling  boxes  is  that  the  settling  action  depends  on  the  arresting  ot 
the  current,  and  with  a given  amount  of  floor  space,  very  much  more 
efficient  settling  can  be  obtained  from  two  boxes  placed  side  by  side  and 
having  half  the  material  pass  through  each  than  from  two  boxes  placed 
in  series,  and  that  the  width  of  the  box  is  of  vastly  more  importance 
than  the  length.  The  depth  is  also  fairly  important,  and  a diving  board 
mast  always  be  introduced  to  prevent  surface  currents.  If  the  boxes 
are  properly  arranged,  nearly  all  the  solid  material  will  be  settled  out  ot 

the  water.  ,,  . . . - 

The  Jeffrey-Robinson  coal  washer,  Fig.  19,  which  operates  on  the  principle  of 
the  Spitzkasten,  c^sists  of  a steel  chamber  B in  the  form  of  an  inverted 
cone,  inside  of  which  are 
projecting  arms  and  stir- 
ring plates  <7,  C revolved 
by  a driving  gear  A.  The 
water  supply  enters  at 
the  bottom  from  the 
water  pipe  P through 
perforations  31.  The  coal 
is  introduced  through  a 
chute  S and  is  kept  in  a 
continual  state  of  agita- 
tion by  the  current  of 
water,  and  being  lighter 
than  the  impurities,  it 
passes  out  through  the 
overflow  K onto  the  con- 
veyors E,  F and  through 
the  chutes  X,  X,  while 
the  water  and  sludge 
drain  through  the  hop- 
per into  the  sludge  tank 
G . whence,  if  necessary, 
the  same  water  can  be 
again  pumped  by  the  pul- 

someter  H back  into  the  . . , ...  „ , 

washer.  (As  mentioned  elsewhere,  it  is  poor  practice  to  use  this  water  over 
again  when  it  is  desired  to  decrease  the  percentage  of  sulphur  m the 
washed  product  as  greatly  as  possible. ) . ^ _ , T , „ 

The  heavy  impurities  sink  to  the  bottom  into  the  chamber  J and  when 
this  is  full  the  upper  of  the  two  valves  shown  is  closed  and  the  lower  valve  is 

opened  to  discharge  the  refuse.  . . , 

The  following  data  in  regard  to  one  of  these  washers  is  given  by 
Air  J.  J.  Ormsbee  in  the  Transactions  of  the  A.  I.  M.  E.  These  results  were 
obtained  at  the  Pratt  Alines,  Alabama,  with  a plant  having  a nominal 
capacity  of  400  tons  per  day.  By  washing  slack  that  passed  between  screen 
bars  spaced  f in.  in  the  clear,  the  washed  coal  contained  42#  less  ash  than 
the  unwashed  coal,  the  reduction  in  sulphur  was  15#,  while  the  volatile 
matter  was  increased  4$,  and  the  fixed  carbon  5#.  W ith  coal  passing  over  8 
perforations,  the  results  were  a reduction  of  48#  m ash,  1 a#  in  sulphur  and  a 
£ain  of  5*  in  volatile  matter  and  fri  fixed  carbon.  These  results  indicate  that 
the  washer  is  better  adapted  to  large  sizes  than  to  fines.  The  amount  of 
water  used  per  ton  of  washed  coal  was  85.1  gallons  and  the  cost  \\as 
2.25  cents  per  ton  for  washing  400  tons,  itemized  as  follows:  Labor  at  washer, 
82  00;  labor  at  boiler,  fuel,  etc.,  84.00;  repairs  and  supplies,  83.00;  total,  89.00. 

Loe  Washer.— For  removing  clay  from  ores  or  other  material,  the  log 
washer  illustrated  in  Fig.  20  has  proved  itself  to  be  efficient.  Lither 
single  or  double  logs  are  employed,  the  form  shown  being  double- 
log  washer.  The  logs  work  over  troughs  which  have  a slight  inclination, 
so  that  the  water  will  flow  from  one  end  to  the  other.  W ater  is  introduced 
at  the  upper  end  and  discharged  at  the  lower  end.  The  material  to  be  washed 
is  introduced  near  the  lower  end  and  is  fed  up  against  the  water  by  spiral 
arms  or  plates  fixed  about  the  logs,  as  shown  in  the  illustration.  As  the 
material  is  advanced,  the  clay  or  other  sticky  substance  is  broken  up, 
washed  away,  and  discharged  at  the  lower  end  with  the  wash  water. 


LOG  AND  TROUGH  WASHERS. 


437 


Fig.  20. 


These  washers  have  "been  extensively  employed  for  cleaning  iron  ores 
occurring  as  rather  hard  masses  in  clay.  , , , - 

There  is  no  general  standard  size  of  these  washers,  hut  most  of  the  double- 
log  washers  for  both  steel  and  wood  logs  are  the  same,  except  in  length  oi 
logs,  the  washer  box  being  7 ft. 

4 in.  wide,  2 ft.  deep  at  discharge 
end,  and  4 ft.  deep  at  receiving 
end.  The  length  of  logs  varies 
from  20  to  30  ft.  The  logs  are 
generally  given  an  elevation  of 
1 in.  in  1 ft.,  and  sometimes  li  in- 
in  1 ft. 

The  capacity  of  an  ore  washer 
depends  very  much  on  the 
quality  of  the  material,  avera- 
ging for  one  pair  of  logs  from  100 
tons  per  day,  when  the  matrix 
is  of  a clayey  nature,  to  350  tons 
with  loose  sandy  material.  The 
capacity  of  a washer  is  based 
on  the  amount  of  material  from 
the  mines  it  will  put  through 
more  than  the  tonnage  of  clean 

ore,  and  this  amount  varies  from  . , 

500  to  1,000  yd.  per  10  hours.  The  amount  of  water  used  varies  from  300  to 
500  gal.  per  minute.  The  total  expense  for  labor  and  fuel,  including  the 
water  supply,  varies  from  5 cents  to  25  cents  per  ton  of  ore,  averaging 
possibly  10  cents  per  ton.  , A 

The  Scaife  trough  washer  consists  of  a semicircular  iron  trough  2 ft. 
in  diameter  and  24  ft.  long.  Inside  is  a series  of  fixed  dams  or  partitions 
that  can  be  made  higher  or  lower,  as  required,  by  means  of  plates.  A shaft 
running  the  entire  length  of  the  trough  and  turning  in  babbitted  journals 
carries  a number  of  stirring  arms  or  forks  and  is  given  a reciprocating 
motion  by  a connecting-rod  attached  to  a driving  pulley  at  its  center.  The 
coal  is  fed  with  water  at  the  upper  end  of  the  trough,  and  by  the  action  of 
the  flowing  water  and  the  agitation  of  the  arms,  the  slate,  pyrites,  and  other 
impurities  settle  at  the  bottom  and  are  caught  behind  the  dams,  while  the 
clean  coal  passes  over  the  dams  and  out  at  the  lower  end  of  the  trough. 
When  the  spaces  behind  the  dams  are  filled,  feeding  is  stopped  and  the 
refuse  in  the  dams  quickly  dumped.  This  form  of  washer  is  particularly 
successful  with  coal  mixed  with  fireclay.  One  washer  handles  from  75  to 
100  tons  of  coal  per  day,  and  one  man  can  attend  to  six  washers.  Each 
washer  requires  less  than  1 H.  P.  to  operate  it.  The  larger  the  coal,  the 
greater  must  be  the  slope  and  the  quantity  of  water  used. 

Jigs. — This  is  a general  term  applied  to  that  class  of  concentrating 
machines  in  which  the  separation  of  the  mineral  from  the  gangue  takes 
place  on  a screen  or  bed  of  material  and  is  effected  by  pulsating  up-and- 
down  currents  of  a fluid  medium. 

There  are  a number  of  different  methods  in  use  for  driving  the  pistons 
that  cause  the  pulsations  of  the  water  in  jigs.  Some  of  these  use  plain 
eccentrics,  giving  the  same  time  to  both  the  up  and  the  down  strokes  of  the 
pistons,  while  others  employ  special  arrangements  of  parts,  which  give  a 
quick  down  stroke  and  a slow  up  stroke,  thus  allowing  the  water  ample 
time  to  Work  its  way  back  through  the  bed  without  any  sucking  action 
from  the  piston.  This  tends  to  make  a better  separation  in  some  cases  than 
the  use  of  the  plain  eccentrics.  , . , , 

Stationary  Screen  Jigs.— This  class  is  illustrated  by  Fig.  21,  which  shows  a 
3-compartment  jig.  The  separation  takes  place  on  screens  supported  on 
wooden  frames  g,  and  is  effected  by  moving  the  water  in  each  compartment 
so  that  it  ascends  through  the  screen,  lifting  the  mineral  and  allowing  it  to 
settle  again,  thus  giving  the  material  an  opportunity  to  arrange  itself  accord- 
ing to  the  law  of  equally  falling  particles.  Each  compartment  is  composed 
of  two  separate  parts,  one  containing  the  screen  on  the  support  g and  the 
other  adjoining  it  and  arranged  so  that  the  piston  in  it  may  impart  the 
necessary  pulsations  to  the  water.  These  pistons  are  usually  loose  fitting  and 
are  operated  by  the  eccentrics  e on  the  shaft  s.  Jigs  operating  on  coarse  ore 
should  be  fed  with  approximately  sized  material,  when  the  ore  will  accumu- 
late near  the  bottom  on  the  screen  and  the  barren  portion  or  gangue  will 


438 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


be  carried  over  the  discharge.  Formerly,  the  concentrates  were  discharged 
from  jigs  intermittently  by  digging  out  the  tailings  first,  then  the  middlings, 
which  are  composed  of  pieces  containing  some  ore  and  some  gangue,  and 
then  the  concentrates,  but  it  has  been  found  that  the  concentrates  will 
flow  over  the  screen  like  a liquid  of  comparatively  heavy  specific  gravity, 


Fig.  21. 


Advantage  has  been  taken  of  this  fact  in  the  design  of  several  forms  of  jig 
discharges.  , , 

The  Heberle  gate,  Fig.  22,  acts  as  follows:  a is  a U-shaped  shield  fastened 
against  the  inside  of  the  jig  and  held  in  place  by  a band  b,  the  ends  of 

which  are  drawn  down  into  the  form  of 
bolts  and  pass  through  the  sides  of  the 
jig,  where  they  are  secured  with  suitable 
nuts.  The  shield  a may  be  raised  or 
lowered  by  loosening  the  band  b.  The 
discharge  takes  place  through  the  open- 
ing / in  the  side  of  the  jig,  the  size  and 
position  of  the  opening  being  regulated 
by  slides  c.  The  concentrates  k rest  on 
the  screen  e supported  by  a grating  d, 
while  the  tailings  i occupy  a higher  posi- 
tion. The  shield  a prevents  the  tailings 
from  flowing  out  through  the  opening  /, 
while  the  concentrates  flow  along  the 
screen  and  rise  to  a height  somewhat 
lower  than  the  top  of  the  tailings  in  the 
jig,  when  they  are  discharged  through  the 
opening  / over  the  spout  h,  as  shown  at 
p.  The  tailings  are  usually  discharged 
over  the  dam  at  the  end  of  the  jig,  and 
in  some  cases  a third  discharge  is  provided  of  the  Heberle-gate  pattern 
and  so  arranged  that  the  middlings  will  flow  out  through  it  and  discharge 
separately  from  the  tailings  and  the  concentrates. 

In  the  case  of  jigs  handling  fine  material,  the  material  may  be  sorted  by 
hydraulic  classifiers  and  then  introduced  on  to  the  jigs.  In  this  class  the 
mineral  will  be  in  the  form  of  relatively  small  pieces,  while  the  gangue  will 
occur  as  relatively  large  pieces.  Advantage  may  be  taken  of  this  fact  by 
regulating  the  mesh  of  the  jig  screen  so  that  the  concentrates  will  pass 
through  into  the  space  below  the  screen,  commonly  called  the  hutch,  while 
the  tailings  will  pass  over  the  tailing  dam.  In  some  cases  the  gate 
discharge  is  employed  on  the  side  to  remove  the  middlings.  The  middlings 
are  recrushed  and  treated  on  other  machines.  This  form  of  concentration 
has  been  used  very  largely  in  connection  with  the  Lake  Superior  copper 
ores,  the  values  of  which  occur  as  metallic  copper  in  a relatively  light 
gangue,  and  also  in  concentrating  tin  ores  that  occur  in  the  light  gangue 
containing  considerable  mica. 


THEOR  Y OF  JIGGING. 


439 


Theory  of  Jigging.-By  far  the  most  exhaustive  investigations  on  the  theory 
of  jigging  carried  on  in  America  are  those  of  Prof.  Robert  H.  Richards,  the 
Massachusetts  Institute  of  Technology,  and  the  greater  part  of  ^following 
theoretical  discussion  is  based  on  his  several  papers  published  m the  Trans 

actions  of  the  American  Institute  of  Mining  Fmgineers. 

Four  laws  of  jigging  are  given  by  the  several  ®f 

equal  settling  particles,  under  free  settling  conditions,  (2)  the  law  ot 
interstitial  currents,  or  settling  under  hindered  settling  conditions;  (3)  the 

la^hlafiretleofathese  is4  the  mosTim^rtant.'but  the  others  are  elements  that 

CanE^ta,^^p1artl^t^U„tre?  W»owing  formulas  to  repre- 
senAhe  relation  between  diameter  of  grains  and  rate  of  falling  in  water  for 
irregularly  shaped  grains:  _______ 

V = 2.73/ — 1).  for  roundish  grains; 

V = 2.44/ J)[S  — 1),  for  average  grains; 

V = 2.37j /W(8  — 1),  for  long  grains; 

V = 1.92i/ D(8  — 1),  for  flat  grains,  _ 

in  which  V = velocity  in  meters  per  second;  D = diameter  of  particles  in 

meByS  means  ofXes^^fferenffomSas.  the  ratios  of 
different  particles  that  will  be  equal  settling  in  water  can  be  computed. 
Professor  Richards  has  not  found  these  formu]as  to  ho  d in  a]l  c^es  in 
practice,  and,  as  the  result  of  elaborate  experiments,  he  gives  the  following 
table  * 

Equal  Settling  Factors  or  Multipliers. 

Table  of  eaual  settling  factors  or  multipliers  for  obtaining  the  diameter  of 
a quartz  grain  that  will  be  equal  settling  under  free  settling  conditions  with 
the  mineral  specified. 


Specific  Gravity. 

Velocity  in  Inches  per  Second. 

Rittinger’s 

Multipliers. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Author’s  Multipliers. 

Anthracite  

Epidote 

Sphalerite 

Pyrrhotite  

Chalcocite  

Arsenopyrite  ... 

Cassiterite 

Anitmony 

Wolframite 

Galena  

Copper  

Quartz  

1.473 

3.380 

4.046 

4.508 

5.334 

5.627 

6.261 

6.706 

6.937 

7.856 

8.479 

2.640 

.500 

1.57 

.352 

1.35 

1.46 

1.73 

1.90 

1.90 

2.11 

2.71 

2.71 

2.71' 

2.71 

.225 

1.05 

1.05 

1.29 

1.47 

1.57 

1.79 

2.00 

1.83 

1.83 

2.00 

.213 

1.13 

1.17 

1.48 

1.62 

1.89 

2.00 

2.00 

2.07 

2.26 

2.36 

1.50 

1.62 

2.00 

2.07 

2.42 

2.73 

2.73 

2.86 

3.00 

3.00 

1.61 

1.64 

2.22 

2.28 

2.56 

2.93 

2.93 

3.04 

3.42 

3.20 

1.56 

1.68 

2.26 

2.41 

2.72 

3.03 

3.03 

3.21 

3.65 

3.58 

1.56 

1.66 

2.13 

2.44 

2.84 

3.05 

2.98 

3.28 

3.76 

3.76 

1.47 

1.56 

2.08 

2.17 

2.94 

3.12 

3.00 

3.26 

3.75 

3.75 

.288 

1.45 

1.85 

2.14 

2.64 
2.82 
3.32 
3.48 

3.64 
4.01 
4.56 

The  significance  of  the  above  table  is  as  follows:  If  a piece  o-  anthracite 
of  a certain  size  falls  in  water  with  a velocity  of  4m.  per  second  a piece  of 
quartz  0.213  times  the  diameter  of  the  anthracite  will  fall  with  the  same 
velocity.  If  a piece  of  copper  of  a certain  size  falls  with  a velocity  of  7 in. 
per  second,  a piece  of  quartz  3.58  times  as  large  as  the  copper  will  fall  with 

^InterstitTal^Currents,  or  Law  of  Settling  Under  Hindered  Settling  Conditions 

If  d equals  the  diameter  of  a falling  particle,  and  D that  of  the  tube  m which 

it  falls,  the  larger  the  fraction  the  greater  will  be  the  retardation  or  loss 


440 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


ODD 


© 


Pyrrhotite 2.808 

Sphalerite 2.127 

Epidote  1.628 

Anthracite  1782 


of  velocity  by  the  particle.  When  this  fraction  equals  1,  the  particle' stops. 
If  in  Fig.  23  (a),  the  larger  circles  represent  particles  of  quartz  and  the 
smaller  circles  equal  settling  particles  of  galena,  then  if  these  mixed  parti- 
cles are  settling  together  or  are  held  in  suspension  by  a rising  current  of 
water,  each  particle  may  be  considered  to  be  falling  in  a tube,  the  walls  of 
which  consist  of  the  surrounding  particles.  Substituting  a circle  in  each 

case  for  the  imaginary  tube,  we  have 
Fig.  23  (6)  representing  the  condi- 
f ) ( ) tions  for  galena  and  quartz,  the 

v,  ^ outer  circle  in  each  case  represent- 

ing  the  imaginary  tube.  Evidently, 

is  much  smaller  for  the  galena 

^ ^ than  for  the  quartz,  and  it  will 

V.  J V J {0t  therefore  be  much  less  impeded  in 

v o.  its  fall  than  the  quartz;  hence,  the 

(a)  Fig.  23.  particles  of  galena  found  adjacent 

to  the  particles  of  quartz  will  be 
smaller  than  the  ratio  that  the  law  of  equal  settling  particles  under 
free  settling  conditions  would  indicate.  Application  of  this  principle  is 
found  when  a mass  of-  grains  is  subjected  to  a rising  current  of  sufficient 
force  to  rearrange  the  grains  according  to  their  settling  power  and  the 
grains  are  said  to  be  treated  under  hindered  settling  conditions,  as  on  the 

6 Interstdfal  factors,  or  multipliers  for  obtaining  the  diameter  of  the  particle 
of  quartz  that  under  hindered  settling  conditions  will  be  found  adjacent 
to  and  in  equilibrium  with  the  particle  of  the  mineral  specified,  are  the 
following; 

Copper 8.598  Cassiterite  4.698 

Galena 5.842  Arsenopyrite . .3.737 

Wolframite...  5.155  Chalcocite 3.115 

Antimony  ...4.897  Magnetite 2.808 

These  signify  that,  after  pulsion  has  done  its  work  on  a jig  bed,  for  exam- 
ple, where  quartz  and  anthracite  are  being  jigged,  the  grains  will  be  so 
arranged  that  the  grains  of  quartz  are  .1782  times  the  diameter  of  the  grains 

of  anthracite  that  are  adjacent  to  and  in  equilibrium  with  them. 

Acceleration. — A particle  of  galena  that  is  equal  settling  to  the  particle  of 
quartz  reaches  its  maximum  velocity  in  perhaps  TV  the  time  required  by  the 
quartz.  The  oft-repeated  pulsations  of  a jig,  therefore,  give  the  galena  par- 
ticles a decided  advantage  over  the  quartz,  placing  beside  the  quartz,  when 
equilibrium  is  reached,  a much  smaller  particle  of  galena  than  we  should 
expect  according  to  the  law  of  equal  settling  particles. 

Suction  acts  to  draw  down  through  the  screen  small  grains,  mainly  oi  tne 
heavier  mineral,  which  are  distributed  among  large  grains.  It  increases  as 
the  length  of  plunger  stroke,  with  the  difference  in  specific  gravity  of  the 
two  minerals,  and  with  the  diminishing  of  the  thickness  of  the  bed  on  the 
sieve,  whether  of  the  heavier  mineral  only  or  of  both  minerals.  The  law 
of  suction  seems  to  be  that  jigging  is  greatly  hindered  by  strong  suction 
where  the  two  minerals  are  nearly  of  the  same  size,  the  quickest  and  best 
work  then  being  done  with  no  suction;  but  when  the  two  minerals  differ 
much  in  size  of  particles,  the  quartz  being  the  larger,  strong  suction  is  not 
only  a great  advantage,  but  may  be  necessary  to  get  any  separation  at  all. 
Experiments  have  indicated  an  approximate  boundary  between  grains  that 
are  helped  and  those  that  are  hindered  by  suction;  namely,  if  the  diameter 
of  the  quartz  particles  is  equal  to  or  greater  than  3.52  times  the  diameter 
of  the  other  mineral  particles,  then  separation  is  helped  by  suction;  it  less, 
separation  is  hindered.  This  value  3.52  (obtained  by  dividing  .0683  by  .0195) 
is  approximate  only,  and  it  will  differ  with  the  fracture  of  the  quartz  under 
consideration;  if  the  quartz  grains  are  much  flattened,  it  will  have  a large 

ValEccentric  jigs  invariably  spend  more  time  on  pulsion  than  accelerated 
jigs.  Is  it  not  fair  to  conclude  that  the  eccentric  jigs  are  better  adapted  tor 
treating  sands  that  require  the  most  pulsion?  Such  sands  are  the  sized 
products  from  the  trommel  and  the  first  spigot  of  the  hydraulic  classifier. 
On  the  other  hand,  mav  not  the  long-protracted  mild  suction  of  the  acceler- 
ated jig  be  best  adapted  to  the  treatment  of  such  products  as  require 
primary  suction  for  their  separation;  fox  example,  the  second  spigot  and 


THEORY  OF  JIGGING. 


44  J 


the  following  spigots  of  the  hydraulic  classifier?  This  may  he  the  reason 

Sfoft^e ineCra "ecSre 

the  condition  as  presented  in  this  particular  by  experiments 

Two  extreme  suggestions  arise  from  a contemplation  o t ^be^per*  5: 
we  have  carried  on:  (1)  On  closely  sized  products,  an  accelerated  Jigshould 
hf^  rim  back  wards  to  lengthen  out  the  pulsion  period,  which  is  the  only 
neriod  that  does  any  work;  and  (2)  the  accelerated  jig  should  be  run  for- 
wards on  the  spigot  products  of  the  hydraulic  separator,  to  increase  t e 

period  of  suctiom  suggestion,  there  are  two  difficulties,  either  of 

which  mlv  cancel  thl  advantage:  the  violent  downward  motion  of  he 

quick  return  will  tend  to  “ blind  up  ’’the  sieve;  and,  second,  the  same  action 
will  tend  to  pulverize  a soft  mineral  like  galena.  with 

Professor  Richards  summarizes  his  experiments  m connection  with 
iigging  as  follows-  The  two  chief  reactions  of  jigging  are  pulsion  and  suc- 
tion. gThe  effect  of  pulsion  depends  on  the  laws  of  interstitial  currents,  or 
of  ooual  settling  particles,  under  hindered  settling  conditions.  The  cbi®£ 
function  of  pulsfon  is  to  save  the  larger  grains  of  the  hea^e^P1^e^1’^tion 
grains  that  settle  faster  and  farther  than  the  waste.  The  effect  of  suction 
depends  on  the  interstitial  factor  of  the  minerals  to  be  separated.  It  this 
factor  is  greater  than  3.70,  suction  will  be  efficient  and  rapid  If  the  factor 
is  less  than  3.70,  suction  will  be  much  pampered  and  leered.  function  of 
lone-  stroke  will  help  to  overcome  this  difficulty.  I he  cnici  luncuon  oi 
suction  is  to  save  the  particles  that  are  too  small  tobesayed  by 

of  interstitial  currents,  acting  through  the  Pul^°?  th&nJr^Wffing  cfo^elv 
mixed  sizes,  pulsion  with  full  suction  should  be  used  For  Jigging  closely 
<5i7Pd  Tvroduots  nulsion  with  a minimum  of  suction  should  be  usea. 

The  degree  of  sizing  needed  as  preparation  for  jigging,  if  perfect  work  is 
desired  depends  S<m  the  interstitial  ffictor  of  the  minerals  to  be  separated. 
If  the  factor  is  above  3.70  (assuming  this  value  to  1 

thpn  sizino-  is  simplv  a matter  of  convenience.  The  fine  slimes  snouia  oi 
course  be  removed-  and  if  it  is  more  convenient  to  send  egg  size,  nut  size, 
pea  Jfze ^ anTsand  size,  each  to  its  own  jig,  the  suitable  screens  should  be 
Provided  for  this  purpose  and  a hydraulic  separator  for  grading  the  finest 
sizes.  But  if  on  the  other  hand,  the  factor  is  below  3.70,  then  the  jigging  of 
mixed  sizes  cannot  give  perfectly  clean  work,  and  the  separation  will  be 
flooroximate  onlv.  To  effect  the  most  perfect  separation,  close  sizing  must 
be  ^adopted  and  the  closer  the  sizes  are  to  one  another,  the  more  rapid  and 
nerfpetPwili  the  iigging  be.  There  may  be  conditions  where  the  jigging  oi 
mixed  sizes  of  tins  cfass  will  be  considered  sufficiently  satisfactory , as  an 

GX  Removal  o^Siflp hur^F romC  C^f ^The  object  of  washing  coal  is  to  remove  the 
slate  and  pyrites,  thus  reducing  the  amount  of  ash  and  sulphur.  Manyforms 
of  wash er s easily  and  cheaply  reduce  the  slate  from  20$  in  the  coal  to  8$  of 
nsh  fn  the  coke  but  it  is  much  more  difficult  to  reduce  4$  of  sulphur  m the 
ronl  to  K or  less  of  sulphur  in  the  coke.  Sulphur  occurs  in  the  coal  m 
three  forms  as  hydrogen  sulphide,  calcium  sulphate,  and  pyrite.  The  first 
is  volatile  and  is  removed  in  coking,  the  second  cannot  usually  be  J^moved 
and  it  is  the  removal  of  the  third  form  with  which 
washing  has  to  do.  The  presence  of  water  in  the  coke  ovens  apparently 
assists  the  removal  of  the  sulphur;  but  wet  coals  require  a longer  time  for 

coking  than  dry  and  therefore,  pyrite  should  be  removed  as  far  as  practicable 

before* charging  the  coal  into  the  coke  ovens.  The  pyrite  m coal  it  c 5“  t 
from  the  mfne  seems  to  be  in  particles  even  fine^ 

This  irrmalnable  nowder  or  flour  pyrites  floats  m air  or  water,  inis  uemg 
F£1S the cram™ practice  of  using  the  water  over  and  over  agam  in  a 
washerv  caLot  Mve  tfie  best  results  In  the  removal  9f  sulphur,  as  some 
flour  Dvrites  will  he  carried  hack  each  time  and  remain  with  the  washed 
coal  PExDerimentsmade  by  Mr.  C.  C.  Upham,  of  New  York  Citv,  show  that 
the  critical  size  at  which  an  almost  complete  division  of  the  coal  and  pyrites 
takes  place  varies  with  coals  from  different  districts  and  beds,  and  m laying 
out  coahwashing  plants,  the  proper  fineness  of  crushing  should  he  deter- 
mined  beforehand  by  careful  experiment. 


442 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


Preparation  of  Anthracite.— The  method  of  preparing  anthracite  coal  is 
clearly  shown,  graphically,  by  the  diagram  below.  This  consists  in  screen- 
ing the  coal  over  bars  and  through  revolving  or  over  shaking  screens, 
together  with  breaking  it  with  rolls  to  produce  the  required  market  size. 


BARS  3" APART 
BARS  4 f APART 
n\un  SCREE H 


Diagram  Showing  Method  of  Preparing  Anthracite  Coal. 

The  large  lumps  of  slate  and  other  impurities  are  separated  by  hand  on  the 
platform  near  the  dump,  while  the  smaller  portions  are  picked  out  by  auto- 
matic pickers  or  by  hand  by  boys  or  old  men  seated  along  the  chutes  leading 
to  the  shipping  pockets  or  bins.  The  smaller  sizes  are  cleaned  by  jigging. 


HANDLING  OF  COAL. 


443 


HANDLING  OF  MATERIAL. 

Anthracite  Coal.— The  following  may  be  taken  as  average  figures  for  the 
angle  or  grade  of  chutes  for  anthracite  coal,  to  be  used  where  the  chutes  are 
lined  with  sheet  steel:  For  broken  or  egg  coal,  2*  in.  per  ft.;  for  stove  or 
chestnut  coal,  3£  in.  per  ft.;  for  pea  coal,  4*  in.  per  ft.;  for  buckwheat  coal, 
6 in.  per  ft.;  for  rice  coal,  7 in.  per  ft.;  for  culm,  8 in.  per  ft. 

If  the  coal  is  to  start  on  the  chute,  1 in.  per  ft.  should  be  added  to  each  of 
the  above  figures;  while  if  the  chutes  are  lined  with  manganese  bronze  m 
place  of  steel,  the  above  figures  can  be  reduced  1 in.  per  ft.  for  coal  in 
motion,  or  would  remain  as  in  the  table  to  start  the  coal.  When  the  run  of 
mine  is  to  be  handled,  as  in  the  main  chute,  at  the  head  of  the  breaker,  the 
angle  should  be  not  less  than  5 in.  per  ft.,  or  practically  22£°  from  the  hori- 
zontal. If  chutes  for  hard  coal  are  lined  with  glass,  the  angle  can  be 
reduced  from  30$  to  50$,  depending  somewhat  on  the  nature  of  the  coal. 
In  all  cases,  the  flatter  the  coal,  the  steeper  the  angle  must  be,  on  account  of 
the  large  friction  surfaces  exposed,  compared  with  the  weight  ot  the  piece. 
If  chutes  are  lined  with  cast  iron,  the  angle  should  be  about  the  same  as 
that  emploved  for  steel,  though  sometimes  a slightly  greater  angle  is  allowed. 

The  following  table  is  printed  through  the  courtesy  of  the  Link-Belt 
Engineering  Co.,  Philadelphia,  Pa.: 

Pitch  at  Which  Anthracite  Coal  Will  Run,  in  Inches  per  Foot. 


Kind  of  Coal. 

Sheet  Iron. 

Cast 

Iron. 

Glass. 

Glass. 

Start 

on. 

Con- 

tinue 

on. 

Start 

on. 

Start 

on. 

Con- 

tinue 

on. 

Start 

on. 

Con- 

tinue 

on. 

Dry. 

Wet. 

Broken  slate 

5£ 

4f 

5* 

3£ 

3 

Dry  egg  slate 

5£ 

4* 

5£ 

3£ 

3 

Dry  stove  slate 

5£ 

4» 

5£ 

3£ 

3 

Dry  chestnut  slate 

L ' 

4» 

5£ 

3£ 

3 

Broken  coal 

2* 

2£ 

Egg  coal 

3| 

3 

2| 

2£ 

2£ 

Stove  coal 

4£ 

4£ 

4£ 

3 

2£ 

2£ 

2£ 

Chestnut  coal 

4f 

4£ 

4£ 

3 

■ 2£ 

3 

2£ 

Pea  coal 

5£ 

5 

51 

3£ 

2£ 

3 

Buckwheat  No.l ... 

3f  * 

3£ 

3£ 

3£ 

O 1 

Buckwheat  No.2... 

3£ 

3£ 

3£ 

3£ 

A 1 

Buckwheat  No.3... 

4f 

3f 

4? 

Buckwheat  No.4.... 

4£ 

4* 

4t 

4£ 

Bituminous  Coal  —When  the  run  of  mine  is  to  be  handled,  the  angle  ot 
the  chutes  should  be  from  35°  to  45°  from  the  horizontal,  or  from  8*  m.  to 
12  in  per  ft.  If  the  coal  is  wet,  the  angle  should  always  be  steeper,  and 
coarse  coal  will  slide  on  a flatter  angle  than  slack  or  fine  coaL 

Ore,  Rock,  Etc.— For  coarse  fairly  dry  ore,  i.  e.,  from  2 in.  or  3 in.  size  up, 
chutes  may  have  an  angle  of  45°,  or  if  the  material  is  always  to  be  in  motion, 
the  ore  will  sometimes  slide  on  40°.  For  fine  ore  or  run  of  mine,  the  chutes 
should  have  an  angle  of  50°  from  the  horizontal  or  practically  14  m.  vertical 
to  1 ft.  horizontal.  . , „ , r x_ 

Flumes  and  Launders.— Water  flumes  are  given  grades  varying  from  4 or  5 to 
20  or  30  ft.  per  mile,  depending  on  the  surface  of  the  ground  and  the  amount 
of  water  to  be  carried.  Practical  results  have  demonstrated  the  fact  that  m 
ordinary  ground  the  water  should  travel  at  the  rate  of  from  180  to  200  ft.  per 

milWhere  rather  coarse  stuff  is  to  be  carried  through  launders  in  a mill  with 
a comparatively  small  amount  of  water,  an  angle  of  2 m.  per  ft.  should  be 
used.  With  an  excess  of  water,  1 in.  per  ft.  will  be  ample.  The  spouting  tor 
vanners  or  launders  from  trommels  carrying  rather  fine  material  should 
have  a grade  of  about  2 in.  per  ft.  In  placer  mining,  the  minimum  grade 


444 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


for  the  sluice  should  not  be  less  than  i in.  per  ft.,  or  about  4j  in.  per  rod. 
Experiments  made  in  river  gravel  have  shown  that  with  a grade  of  from  1 m 
20  to  1 in  25,  60  cu.  ft.  per  min.  will  wash  140  to  175  cu.  yd.  per  day  of  24  hours. 

No  absolutely  definite  figures  can  be  given  on  this  subject,  owing  to  the 
fact  that  the  nature  of  the  ore  plays  an  important  part,  and  while  angular 
quartzose  ore  can  be  transported  at  a comparatively  flat  angle,  it  may  be 
necessary  to  use  quite  a steep  angle  if  the  material  is  of  a clayey  nature  or 
contains  many  large  flat  plates,  exposing  large  friction  surfaces  when  com- 
pared to  the  mass  of  the  pieces.  „ x.  _ . _ _ . , 

The  following  tables  are  printed  through  the  courtesy  of  the  Link-Belt 
Engineering  Co.,  Philadelphia,  Pa.: 

Horizontal  Pressure  Exerted  by  Bituminous  Coal  Against  Vertical 
Retaining  Walls  per  Foot  of  Length. 


97  so.Y' 

/ m 


Surface  horizontal  { {^^0  lowest  ft. 

Surface  sloping  { preslurefowest  ft. 
Angle  of  repose 

d — height  of  wall  in  feet  or  a b 


= 6.37  d2 

= 6.37(2  ci  — 1) 
= 10  d2 

= 10(2  d — 1) 

= 35° 


BITUMINOUS. 


4-j 

Horizontal 
Surface. 
b m. 

Sloping 
Surface. 
b e. 

rt 

Horizontal 
Surface. 
b m. 

Sloping 

Surface. 

be. 

S 

rO 

A 

<D 

A 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

e 

rO 

•g 

A 

© 

A 

. j 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

1 

6.4 

6.4 

10 

10 

26 

4,305 

325 

6,760 

510 

2 

25.0 

19.0 

40 

30 

27 

4,641 

338 

7,290 

530 

3 

57.0 

32.0 

- 90 

50 

28 

4,993 

350 

7,840 

550 

4 

102.0 

45.0 

160 

70 

29 

5,358 

363 

8,410 

570 

5 

159.0 

57.0 

250 

90 

30 

5,733 

376 

9,000 

590 

6 

229.0 

70.0 

360 

110 

31 

6,122 

389 

9,610 

610 

7 

312.0 

83.0 

490 

130 

32 

6,523 

401 

10,240 

630 

8 

407.0 

96.0 

640 

150 

33 

6,935 

414 

10,890 

650 

9 

516.0 

108.0 

810 

170 

34 

7,362 

427 

11,560 

670 

10 

637.0 

121.0 

1,000 

190 

35 

7,778 

440 

12,250 

690 

11 

770.0 

134.0 

1,210 

210 

36 

8,253 

452 

12,960 

710 

12 

917.0 

146.0 

1,440 

230 

37 

8,754 

465 

13,690 

730 

13 

1,076.0 

159.0 

1,690 

250 

38 

9,193 

478 

14,440 

750 

14 

1,248.0 

172.0 

1,960 

270 

39 

9,682 

490 

15,210 

770 

15 

1,433.0 

185.0 

2,250 

290 

40 

10,192 

503 

16,000 

790 

16 

1,630.0 

197.0 

2.560 

310 

41 

10,669 

516 

16,810 

810 

17 

1,840.0 

210.0 

2,890 

330 

42 

11,236 

529 

17,640 

830 

18 

2,063.0 

223.0 

3,240 

350 

43 

11,797 

541 

18,490 

850 

19 

2,298.0 

236.0 

3,610 

370 

44 

12,331 

554 

19,360 

870 

20 

2,548.0 

248.0 

4,000 

390 

45 

12,968 

567 

20,250 

890 

21 

2,809.0 

261.0 

4,410 

410 

46 

13,478 

580 

21,160 

910 

22 

3^083.0 

274.0 

4,840 

430 

47 

14,100 

592 

22,090 

930 

23 

3,369.0 

287.0 

5,290 

450 

48 

14,679 

605 

23,040 

950 

24 

3,669.0 

299.0 

5,760 

470 

49 

15,275 

618 

24,010 

970 

25 

3*981.0 

312.0 

6,250 

490 

50 

15,925 

631 

j 25,000 

990 

Weight  of  coal  = 47  lb.  per  cu.  ft. 


HANDLING  OF  COAL. 


445 


Horizontal  Pressure  Exerted  by  Anthracite  Coal  Against  Vertical 
Retaining  Walls  per  Foot  of  Length. 


total  pressure  = 
pressure  lowest  ft.  = 


Surface  horizontal 

Surface  sloping  { pVessure  lowest  ft. 
Angle  of  repose 
d = height  of  wall  in  feet. 


9.78  d2 
9.78(2  d- 1) 
14.22  d2 
= 14.22(2  d-1) 
= 27° 


ANTHRACITE. 


4-a 

q 

Horizontal 

Surface. 

bm. 

Sloping 

Surface. 

be. 

8 

rO 

6 

6 

r-H  fH 

03  3 

g 

'S  p 

02  02 

& 

n 

02 
O 02 

Ph 

xn  0> 

Z* 

Qj  O 

"O  02 

£ 

02 

<u 

u 1> 
Q.  O 

1 

9.78 

9.78 

14.22 

14.22 

2 

39.12 

29.34 

56.88 

42.66 

3 

88.02 

48.90 

127.98 

71.10 

4 

156.48 

68.46 

227.52 

99.54 

5 

244.50 

88.02 

355.50 

127.98 

6 

352.08 

107.58 

511.92 

156.42 

7 

479.22 

127.14 

696.78 

184.86 

8 

625.92 

146.70 

910.08 

213.30 

9 

792.18 

166.26 

1,151.82 

241.74 

10 

978.00 

185.82 

1,422.00 

270.18 

11 

1,183.38 

205.38 

1,720.62 

298.62 

12 

1,408.32 

224.94 

2,047.68 

327.06 

13 

1,652.82 

244.50 

2,403.18 

355.50 

14 

1,916.88 

264.06 

2,787.12 

383.94 

15 

2,200.50 

283.62 

3,199.50 

412.38 

16 

2,503.68 

303.18 

3,640.32 

440.82 

17 

2,826.42 

322.74 

4,109.56 

469.26 

18 

3,168.72 

342.30 

4,607.28 

497.70 

19 

3,530.58 

361.86 

5,133.42 

526.14 

20 

3,912.00 

381.42 

5,688.00 

554.58 

21 

4,313.00 

400.98 

6,271.00 

583.26 

22 

4,733.50 

420.54 

6,882.50 

611.46 

23 

5,173.70 

440.10 

7,522.50 

639.90 

24 

5,633.30 

459.67 

8,190.70 

668.35 

25 

6,112.60 

479.22 

8,887.50 

696.79 

4-S 

P 

Horizontal 

Surface. 

bm. 

Sloping 

Surface. 

be. 

e 

rO 

A 

■P 

ft 

o» 

p 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

26 

6,611.1 

498.78 

9,612.8 

725.21 

27 

7,129.5 

518.35 

10,366.0 

753.67 

28 

7,667.6 

537.90 

11,149.0 

782.10 

29 

8,225.0 

557.46 

11,988.0 

810.54 

30 

8,802.0 

577.01 

12,797.0 

839.00 

31 

9,398.5 

596.59 

13,665.0 

867.41 

32 

10,015.0 

616.14 

14,561.0 

895.86 

33 

10,650.0 

635.70 

15,486.0 

924.30 

34 

11,306.0 

655.26 

16,439.0 

952.70 

35 

11,980.0 

674.81 

17,420.0 

981.19 

36 

12,675.0 

694.39 

18,429.0 

1,009.60 

37 

13,389.0 

713.94 

19,467.0 

1,038.10 

38 

14,123.0 

733.50 

20,533.0 

1,066.50 

39 

14,875.0 

753.07 

21,629.0 

1,095.00 

40 

15,648.0 

772.63 

22,752.0 

1,123.40 

41 

16,440.0 

792.20 

23,904.0 

1,151.80 

42 

17,252.0 

811.74 

25,084.0 

1,180.30 

43 

18,083.0 

830.73 

26,293.0 

1,208.70 

44 

18,934.0 

850.86 

27,530.0 

1,237.20 

45 

19,804.0 

870.41 

28,793.0 

1,265.60 

46 

20,695.0 

889.99 

30,090.0 

1,294.00 

47 

21,605.0 

909.54 

31,412.0 

1,322.30 

48 

22,533.0 

929.10 

32,763.0 

1,350.90 

49 

23,482.0 

948.66 

34,143.0 

1,379.40 

50 

24,450.0 

968.21 

35,550.0 

1,407.90 

Horsepowers  for  Coal  Conveyors  (Coal  Included). 

Speed,  100  ft.  per  minute.  Conveyors,  100  ft.  long.  Standard  steel  troughs. 


■"I® 

°.o 

flP 


Size  of 
Flights 
In. 


4 X 10 
4X12 
5X12 
5X15 
6X18 


Horizontal . 


Inclined. 


12  In. 

Between 

Flights. 


2} 

3 

3* 

4* 

54 


18  In. 

Between 

Flights. 


2 

24 

3 

34 

44 


12  In. 
Between 
Flights. 


3 
34 

4 
54 
64 


o .g 

N rd 

5° 


Size  of 
Flights. 
In. 


5X15 
6X18 
8X  18 
8 X 20 
8 X 24 
10  X 24 


Horizontal. 


16  In. 

Between 

Flights. 


4 

5 

7 

8 
94 

124 


24  In. 

Between 

Flights. 


34 

4 

5 

6 

7 

8 


Inclined. 


16  In. 

Between 

Flights. 


44 

54 

8 

10 

114 

14 


446 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


Weights  and  Capacities  of  Standard  Steel  Buckets. 


Chain. 

Size  of  Bucket. 
In. 

Weight  of 
Bucket. 
Lb. 

Capacity  of 
Bucket. 
Lb. 

Capacity  of  Elevator.  100'  per  Min. 

Number  of 
Drawing. 

Lb.  per  Min. 

Net  Tons  per  Hr. 

a> 

W) 

*d  - 

12  X 9 X 11? 

181 

11 

1,100 

33.0 

5,357 

o 

Q 

14  X 9X11? 

221 

121 

1,250 

37.5 

5,357 

0 

18  X 9X11? 

27 

161 

1,650 

49.5 

5,357 

24  X 9 X Ilf 

36 

22 

2,200 

66.0 

5,357 

12X10  X 161 

20 

19 

1,380 

41.4 

5,357 

tS 

bC 

18  X 10  X 161 

29 

281 

2,072 

62.2 

5,357 

'O 

O 

24X10X161 

38 

38 

2,760 

82.8 

5,357 

ft 

30  X 10  X 161 

461 

471 

3,450 

103.5 

5,357 

a 

18  X 12  X 161 

31 

33 

2,400 

72.0 

5,357 

24  X 12  X 161 

40 

44 

3,200 

96.0 

5,357 

30  X 12  X 161 

48 

55 

4,000 

120.0 

5,357 

Buckets  taken  £ full.  Buckets  continuous.  1 lb.  of  coal  = 34  cu.  in. 


Elevating  Capacities  of  Malleable  Iron  Buckets. 

Table  gives  tons  (2,000  lb.)  of  pea  coal  per  hour  at  100  ft.  per  minute. 


Buckets. 


Capacities. 


Distance  Between  Buckets  in  In. 


Size 

In. 

Wt. 

Lb. 

Cu. 

In. 

Lb. 

8 

10 

1 

12 

14 

16 

18 

20 

22 

24 

2f 

X 

4 

0.75 

15 

0.48 

2.16 

1.73 

1.44 

1.23 

1.08 

1.94 

31 

x 

5 

1.50 

31 

0.97 

4.36 

3.49 

2.91 

2.49 

2.18 

4 

X 

6 

2.00 

51 

1.57 

7.06 

5.65 

4.71 

4.04 

3.53 

3.14 

2.83 

3.81 

41 

x 

7 

2.56 

75 

2.33 

10.38 

8.39 

6.99 

5.99 

5.19 

4.66 

4.19 

4.72 

5 

x 

8 

3.56 

102 

3.15 

11.34 

9.45 

8.10 

7.09 

6.30 

5.67 

5.15 

6 

x 

10 

5.47 

185 

5.73 

17.19 

14.73 

12.88 

11.46 

10.31 

9.38 

8.59 

7 

x 

12 

8.97 

287 

8.90 

22.88 

20.02 

17.80 

16.02 

14.56 

13.35 

7 

X 

14 

11.41 

295 

9.14 

20.56 

18.28 

16.45 

14.95 

13.71 

10 

X 

18 

1 

1 

Weight  of  1 cu.  ft.  of  pea  coal  = 53.5  lb.  32.3  cu.  in.,  or  .0187  cu.  ft.  = 1 lb. 


Conveying  Capacities  of  Flights  at  100  Ft.  Per  Minute. 


(Tons  of  Pea  Coal  per  Hour.) 


Size 

of 

Flight. 

In. 

Horizontal. 

Inclined. 

10° 

20° 

30° 

Lb.  Coal 
per 

Flight. 

Every 
16  In. 

Every 
18  In. 

Every 
24  In. 

Every 
24  In. 

Every 
24  In. 

Every 
24  In. 

4 X 10 

33.75 

30 

22.5 

15 

18.0 

14.25 

10.5 

4 X 12 

42.75 

38 

28.5 

19 

24.0 

18.00 

13.5 

5 X 12 

51.75 

46 

34.5 

23 

28.5 

22.50 

16.5 

5 X 15 

69.75 

62 

46.5 

31 

40.5 

31.50 

22.5 

6 X 18 

80 

60.0 

40 

49.5 

40.50 

31.5 

8X18 
8X  20 
8 X 24 
10  X 24 

120 

90.0 

105.0 

135.0 
172.5 

60 

70 

90 

115 

72.0 

84.0 
120.0 
150.0 

57.00 
66.50 

96.00 
120.00 

48.0 

56.0 

72.0 

90.0 

Note. — These  ratings  are  for  continuous  feed.  2,000  lb.  — 1 ton. 


HANDLING  OF  COAL. 


447 


Horsepower  for  Bucket  Elevators, 

N = number  taken  from  table; 

= height  of  elevatpr  in  feet; 
co  = weight  of  material  in  one  bucket; 
d = distance  apart  of  buckets,  in  inches. 


Revolu- 

tions 

per 

Minute. 

Diameter  of  Head-Wheels. 

Revolu- 

tions 

per 

Minute. 

22  In. 

24  In. 

26  In. 

28  In. 

30  In. 

32  In. 

10 

.064 

.070 

.075 

.080 

.087 

.093 

10 

12 

.077 

.083 

.090 

.097 

.104 

.111 

12 

14 

.089 

.096 

.106 

.114 

.121 

.130 

14 

16 

.102 

.111 

.121 

.130 

.140 

.148 

16 

18 

.115 

.125 

.136 

.146 

.157 

.167 

18 

20 

.128 

.139 

.151 

.162 

.174 

.186 

20 

22 

.140 

.153 

.166 

.179 

.191 

.204 

22 

24 

.153 

.167 

.181 

.195 

.209 

.223 

24 

26 

.166 

.181 

.196 

.211 

.226 

.242 

26 

28 

.179 

.195 

.211 

.227 

.244 

.260 

28 

30 

.191 

.209 

.226 

.244 

.261 

.279 

30 

32 

.204 

.223 

.241 

.260 

.278 

.297 

32 

34 

.217 

.237 

.256 

.276 

.296 

.316 

34 

36 

.230 

.251 

.271 

.292 

.313 

.334 

36 

38 

.242 

.265 

.287 

.309 

.331 

.353 

38 

40 

.255 

.279 

.302 

.325 

.348 

.372 

40 

COST  OF  UNLOADING  COAL. 

Coal  is  generally  unloaded  from  railroad  cars  into  the  hold  of  a vessel  by 
some  form  of  unloader,  which  usually  raises  the  car  bodily  and  dumps  it 
directly  into  the  hold  of  the  vessel.  In  this  way  the  cost  of  unloading  has 
been  reduced  to  a very  small  figure,  and  the  speed  of  unloading  greatly 
increased.  The  cost  of  unloading  is  given  by  the  makers  of  the  Brown  hoist 
as  varying  from  2£  cents  per  ton  up  to  4£  cents  per  ton;  deducting  in  each 
case  2 cents  for  trimming  the  coal  in  the  vessel,  the  actual  cost  of  loading 
varies  from  £ cent  to  2£  cents  per  ton,  depending  on  the  conditions.  Along 
the  Lakes  it  is  customary  to  pay  a premium  of  £ cent  per  ton  to  all  connected 
with  the  loading,  for  all  coal  loaded  in  excess  of  2,500  tons  per  day  and  1,800 
tons  per  night.  The  Brown  hoist  has  a guaranteed  capacity  of  at  least  800 
tons  per  hour,  but  this  has  been  greatly  exceeded  in  practice  TheMcMyler 
end  dump  has  a record  of  4.65  tons  per  minute,  and  the  McMyler  side  dump 
of  8.41  tons  per  minute.  These  figures  apply  to  the  lake  cities  of  the  U.  b. 

The  C.  W.  Hunt  Co.,  West  New  Brighton,  N.  Y.,  gives  the  follovvmg 
figures  for  handling  coal  along  the  Atlantic  seaboard:  The  cost  of  shoveling 
coal  by  hand  in  the  hold  of  the  vessel  into  ordinary  iron  buckets  is  about  6 
to  7 cents  per  ton  of  2,000  lb.;  the  cost  for  iron  ore,  phosphate  rock,  or  sand, 
about  10 i less.  The  cost  of  shoveling  coal  and  hoisting  it  out  of  vessel  to  the 
wharf  with  an  ordinary  hoist  with  manila  rope  is  12  to  13  cents  per  ton,  so 
that  the  hoisting  costs  about  the  same  as  the  shoveling.  The  cost  for  both 
shoveling  and  hoisting  with  a steam  engine  is  10  to  11  cents  per  ton.  ine 
cost  when  using  a steam  shovel  or  grab  bucket  for  taking  up  coal  out  of  the 
vessel  varies  greatly  in  different  classes  of  vessels,  but  usually  runs  from 
about  1£  to  5 cents  per  ton,  averaging  about  3 cents.  After  the  coal  is 
hoisted,  it  can  be  carried  into  storage  with  an  automatic  railway  or  other 
efficient  plant,  at  a cost  of  about  1 to  1£  cents  per  ton  For  great  distances  a 
cable  railway  or  a convevor  can  be  used,  which  handles  the  material  about 
as  cheaply  as  for  short  distances,  but  the  cost  of  plant  is  greatly  increased. 

In  unloading  anthracite  from  cars  on  a trestle  into  pockets  or  on  the 
ground,  the  loss  on  all  sizes  is  2 to  3j$  when  the  coal  is  not  resized;  when  it 
is  resized  the  loss  is  8£  to  9j&. 


448 


BEIQ  UETING. 


The  cost  of  stocking  and  unloading  anthracite  by  the  Dodge  system  is 
given  by  Mr.  Piez,  “ Mines  and  Minerals/  * June,  1898,  page  488,  as  follows: 


Year. 

Engine  Service, 
Stocking  and 
Lifting,  per  Ton. 
Cents. 

Office  Expense, 
per  Ton.  Cents. 

Steam,  Wages 
and  Fuel,  per 
Ton.  Cents. 

Labor,  Dumping 
and  Lifting,  per 
Ton.  Cents. 

Repairs,  per 
Ton.  Cents. 

Supplies,  per 
Ton.  Cents. 

Total,  per  Ton. 
Cents. 

1895 

.87 

.29 

.97 

2.67 

.78 

.25 

5.83 

1896  

.78 

.30 

.82 

2.19 

.90 

.27 

5.26 

1897  

.69 

.32 

.62 

1.88 

.97 

.16 

4.64 

BRIQUETING. 

Machines  Employed— Fuel,  fuel  dust,  and  other  products  may  be  briqueted 
by  a number  of  different  styles  of  machines,  but  all  these  may  be  divided 
into  two  classes,  briquet  and  eggette  machines.  The  eggette  machines  have 
a pair  of  rollers,  the  faces  of  which  are  provided  with  semispherical  or  semi- 
ovoid  openings.  The  material  that  is  fed  between  these  rolls  crowds  into 
the  openings  of  the  two  rolls,  thus  forming  small  spheres.  The  material  is 
mixed  with  a suitable  bond  before  being  fed  to  the  rolls,  and  the  eggettes  are 
received  on  any  suitable  form  of  traveling  belt  or  chute  and  removed  for 
drying  or  storage.  This  style  of  machine  has  not  been  used  to  any  great 
extent  in  this  country.  The  briqueting  machines  all  act  more  or  less  on  the 
principle  of  the  brick  machine,  having  some  kind  of  a die  or  mold  into 
which  the  material  is  crowded.  The  material  is  either  pressed  as  it  is  being 
fed  into  the  mold  or  subsequently  by  some  form  of  plunger.  For  some 
materials,  common  brick  machines,  such  as  are  used  in  the  manu- 
facture of  building  brick,  are  employed,  while  in  others  special  forms  are 
necessary.  , . 

Briqueting  of  Fuel.— Fuel  briquets  have  not  come  into  general  use  m the 
United  States  for  two  reasons:  (1)  on  account  of  the  great  amount  of  cheap 
fuel  available,  which  has  prevented  the  utilization  of  culm,  coal  dust,  etc.; 
and  (2)  on  account  of  the  lack  of  or  high  price  of  suitable  bonding  material. 
This  latter  condition  is  now  being  removed  by  the  introduction  of  by-product 
coke  ovens,  from  which  supplies  of  coal  tar  can  be  obtained.  Aside  from  peat 
and  certain  kinds  of  brown  coal,  and  possibly  some  caking  coals,  it  is  neces- 
sary to  employ  a bond  in  the  making  of  any  fuel  briquets.  This  is  especially 
true  in  the  case  of  anthracite  coal  The  present  tendency  is  to  employ  no 
inorganic  bonding  materials,  as  they  increase  the  ash.  The  material  to  be 
briqueted  should  be  as  clean  and  free  from  dirt  or  slate  as  possible,  and  the 
particles  should  be  of  practically  uniform  size,  the  most  satisfactory  product 
being  from  coal  crushed  to  about  fin.  cube  size.  The  coal  must  be  thor- 
oughly mixed  with  bonding  material  and  then  subjected  to  a heavy  pressure. 
One  advantage  claimed  for  briquets  is  that  they  can  be  made  of  such  a form 
as  to  occupy  less  space  than  the  original  fuel.  The  French  navy  has  found 
it  possible  to  store  10^  more  briquets  than  coal  in  a given  space,  and  also 
that  the  loss  by  breakage  and  pulverization  is  very  much  less.  Under  favor- 
able conditions,  fuel  can  be  briqueted  for  20  cents  per  ton,  and  the  following 
are  some  of  the  advantages  claimed  for  these  briquets:  They  are  sound 
throughout  and  will  not  decrepitate  while  burning,  thus  reducing  the 
loss  by  fine  material  working  through  the  grates.  The  bond,  if  properly 
selected,  renders  the  briquets  practically  waterproof,  so  that  they  are  not 
injured  if  kept  in  storage,  do  not  evolve  combustible  gases,  nor  ignite  from 
spontaneous  combustion.  There  is  no  fine  material  mixed  with  the  briquets, 
and  hence  a more  uniform  fire  can  be  maintained  with  them. 

Briqueting  of  Flue  Dust.— Flue  dust  from  iron  blast  furnaces  has  been  suc- 
cessfully briqueted  in  a number  of  instances.  One  firm  employs  a common 
brick  machine,  making  bricks  2£  in.  X 4f  in.  X 9 in.  With  this  machine, 
they  mix  the  flue  dust  with  3$  of  lime  and  3^  of  cement,  the  lime  acting  as 
a flux  in  the  furnace.  These  machines  work  with  comparatively  light  pres- 
sure. When  regular  briqueting  machines,  producing  round  bricks  and 


TREATMENT  OF  INJURED  PERSONS. 


449 


employing  high  pressures  are  employed,  no  cementne^ 
being  mixed  with  4 4 to 


are  loaded  ^into  barrels  and  taken  direct  to  the  blast  furnace,  with  as 

u Another  firm,  figuring  on  a basis  of  130  tons  per  24  hours,  and  using  3j6 
lime  in  the  solution,  gave  the  following  figures: 

4 tons  lime,  13.00  per  **r:5 

2 machine  tenders  (day  and  night),  12hours,  at  #2.50... 

2 laborers  (day  and  night),  12  hours,  at  $1.75 

Oil  and  waste  - - 

Interest  on  cost  of  plant 1 . ^ ' 

Thi*  is  less  than  20  cents  per  ton.  This  estimate  does  not  take  into  con- 
sideration the  cost  of  power,  which  would  be  about  35  H.  P.,  nor  does  it  take 
into  consideration  hauling  of  material  to  plant  and  removing  of  briquets. 

Cubic  Feet  Occupied  by  2,000  Pounds  of  Yabious  Coals. 

( Link-Belt  Engineering  Co .,  Philadelphia , Pa.) 


5.00 

3.50 

2.00 

1.50 


Varieties. 


Lackawanna,  anthracite.. 

Garfield  red  ash,  anthracite  . 
Ly kens  Valley,  anthracite  .... 

Shamokin,  anthracite  :-— 

Plymouth  red  ash,  anthracite. 

Wilkes-Barre,  anthracite 

Lehigh,  anthracite 

Lorberry,  anthracite 

Scranton,  anthracite 

Pittston,  anthracite  


Broken. 

Egg. 

Stove. 

37.10 

36.65 

34.90 

37.30 

36.95 

36.35 

37.55 

37.25 

37.55 

38.05 

37.70 

37.25 

34.90 

34.85 

34.75 

34.95 

34.35 

33.75 

33.30 

33.80 

33.55 

34.65 

34.20 

33.80 

35.35 

35.20 

34.60 

35.45 

34.95 

34.35 

34.35 

36.35 
37.25 
37.25 

34.70 
34.00 

32.55 

33.55 
33.30 

33.70 


Pea, 


37.25 

37.50 

38.50 

38.50 
36.90 
36.90 
33.05 
35.20 
34.95 

35.50 


Cumberland,  bituminous 36.65 

Clearfield,  bituminous 33.55 

New  River,  bituminous. | 40.15 


Pocahontas,  bituminous 

American  cannel,  bituminous 
English  cannel,  bituminous... 


34.00 

41.50 

42.30 


TREATMENT  OF  INJURED  PERSONS. 

The  dangers  to  be  feared  in  case  of  wounds,  are:  shock  or  collapse , loss  of 

blood , and  unnecessary  suffering  in  the  moving  qf  the  Pat™nt.  insen- 

Tn  shock  the  iniured  person  lies  pale,  faint,  and  cold,  sometimes 
sible  with  feeble  pulse  and  superficial  breathing.  The  cause  of  death  in 
case  of  a shock  is  arrest  of  heart  action,  produced  by  the  suspension  of  the 
functions  of  the  brain  and  spinal  cord.  In  treatment,  the  two  most  import- 
ant" of  the  injured  person;  (2)  the  application  of 

eX  ThTinTured^erson  should  at  once  be  placed  in  a recumbent  portion,  his 
head  resting1  on  a plane  lower  than  that  of  his  trunk,  legs,  and  feet.  He 
should  be  lell  wrapped  up  and  protected  from  the  chilling  influences  of 
external  air  When  there  is  danger  of  immediate  death,  stimulants  should 
bfliven;  in  all  other  conditions  of  shock,  stimulants  are  injurious 

Sss  of  Blood. — In  case  of  loss  of  blood,  two  conditions  Pres^\thems^ 
m \ The  bleeding  is  arrested  spontaneously  or  otherwise,  but  the  injured 
tli  symptoms  of loss .of  blood;  (2 'the  injured  pers0n  is 
actually  bleeding  and  he  is,  or  is  not,  suffering  from  loss  of  blood. 

In  the  first  condition,  life  is  threatened  by  anemia .of  brain  spinal 

cord,  and  all  the  efforts  of  treatment  are  to  direct  the  flow  of  whatever 


450 


TEE  A TMENT  OF  INJURED  PERSONS. 


quantity  of  blood  may  still  remain  in  the  body  to  the  vital  centers  in  the 
brain  and  spinal  cord.  This  is  most  efficiently  done  by  placing  the  injured 
person  in  a recumbent  position,  with  his  head  resting  on  a plane  somewhat 


Fig.  1. 


Fig.  2. 


lower  than  that  of  his  trunk  and  legs.  In  graver  cases,  constricting  bands 
should  be  applied  to  both  arms,  as  near  the  shoulders  as  possible,  and  to 
both  thighs,  as  near  the  abdomen  as  possible.  This  last  maneuver  directs 
the  entire  quantity  of  blood  in  the  body  to  the  suffering  centers,  the  centers 
of  life  itself.  Stimulants  may  be  sparingly  administered. 

If  there  is  bleeding,  do  not  try  to  stop  it  by  binding  up  the  wound.  The 
current  of  blood  to  the  part  must  be  checked.  To  do  this,  find  the  artery,  by  *ts 
beating;  lay  a firm  and  even  compress  or  pad  (made  of  cloth  or  rags  rolled 
up,  or  a round  stone  or  piece  of  wood  well  wrapped)  over  the  artery 
( Fig.  1 ) . Tie  a handkerchief  around  the  limb  and  compress;  put  a 
bit  of  stick  through  the  handkerchief  and  twist  the  latter  up 
until  it  is  just  tight  enough  to  stop  the  bleed- 
ing; then  put  one  end  of  the  stick  under 
the  handkerchief,  to  prevent  untwisting, 
as  in  Fig.  2. 

The  artery  in  the  thigh  runs  along  the 
inner  side  of  the  muscle  in  front  near  the 
bone,  as  shown  by  dotted  line  in  Fig.  8. 

A little  above  the  knee  it  passes  to  the 
back  of  the  bone.  In  injuries  at  or  above 
the  knee,  apply  the  compress  higher  up. 
on  the  inner  side  of  the  thigh,  at  the  point 
P,  Fig.  3,  with  the  knot  on  the  outside  of 
the  thigh. 

When  the  leg  is  injured  below  the 
knee,  apply  the  compress  at  the  back  of 
the  thigh,  just  above  the  knee,  at  P,  Fig.  4, 
and  the  knot  in  front,  as  in  Figs.  1 and  2. 

The  artery  in  the  arm  runs  down  the  inner  side  of  the  large  muscle  in 
front,  quite  close  to  the  bone,  as  shown  by  dotted  line;  low  down  it  is  further 
forwards,  towards  the  bend  of  the  elbow.  It  is  most  easily  compressed  a 
little  above  the  middle,  at  P.  Fig.  5.  Care  should  be  taken  to  examine  the 
limb  from  time  to  time,  and  to  lessen  the  compression  if  it  becomes  cold 
or  purple;  tighten  up  the  handkerchief 
again  if  the  bleeding  begins  afresh. 

To  Transport  a Wounded  Person  Comfortably. 

Make  a soft  and  even  bed  for  the  injured 
part,  of  straw,  folded  blankets,  quilts,  or 


Fig.  3. 


Fig.  4. 


Fig.  5 


Fig.  6. 


pillows,  laid  on  a board  with  side  pieces  of  board  nailed  on.  when  this  can 
be  done.  If  possible,  let  the  patient  be  laid  on  a door,  shutter,  settee,  or 
some  firm  support,  properly  covered.  Have  sufficient  force  to  lift  him 
steadily,  and  let  those  that  bear  him  not  keep  step. 

Should  any  important  arteries  be  opened,  apply  the  handkerchief,  as 
recommended.  Secure  the  vessel  by  a surgeon’s  dressing  forceps,  or  by  a 


TREATMENT  OF  PERSONS  OVERCOME  BY  GAS. 


451 


hook  then  have  a silk  ligature  put  around  the  vessel,  and  tighten,  should 
the  bleeding  be  from  arterial  vessels  of  small  size,  apply  persulphate  of  iron, 
either  in  tmcture  or  in  powder,  by  wetting  a piece  of  lmt  or  sponge  with  the 
solution1  then  after  bleeding  ceases,  apply  a compress  against  the  parts,  to 
sustain  them  during  the  application  of  the  persulphate  of  iron,  and  to 
vent ^ furthe^bleeding,  should  it  occur.  The  persulphate  of  iron  should  be 

ke  meedin^rom1  1 cVl^WoTivc! A %ad  or  compress  is  placed  immediately 
before  the  ear  over  the  region  marked  by  a dotted  line,  Fig.  6.  The  com- 
nress  is  firmly  secured  by  a handkerchief.  If  this  ^o®s  not ^rest  bleeding,  a 
similar  compress  on  the  opposite  side  should  be  applied.  Should  the  bleed- 
inTissurfmmTwound  of  the  posterior  or  back  part  of  the  head,  a compress 
should  be  placed  behind  the  ear,  over  the  region  marked  by  the  dotted  line, 
Fig.  6,  and  firmly  secured  by  a handkerchief  or  bandage. 

TREATMENT  OF  PERSONS  OVERCOME  BY  GAS. 

Miners  are  exposed  to  asphyxia  when  the  circulation  of  the  air  is  not  suf- 
ficiently active,  when  the  mine  exhales  a quantity  of  deleterious  gas,  when 
they  imprudently  penetrate  into  old  and  abandoned  workings,  and  when 

th6The  symptoms  of  asphyxia  are  sudden  cessation  of  the  respiration,  of  the 

pulsations  of  the  heart,  and  of  the  action  of  the  senses;  the 

swollen  and  marked  with  reddish  spots,  the  eyes  are  protruded,  the  features 

are  distorted,  and  the  face  is  often  livid,  etc.  . ^ 

The  best  and  first  remedy  to  employ,  and  m which  the  greatest  confidence 
ought  to  be  placed,  is  the  renewal  of  the  air  necessary  for  respiration. 

PrTeeprompflywithdraw  the  asphyxiated  person  from  the  deleterious  place 

and  exf^se^him^to roun(j  the  neck  and  chest,  and  dash  cold  water 

in  ‘ke^ace^and  shouldebehmade  to  irritate  the  mucous  membrane  with i the 
feathered  end  of  a quill,  which  should  be  gently  moved  in  the  nostrils  of  the 
insensible  person,  or  to  stimulate  it  with  a bottle  of  volatile  alkali  placed 

under  .tbe  ^ Up  warmth  of  the  body,  and  apply  mustard  plasters  over  the 

heart  an produce  respiration,  Doctor  Sylvester’s  method 
of  producing  artificial  respiration  should  be  tried  as  follows: 

Place  the  patient  on  the  back  on  a flat  surface,  inclined  a little  upwards 
from  the  feet;  raise  and  support  the  head  and  shoulders  on  a smaU  firm 
cushion  or  folded  article  of  dress  placed  under  the  shoulder  blades.  D raw 
forwards  the  patient’s  tongue  and  keep  it  projecting  beyond  the  lips,  an 
elastic  band  over  the  tongue  and  under  the  chin  will  answer  this  purpose,  or 
a piece  of  string  or  tape  may  be  tied  around  them,  or  by  raising  the  lower 
iaw  the  teeth  may  be  made  to  retain  the  tongue  in  that  position.  Remove 
all  tight  clothing  from  about  the  neck  and  chest,  especially  the  suspenders. 
Theng standing  at  the  patient’s  head,  grasp  the  arms  just  above  the  elbows, 
and  draw  the  arms  gently  and  steadily  upwards  above  the  head,  and  keep 
them  stretched  upwards  for  2 seconds  (by  this  means  air  is  diawn  into  the 
lungs').  Then  turn  down  the  patient’s  arms  and  press  them  gently  and 
firmly  for  2 seconds  against  the  sides  of  the  chest  (by  this  means  air  is  Pressed 
out  of  the  lungs) . Repeat  these  measures  alternately , deliberately , and  per- 
severingly  about  15  times  in  a minute,  until  a spipntaneous  effort  to  respire 
is  perceived,  immediately  upon  which  cease  to  imitate  the  movements  of 
breathing,  and  proceed  to  induce  circulation  and  warmth. 

6 To  promote  warmth  and  circulation,  rub  the  limbs  upwards  with  firm, 

grasping  pressure  and  energy,  using  handkerchiefs  flannels,  etc.  Apply  hot 
flannels!  bottles  of  hot  water,  heated  bricks,  etc.  to  the  pit  of  the  stomach, 
the  arm  pits,  between  the  thighs,  and  to  the  soles  of  the  feet.  , . 

7 On  the  restoration  of  life,  a teaspoonful  of  warm  water  should  be  given, 
and  then,  if  the  power  of  swallowing  has  returned,  small  quantities  of  wine, 
warm  brandy  and  water,  or  coffee  should  be  administered. 

8.  These  remedies  should  be  promptly  applied,  and  as  death  does  not 
certainly  appear  for  a long  time,  they  ought  only  to  be  discontinued^  when  it 
is  clearly  confirmed.  Absence  of  the  pulsation  of  the  heart  is  not  a sure  sign 
of  death,  neither  is  the  want  of  respiration. 


452 


COAL  DEALER'S  TABLE. 


Coal  Dealers’  Computing  Table,  for  Ascertaining  the  Price  of  Any 
Number  of  Pounds,  at  a Given  Price  per  Ton  of  2,000  Pounds. 


Lb. 

$0.75 

$1.00 

$1.25 

$1.50 

$1.75 

$2.00 

$2.25 

$2.50 

$2.75 

10 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

20 

.01 

.01 

.01 

.02 

.02 

.02 

.02 

.03 

.03 

30 

.01 

.02 

.02 

.02 

.03 

.03 

.03 

.04 

.04 

40 

.02 

.02 

.03 

.03 

.04 

.04 

.04 

.05 

.06 

50 

.02 

.02 

.03 

.04 

.04 

.05 

.06 

.06 

.07 

60 

.02 

.03 

.04 

.05 

.05 

.06 

.07 

.08 

.08 

70 

.03 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

.10 

80 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

.10 

.11 

90 

.03 

.04 

.06 

.07 

..08 

.09 

.10 

.11 

.12 

100 

.04 

.05 

.06 

.08 

.09 

.10 

.11 

.13 

.14 

200 

.08 

.10 

.13 

.15 

.17 

.20 

.23 

.25 

.28 

300 

.11 

.15 

.19 

.23 

.26 

.30 

.34 

.38 

.41 

400 

.15 

.20 

.25 

.30 

.35 

.40 

.45 

.50 

.55 

500 

.19 

.25 

.31 

.38 

44 

.50 

.56 

.63 

.69 

600 

.23 

.30 

.37 

.45 

.53 

.60 

.68 

.75 

.83 

700 

.26 

.35 

.44 

.53 

.61 

.70 

.77 

.88 

.96 

800 

.30 

.40 

.50 

.60 

.70 

.80 

.90 

1.00 

1.10 

900 

.34 

.45 

.56 

.68 

.79 

.90 

1.01 

1.13 

1.24 

1,000 

.38 

.50 

.63 

.75 

.88 

1.00 

1.13 

1.25 

1.38 

1,100 

.41 

.55 

.69 

.83 

.96 

1.10 

1.24 

1.38 

1.51 

1,200 

.45 

.60 

.75 

.90 

1.05 

1.20 

1.35 

1.50 

1.65 

L300 

.49 

.65 

.81 

.98 

1.14 

1.30 

1.46 

1.63 

1.79 

L400 

.52 

.70 

.88 

1.05 

1.22 

1.40 

1.58 

1.75 

1.93 

1,500 

.56 

.75 

.94 

1.13 

1.31 

1.50 

1.69 

1.88 

2.06 

1,600 

.60 

.80 

1.00 

1.20 

1.40 

1.60 

1.80 

2.00 

2.20 

1,700 

.64 

.85 

1.06 

1.28 

1.49 

1.70 

1.91 

2.13 

2.34 

1,800 

.68 

.90 

1.13 

1.35 

1.58 

1.80 

2.03 

2.25 

2.48 

1,900 

.71 

.95 

1.19 

1.43 

1.66 

1.90 

2.14 

2.38 

2.61 

Lb. 

$3.00 

$3.25 

$3.50 

$3.75 

$4.00 

$4.25 

$4.50 

$4.75 

$5.00 

10 

.02 

.02 

.02 

.02 

.02 

.03 

.03 

.03 

20 

.03 

.03 

.04 

.04 

.04 

.05 

.05 

.05 

.05 

30 

.05 

.05 

.05 

.06 

.06 

.07 

.07 

.07 

.08 

40 

.06 

.07 

.07 

.08 

.08 

.09 

.09 

.10 

.10 

50 

.08 

.08 

.09 

.09 

.10 

.11 

.12 

,12 

.13 

60 

.09 

.10 

.11 

.11 

.12 

.13 

.14 

.15 

.15 

70 

.11 

.11 

.12 

.13 

.14 

.15 

.16 

.17 

.18 

80 

.12 

.13 

.14 

.15 

.16 

.17 

.18 

.19 

.20 

90 

.14 

.15 

.16 

.17 

.18 

.19 

.20 

.22 

.23 

100 

.15 

.16 

.18 

.19 

.20 

.22 

.23 

.24 

.25 

200 

.30 

.33 

.35 

.38 

.40 

.43 

.45 

.48 

.50 

300 

.45 

.49 

.53 

.56 

.60 

.64 

.68 

.72 

.75 

400 

.60 

.65 

.70 

.75 

.80 

.85 

.90 

.95 

1.00 

500 

.75 

.81 

.88 

.94 

1.00 

1.07 

1.13 

1.19 

1.25 

600 

.90 

.98 

1.05 

1.13 

1.20 

1.28 

1.35 

1.43 

1.50 

700 

1.05 

1.14 

1.23 

1.31 

1.40 

1.49 

1.58 

1.67 

1.75 

800 

1.20 

1.30 

1.40 

1.50 

1.60 

1.70 

1.80 

1.90 

2.00 

900 

1.35 

1.46 

1.58 

1.69 

1.80 

1.92 

2.03 

2.14 

2.25 

1,000 

1.50 

1.63 

1.75 

1.88 

2.00 

2.13 

2.25 

2.38 

2.50 

1,100 

1.65 

1.79 

1.93 

2.06 

2.20 

2.34 

2.48 

2.62 

2.75 

1,200 

1.80 

1.95 

2.10 

2.25 

2.40 

2.55 

2.70 

2.85 

3.00 

1,300 

1.95 

2.11 

2.28 

2.44 

2.60 

2.77 

2.93 

3.09 

3.25 

1,400 

2.10 

2.28 

2.45 

2.63 

2.80 

2.98 

3.15 

3.33 

3.50 

1,500 

2.25 

2.44 

2.63 

2.81 

3.00 

3.19 

3.38 

3.57 

3.75 

1,600 

2.40 

2.60 

2.80 

3.00 

3.20 

3.40 

3.60 

3.80 

4.00 

1,700 

2.55 

2.76 

2.98 

3.19 

3.40 

3.62 

3.83 

4.04 

4.25 

1,800 

2.70 

2.93 

3.15 

3.38 

3.60 

3.83 

4.05 

4 28 

4.50 

1,900 

2.85 

3.09 

3.33 

3.56 

3.80 

4.04 

4.28 

4.52 

4.75 

NATURAL  SINES  AND  COSINES, 


453 


TABLE  OF  NATURAL  SINES,  COSINES, 
TANGENTS,  AND  COTANGENTS. 


EXPLANATION. 

Given  an  angle,  to  find  its  sine,  cosine,  tangent,  and  cotangent: 

Example— Find  the  sine,  cosine,  tangent,  and  cotangent  of  37° 24 . . 
Look  in  the  table  of  natural  sines  along  the  tops  of  the  pages,  and  find  37  . 
Glancing  down  the  left-hand  column  marked  ('),  until  24  is  found,  find 
opposite  this  24  in  the  column  marked  sine  and  headed  3/°,  the  number 
.60738;  then  .60738  = sin  37°  24'.  Similarly,  find  m the  column  marked 
cosine  and  headed  37°,  the  number  .79441,  which  corresponds  to  cos  3/°  24'. 
So  also,  find  in  the  column  marked  tangent  and  headed  3/°,  and  opposite  24  , 
the  number  .76456;  and  in  the  column  marked  cotangent  and  headed  37  , ana 
opposite  24',  the  number  1.30795.  , , , ...  . ... 

In  most  of  the  tables  published,  the  angles  run  only  from  0°  to  45°  at  the 
heads  of  the  columns;  to  find  an  angle  greater  than  45°,  look  at  the  bottom  of 
the  vaqe  and  glance  upwards , using  the  extreme  right-hand  column  to  find 
minutes , which  begin  with  0 at  the  bottom  and  run  upwards,  1,  2,  3,  etc. 
up  to  60. 

Example.— Find  the  sine  of  77°  43'.  _ _ . , 

Look  along  the  bottom  of  the  tables  until  the  column  marked  sine  and 
marked  77°  is  found.  Glancing  up  the  column  of  minutes  on  the  right  until 
43'  is  found,  find  opposite  43'  in  the  column  marked  sine  at  the  bottom  and 
marked  77°,  the  number  .97711;  this  is  the  sine  of  //°43  . Similarly,  the 
cosine,  tangent,  and  cotangent  may  be  found. 

To  find  the  sine,  cosine,  tangent,  or  cotangent  Of  an  angle  whose  exact 

value  is  not  given  in  the  table:  , . 

ru|  e—Find  in  the  table  the  sine , cosine , tangent , or  cotangent  corresponding 

to  the  degrees  and  minutes  of  the  angle.  . 

For  the  seconds,  find  the  difference  of  the  values  of  the  sine,  cosine,  tangent,  or 
cotangent  taken  from  the  table  between  which  the  seconds  of  the  angle  fall;  multiply 
this  difference  by  a fraction  whose  numerator  is  the  number  of  seconds  m the  given 
angle  and  whose  denominator  is  60.  . . , ^ v 

If  sine  or  tangent,  add  this  correction  to  the  value  first  found;  if  cosine  or 

cotangent,  subtract  the  correction.  

Example.— Find  the  sine,  cosine,  tangent,  and  cotangent  of  56  43  17  . 
Sin  56°  43'  = .83597.  Sin  56°  44'  = .83613.  Since  56°  43  17  is  greater  than 
56°  43'  and  less  than  56°  44',  the  value  of  the  sine  of  the  angle  lies  between 

V?  * 2 a ’ QQC1Q  QQWV7  — 0001  mil  1 tlTll VI T1  & 


til 0.11  OO  11  i Hlv  V tllUC  LAAvy  oaaav/  p « . « i • 

“83597  and  .83613;  the  difference  equals  .83613  — .83597  = .00016;  multiplying 
this  by  the  fraction  M,  .00016  X ii  = 00005.  nearly,  which  is  to  be  added 


.00005,  nearly,  which  is  to  be  added 
to  .83597,  the  "value  first  found',  or  .83597  + .00005  = .83602.  Hence,  sm 
56°  43'  1 7"  = 83602 

Cos  56°  43'  = 54878;  cos  56°  44'  = .54854;  the  difference  equals  .54878 
_ 54054  _>  00024  and  .00024  Y U = .00007,  nearly.  Now,  since  the  cosine  is 
deshed!  we  must’ sSak  this  correction  from  cos  56°  43'  or  .54878;  subtract- 
ing, .54878  - .00007  = .54871.  Hence,  cos  56°  43'  17"  = .54871.  . 

Given  the  sine,  cosine,  tangent,  or  cotangent,  to  find  the  angle  corresponding^ 

Example.— The  sine  of  an  angle  is  .47486;  what  is  the  angle?  ,, 

Consulting  the  table  of  natural  sines,  glance  down  the  columns  marked 
sine  until  .47486  is  found,  opposite  21'  in  the  ^ft-hand  column  and  under  the 
column  headed  28°.  Therefore,  the  angle  whose  sine  = .47486  is  28°  21 , or 
sin  28°  21'  = .47486. 

To  find  the  angle  corresponding  to  a given  sine,  cosine,  tangent,  or 
cotangent  whose  exact  value  is  not  contained  in  the  table:  ... 

RU| %—Find  the  difference  of  the  two  numbers  in  the  table  between  which  the 
given  sine , cosine,  tangent,  or  cotangent  falls,  and  use  the  number  of  parts  m this 
difference  as  the  denominator  of  a fraction. 


454 


NATURAL  SINES  AND  COSINES. 


Find  the  difference  between  the  number  belonging  to  the  smaller  angle  and  the 
given  sine , cosine,  tangent , or  cotangent,  and  use  the  number  of  parts  in  the  dif- 
ference just  found,  as  the  numerator  of  the  fraction  mentioned  above.  Multiply 
this  fraction  by  60,  and  the  result  will  be  the  number  of  seconds  to  be  added  to  the 
smaller  angle.  . , 

Example. — Find  the  angle  whose  sine  equals  .5/698.  . 

Looking  in  the  table  of  natural  sines,  in  the  column  marked  sine,  it  is 
found  between  .57691  = sin  35°  14'  and  .57715  = 35°  15'.  The  difference 
between  them  is  .57715  — .57691  = .00024,  or  24  parts.  The  difference  between 
the  sine  of  the  smaller  angle,  or  sin  35°  14'  = .57691,  and  the  given  sine,  or 
.57698,  is  .57698  — .57691  = .00007,  or  7 parts.  . „ 

Then,  ^ X 60  = 17.5",  and  the  angle  = 35°  14'  17.5",  or  sm  3o°  14  17.(/ 


= .57698.  „ „ . . _ 

The  cosecant  of  an  angle  is  equal  to  the  reciprocal  of  its  sine,  and  the 
secant  is  equal  to  the  reciprocal  of  its  cosine.  Hence,  to  multiply  a quantity 
bv  the  cosecant,  divide  it  by  the  sine;  or,  to  divide  it  by  the  cosecant 
niultiplv  it  bv  the  sine.  Similarlv,  to  multiply  a quantity  by  the  secant  ol 
an  angle,  divide  it  by  the  cosine;  or,  to  divide  it  by  the  secant,  multiply  it 
by  the  cosine. 


NATURAL  SINES  AND  COSINES. 


455 


0° 

1° 

2° 

3° 

4° 

/ 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

.00000 

.00029 

.00058 

.00087 

.00116 

.00145 

.00175 

.00204 

.00233 

.00262 

.00291 

.00320 

.00349 

.00378 

.00407 

.00436 

.00465 

.00495 

.00524 

.00553 

.00582 

.00611 

.00640 

.00669 

.00698 

.00727 

.00756 

.00785 

.00814 

.00844 

.00873 

.00902 

.00931 

.00960 

.00989 

.01018 

.01047 

.01076 

.01105 

.01134 

.01164 

.01193 

.01222 

.01251 

.01280 

.01309 

.01338 

.01367 

.01396 

.01425 

.01454 

.01483 

.01513 

.01542 

.01571 

.01600 

.01629 

.01658 

.01687 

.01716 

.01745 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

.99999 

.99999 

.99999 

.99999 

.99999 

.99999 

.99999 

.99999 

.99998 

.99998 

.99998 

.99998 

.99998 

.99998 

.99997 

.99997 

.99997 

.99997 

.99996 

.99996 

.99996 

.99996 

.99995 

.99995 

.99995 

.99995 

.99994 

.99994 

.99994 

.99993 

.99993 

.99993 

.99992 

.99992 

.99991 

.99991 

.99991 

.99990 

.99990 

.99989 

.99989 

.99989 

.99988 

.99988 

.99987 

.99987 

.99986 

.99986 

.99985 

.99985 

.01745 

.01774 

.01803 

.01832 

.01862 

.01891 

.01920 

.01949 

.01978 

.02007 

.02036 

.02065 

.02094 

.02123 

.02152 

.02181 

.02211 

.02240 

.02269 

.02298 

.02327 

.02356 

.02385 

.02414 

.02443 

.02472 

.02501 

.02530 

.02560 

.02589 

.02618 

.02647 

.02676 

.02705 

.02734 

.02763 

.02792 

.02821 

.02850 

.02879 

.02908 

.02938 

.02967 

.02996 

.03025 

.03054 

.03083 

.03112 

.03141 

.03170 

.03199 

.03228 

.03257 

.03286 

.03316 

.03345 

.03374 

.03403 

.03432 

.03461 

.03490 

.99985 

.99984 

.99984 

.99983 

.99983 

.99982 

.99982 

.99981 

.99980 

.99980 

.99979 

.99979 

.99978 

.99977 

.99977 

.99976 

.99976 

.99975 

.99974 

.99974 

.99973 

.99972 

.99972 

.99971 

.99970 

.99969 

.99969 

.99968 

.99967 

.99966 

.99966 

.99965 

.99964 

.99963 

.99963 

.99962 

.99961 

.99960 

.99959 

.99959 

.99958 

.99957 

.99956 

.99955 

.99954 

.99953 

.99952 

.99952 

.99951 

.99950 

.99949 

.99948 

.99947 

.99946 

.99945 

.99944 

.99943 

.99942 

.99941 

,99940 

.99939 

.03490 

.03519 

.03548 

.03577 

.03606 

.03635 

.03664 

.03693 

.03723 

.03752 

.03781 

.03810 

.03839 

.03868 

.03897 

.03926 

.03955 

.03984 

.04013 

.04042 

.04071 

.04100 

.04129 

.04159 

.04188 

.04217 

.04246 

.04275 

.04304 

.04333 

.04362 

.04391 

.04420 

.04449 

.04478 

.04507 

.04536 

.04565 

.04594 

.04623 

.04653 

.04682 

.04711 

.04740 

.04769 

.04798 

.04827 

.04856 

.04885 

.04914 

.04943 

.04972 

.05001 

.05030 

.05059 

.05088 

.05117 

.05146 

.05175 

.05205 

.05234 

.99939 

.99938 

.99937 

.99936 

.99935 

.99934 

.99933 

.99932 

.99931 

.99930 

.99929 

.99927 

.99926 

.99925 

.99924 

.99923 

.99922 

.99921 

.99919 

.99918 

.99917 

.99916 

.99915 

.99913 

.99912 

.99911 

.99910 

.99909 

.99907 

.99906 

.99905 

.99904 

.99902 

.99901 

.99900 

.99898 

.99897 

.99896 

.99894 

.99893 

.99892 

.99890 

.99889 

.99888 

.99886 

.99885 

.99883 

.99882 

.99881 

.99879 

.99878 

.99876 

.99875 

.99873 

.99872 

.99870 

.99869 

.99867 

.99866 

.99864 

.99863 

.05234 

.05263 

.05292 

.05321 

.05350 

.05379 

.05408 

.05437 

.05466 

.05495 

.05524 

.05553 

.05582 

.05611 

.05640 

.05669 

.05698 

.05727 

.05756 

.05785 

.05814 

.05844 

.05873 

.05902 

.05931 

.05960 

.05989 

.06018 

.06047 

.06076 

.06105 

.06134 

.06163 

.06192 

.06221 

.06250 

.06279 

.06308 

.06337 

.06366 

.06395 

.06424 

.06453 

.06482 

.06511 

.06540 

.06569 

.06598 

.06627 

.06656 

.06685 

.06714 

.06743 

.06773 

.06802 

.06831 

.06860 

.06889 

.06918 

.06947 

.06976 

.99863 

.99861 

.99860 

.99858 

.99857 

.99855 

.99854 

.99852 

.99851 

.99849 

.99847 

.99846 

.99844 

.99842 

.99841 

.99839 

•99838 

.99836 

.99834 

.99833 

.99831 

.99829 

.99827 

.99826 

.99824 

.99822 

.99821 

.99819 

.99817 

.99815 

.99813 

.99812 

.99810 

.99808 

.99806 

.99804 

.99803 

.99801 

.99799 

.99797 

.99795 

.99793 

.99792 

.99790 

.99788 

.99786 

.99784 

.99782 

.99780 

.99778 

.99776 

.99774 

.99772 

.99770 

.99768 

.99766 

.99764 

.99762 

.99760 

.99758 

.99756 

.06976 

.07005 

.07034 

.07063 

.07092 

.07121 

.07150 

.07179 

.07208 

.07237 

.07266 

.07295 

.07324 

.07353 

.07382 

.07411 

.07440 

.07469 

.07498 

.07527 

.07556 

.07585 

.07614 

.07643 

.07672 

.07701 

.07730 

.07759 

.07788 

.07817 

.07846 

.07875 

.07904 

.07933 

.07962 

.07991 

.08020 

.08049 

.08078 

.08107 

.08136 

.08165 

.08194 

.08223 

.08252 

.08281 

.08310 

.08339 

.08368 

.08397 

.08426 

.08455 

.08484 

.08513 

.08542 

.08571 

.08600 

.08629 

.08658 

.08687 

.08716 

.99756 

.99754 

.99752 

.99750 

.99748 

.99746 

.99744 

.99742 

.99740 

.99738 

.99736 

.99734 

.99731 

.99729 

.99727 

.99725 

.99723 

.99721 

.99719 

.99716 

.99714 

.99712 

.99710 

.99708 

.99705 

.99703 

.99701 

.99699 

.99696 

.99694 

.99692 

.99689 

.99687 

.99685 

.99683 

.99680 

.99678 

.99676 

.99673 

.99671 

.99668 

.99666 

.99664 

.99661 

.99659 

.99657 

.99654 

.99652 

.99649 

.99647 

.99644 

.99642 

.99639 

.99637 

.99635 

.99632 

.99630 

.99627 

.99625 

.99622 

.99619 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

.24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 « 

7 

6 

5 

4 

3 

2 

1 

0 

t 

/ 

Cosine 

Sine 

Cosine 

! Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

89° 

88° 

87° 

86° 

85° 

456 


NA  TURAL  SINES  AND  COSINES. 


5° 

6° 

7° 

8° 

9° 

t 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

o 

08716 

.99619 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

60 

1 

08745 

.99617 

.10482 

.99449 

.12216 

.99251 

.13946 

.99023 

.15672 

.98764 

59 

08774 

.99614 

.10511 

.99446 

.12245 

.99248 

.13975 

.99019 

.15701 

.98760 

58 

3 

08803 

99612 

.10540 

.99443 

.12274 

.99244 

.14004 

.99015 

.15730 

.98755 

57 

08831 

99609 

.10569 

.99440 

.12302 

.99240 

.14033 

.99011 

.15758 

.98751 

56 

5 

08800 

99607 

.10597 

.99437 

.12331 

.99237 

.14061 

.99006 

.15787 

.98746 

55 

0 

*08889 

.99604 

.10626 

.99434 

.12360 

.99233 

.14090 

.99002 

.15816 

.98741 

54 

7 

08918 

.99602 

.10655 

.99431 

.12389 

.99230 

.14119 

.98998 

.15845 

.98737 

53 

g 

08947 

.99599 

.10684 

.99428 

.12418 

.99226 

.14148 

.98994 

.15873 

.98732 

52 

9 

08976 

.99596 

.10713 

.99424 

.12447 

.99222 

.14177 

.98990 

.15902 

.98728 

51 

10 

!o9005 

.99594 

.10742 

.99421 

.12476 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

09034 

99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

09063 

99588 

.10800 

.99415 

.12533 

.99211 

.14263 

.98978 

.15988 

.98714 

48 

13 

09092 

99586 

.10829 

.99412 

.12562 

.99208 

.14292 

.98973 

.16017 

.98709 

47 

09121 

99583 

.10858 

.99409 

.12591 

.99204 

.14320 

.98969 

.16046 

.98704 

46 

15 

09150 

99580 

.10887 

.99406 

.12620 

.99200 

.14349 

.98965 

.16074 

.98700 

45 

09179 

99578 

.10916 

.99402 

.12649 

.99197 

.14378 

.98961 

.16103 

.98695 

44 

09908 

99575 

.10945 

.99399 

.12678 

.99193 

.14407 

.98957 

.16132 

.98690 

43 

09937 

99572 

.10973 

.99396 

.12706 

.99189 

.14436 

.98953 

.16160 

.98686 

42 

19 

09266 

.99570 

.11002 

.99393 

.12735 

.99186 

.14464 

.98948 

.16189 

.98681 

41 

20 

^09295 

.99567 

.11031 

.99390 

.12764 

.99182 

.14493 

.98944 

.16218 

.98676 

40 

21 

09324 

.99564 

.11060 

.99386 

.12793 

.99178 

.14522 

.98940 

.16246 

.98671 

39 

22 

09353 

.99562 

.11089 

.99383 

.12822 

.99175 

.14551 

.98936 

.16275 

.98667 

38 

23 

09382 

99559 

.11118 

.99380 

.12851 

.99171 

.14580 

.98931 

.16304 

.98662 

37 

94- 

0941 1 

.99556 

.11147 

.99377 

.12880 

.99167 

.14608 

.98927 

.16333 

.98657 

36 

25 

09440 

.99553 

.11176 

.99374 

.12908 

.99163 

.14637 

.98923 

.16361 

.98652 

35 

26 

09469 

.99551 

.11205 

.99370 

.12937 

.99160 

.14666 

.98919 

.16390 

.98648 

34 

27 

*09498 

.99548 

.11234 

.99367 

.12966 

.99156 

.14695 

.98914 

.16419 

.98643 

33 

28 

]09527 

.99545 

.11263 

.99364 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638 

32 

29 

!o9556 

.99542 

.11291 

.99360 

.13024 

.99148 

.14752 

.98906 

.16476 

.98633 

31 

30 

]o9585 

.99540 

.11320 

.99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629 

30 

31 

.09614 

.99537 

.11349 

.99354 

.13081 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

.09642 

.99534 

.11378 

.99351 

.13110 

.99137 

.14838 

.98893 

.16562 

.98619 

08 

33 

.09671 

.99531 

.11407 

.99347 

.13139 

.99133 

.14867 

.98889 

.16591 

.98614 

27 

34 

.09700 

^99528 

.11436 

.99344 

.13168 

.99129 

.14896 

.98884 

.16620 

.98609 

| 26 

35 

.09729 

.99526 

.11465 

.99341 

.13197 

.99125 

.14925 

.98880 

.16648 

.98604 

25 

36 

.09758 

.99523 

.11494 

.99337 

.13226 

.99122 

.14954 

.98876 

.16677 

.98600 

24 

37 

.09787 

.99520 

.11523 

.99334 

.13254 

.99118 

.14982 

.98871 

.16706 

.98595 

23 

38 

.09816 

.99517 

.11552 

.99331 

.13283 

.99114 

.15011 

.98867 

.16734 

.98590 

22 

39 

.09845 

.99514 

.11580 

.99327 

.13312 

.99110 

.15040 

.98863 

.16763 

.98585 

21 

40 

!09874 

.99511 

.11609 

.99324 

.13341 

.99106 

.15069 

.98858 

.16792 

.98580 

20 

41 

.09903 

.99508 

.11638 

.99320 

.13370 

.99102 

.15097 

.98854 

.16820 

.98575 

19 

42 

.09932 

.99506 

.11667 

.99317 

.18399 

.99098 

.15126 

.98849 

.16849 

.98570 

18 

43 

!o9961 

.99503 

.11696 

.99314 

.13427 

.99094 

.15155 

.98845 

.16878 

.98565 

17 

44 

!o9990 

.99500 

.11725 

.99310 

.13456 

.99091 

.15184 

.98841 

.16906 

.98561 

16 

45 

J0019 

.99497 

.11754 

.99307 

.13485 

.99087 

.15212 

.98836 

.16935 

.98556 

15 

46 

J0048 

.99494 

.11783 

.99303 

.13514 

.99083 

.15241 

.98832 

.16964 

.98551 

14 

47 

.10077 

.99491 

.11812 

.99300 

.13543 

.99079 

.15270 

.98827 

.16992 

.98546 

13 

48 

.10106 

.99488 

.11840 

.99297 

.13572 

.99075 

.15299 

.98823 

.17021 

.98541 

12 

49 

!l0135 

.99485 

.11869 

.99293 

.13600 

.99071 

.15327 

.98818 

.17050 

.98536 

11 

50 

'.10164 

.99482 

.11898 

.99290 

.13629 

.99067 

.15356 

.98814 

.17078 

.98531 

10 

51 

.10192 

.99479 

.11927 

.99286 

.13658 

.99063 

.15385 

.98809 

.17107 

.98526 

9 

52 

!l0221 

.99476 

.11956 

.99283 

.13687 

.99059 

.15414 

.98805 

.17136 

.98521 

8 

53 

!l0250 

.99473 

.11985 

.99279 

.13716 

.99055 

.15442 

.98800 

.17164 

.98516 

7 

54 

.10279 

.99470 

.12014 

.99276 

.13744 

.99051 

.15471 

.98796 

.17193 

.98511 

6 

55 

!l03G8 

.99467 

.12043 

.99272 

.13773 

.99047 

.15500 

.98791 

.17222 

.98506 

5 

56 

.10337 

.99464 

.12071 

.99269 

.13802 

.99043 

.15529 

.98787 

.17250 

.98501 

4 

57 

.10366 

.99461 

.12100 

.99265 

.13831 

.99039 

.15557 

.98782 

.17279 

.98496 

3 

58 

.10395 

.99458 

.12129 

.99262 

.13860 

.99035 

.15586 

.98778 

.17308 

.98491 

2 

59 

J0424 

.99455 

.12158 

.99258 

.13889 

.99031 

.15615 

.98773 

.17336 

.98486 

1 

60 

’.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

.17365 

.98481 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

f 

84° 

83° 

82° 

81° 

80° 

NATURAL  SINES  AND  COSINES. 


457 


10° 

11° 

12° 

13° 

14c 

> 

r 

t - 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 
69 
80 

.17365 

.17393 

.17422 

.17451 

.17479 

.17508 

.17537 

.17565 

.17594 

.17623 

.17651 

.17680 

.17708 

.17737 

.17766 

.17794 

.17823 

.17852 

.17880 

.17909 

.17937 

.17966 

.17995 

.18023 

.18052 

.18081 

.18109 

.18138 

.18166 

.18195 

.18224 

.18252 

.18281 

.18309 

.18338 

.18367 

.18395 

.18424 

.18452 

.18481 

.18509 

.18538 

.18567 

.18595 

.18624 

.18652 

.18681 

.18710 

.18738 

.18767 

.18795 

.18824 

.18852 

.18881 

.18910 

.18938 

.18967 

.18995 

.19024 

.19052 

.19081 

.98481 

.98476 

.98471 

.98466 

.98461 

.98455 

.98450 

.98445 

.98440 

.98435 

.98430 

.98425 

.98420 

.98414 

.98409 

.98404 

.98399 

.98394 

.98389 

.98383 

.98378 

.98373 

.98368 

.98362 

.98357 

.98352 

.98347 

.98341 

.98336 

.98331 

.98325 

.98320 

.98315 

.98310 

.98304 

.98299 

.98294 

.98288 

.98283 

.98277 

.98272 

.98267 

.98261 

.98256 

.98250 

.98245 

.98240 

.98234 

.98229 

.98223 

.98218 

.98212 

.98207 

.98201 

.98196 

.98190 

.98185 

.98179 

.98174 

.98168 

.98163 

.19081 

.19109 

.19138 

.19167 

.19195 

.19224 

.19252 

.19281 

.19309 

.19338 

.19366 

.19395 

.19423 

.19452 

.19481 

.19509 

.19538 

.19566 

.19595 

.19623 

.19652 

.19680 

.19709 

.19737 

.19766 

.19794 

.19823 

.19851 

.19880 

.19908 

.19937 

.19965 

.19994 

.20022 

.20051 

.20079 

.20108 

.20136 

.20165 

.20193 

.20222 

.20250 

.20279 

.20307 

.20336 

.20364 

.20393 

.20421 

.20450 

.20478 

.20507 

.20535 

.20563 

.20592 

.20620 

.20649 

.20677 

.20706 

.20734 

.20763 

.20791 

.98163 

.98157 

.98152 

.98146 

.98140 

.98135 

.98129 

.98124 

.98118 

.98112 

.98107 

.98101 

.98096 

.98090 

.98084 

.98079 

.98073 

.98067 

.98061 

.98056 

.98050 

.98044 

.98039 

.98033 

.98027 

.98021 

.98016 

.98010 

.98004 

.97998 

.97992 

.97987 

.97981 

.97975 

.97969 

.97963 

.97958 

.97952 

.97946 

.97940 

.97934 

.97928 

.97922 

.97916 

.97910 

.97905 

.97899 

.97893 

.97887 

.97881 

.97875 

.97869 

.97863 

.97857 

.97851 

.97845 

.97839 

.97833 

.97827 

.97821 

.97815 

.20791 

.20820 

.20848 

.20877 

.20905 

.20933 

.20962 

.20990 

.21019 

.21047 

.21076 

.21104 

.21132 

.21161 

.21189 

.21218 

.21246 

.21275 

.21303 

.21331 

.21360 

.21388 

.21417 

.21445 

.21474 

.21502 

.21530 

.21559 

.21587 

.21616 

.21644 

.21672 

.21701 

.21729 

.21758 

.21786 

.21814 

.21843 

.21871 

.21899 

.21928 

.21956 

.21985 

.22013 

.22041 

.22070 

.22098 

.22126 

.22155 

.22183 

.22212 

.22240 

.22268 

.22297 

.22325 

.22353 

.22382 

.22410 

.22438 

.22467 

.22495 

.97815 

.97809 

.97803 

.97797 

.97791 

.97784 

.97778 

.97772 

.97766 

.97760 

.97754 

.97748 

.97742 

.97735 

.97729 

.97723 

.97717 

.97711 

.97705 

.97698 

.97692 

.97686 

.97680 

.97673 

.97667 

.97661 

.97655 

.97648 

.97642 

.97636 

.97630 

.97623 

.97617 

.97611 

.97604 

.97598 

.97592 

.97585 

.97579 

.97573 

.97566 

.97560 

.97553 

.97547 

.97541 

.97534 

.97528 

.97521 

.97515 

.97508 

.97502 

.97496 

.97489 

.97483 

.97476 

.97470 

.97463 

.97457 

.97450 

.97444 

.97437 

.22495 

.22523 

.22552 

.22580 

.22608 

.22637 

.22665 

.22693 

.22722 

.22750 

.22778 

.22807 

.22835 

.22863 

.22892 

.22920 

.22948 

.22977 

.23005 

.23033 

.23062 

.23090 

.23118 

.23146 

.23175 

.23203 

.23231 

.23260 

.23288 

.23316 

.23345 

.23373 

.23401 

.23429 

.23458 

.23486 

.23514 

.23542 

.23571 

.23599 

.23627 

.23656 

.23684 

.23712 

.23740 

.23769 

.23797 

.23825 

.23853 

.23882 

.23910 

.23938 

.23966 

.23995 

.24023 

.24051 

.24079 

.24108 

.24136 

.24164 

.24192 

.97437 

.97430 

.97424 

.97417 

.97411 

.97404 

.97398 

.97391 

.97384 

.97378 

.97371 

.97365 

.97358 

.97351 

.97345 

.97338 

.97331 

.97325 

.97318 

.97311 

.97304 

.97298 

.97291 

.97284 

.97278 

.97271 

.97264 

.97257 

.97251 

.97244 

.97237 

.97230 

.97223 

.97217 

.97210 

.97203 

.97196 

.97189 

.97182 

.97176 

.97169 

.97162 

.97155 

.97148 

.97141 

.97134 

.97127 

.97120 

.97113 

.97106 

.97100 

.97093 

.97086 

.97079 

.97072 

.97065 

.97058 

.97051 

.97044 

.97037 

.97030 

.24192 

.24220 

.24249 

.24277 

.24305 

.24333 

.24362 

.24390 

.24418 

.24446 

.24474 

.24503 

.24531 

.24559 

.24587 

.24615 

.24644 

.24672 

.24700 

.24728 

.24756 

.24784 

.24813 

.24841 

.24869 

.24897 

.24925 

.24954 

.24982 

.25010 

.25038 

.25066 

.25094 

.25122 

.25151 

.25179 

.25207 

.25235 

.25263 

.25291 

.25320 

.25348 

.25376 

.25404 

.25432 

.25460 

.25488 

.25516 

.25545 

.25573 

.25601 

.25629 

.25657 

.25685 

.25713 

.25741 

.25769 

.25798 

.25826 

.25854 

.25882 

.97030 

.97023 

.97015 

.97008 

.97001 

.96994 

.96987 

.96980 

.96973 

.96966 

.96959 

.96952 

.96945 

.96937 

.96930 

.96923 

.96916 

.96909 

.96902 

.96894 

.96887 

.96880 

.96873 

.96866 

.96858 

.96851 

.96844 

.96837 

.96829 

.96822 

.96815 

.96807 

.96800 

.96793 

.96786 

.96778 

.96771 

.96764 

.96756 

.96749 

.96742 

.96734 

.96727 

.96719 

.96712 

.96705 

.96697 

.96690 

.96682 

.96675 

.96667 

.96660 

.96653 

.96645 

.96638 

.96630 

.96623 

.96615 

.96608 

.96600 

.96593 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

t 

Cosine 

> Sine 

Cosine 

; Sine 

Cosine 

: Sine 

Cosine 

Sine 

Cosine 

i Sine 

- t 

1 

79° 

78° 

77° 

76° 

75° 

... 

458 


NATURAL  SINES  AND  COSINES , 


15° 

16° 

17° 

18°  | 

19° 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.25882 

.96593 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

60 

1 

.25910 

.96585 

.27592 

.96118 

.29265 

.95622 

.30929 

.95097 

.32584 

.94542 

59 

2 

.25938 

.96578 

.27620 

.96110 

.29293 

.95613 

.30957 

.95088 

.32612 

.94533 

58 

3 

.25966 

.96570 

.27648 

.96102 

.29321 

.95605 

.30985 

.95079 

.32639 

.94523 

57 

4 

.25994 

.96562 

.27676 

.96094 

.29348 

.95596 

.31012 

.95070 

.32667 

.94514 

56 

5 

.26022 

.96555 

.27704 

.96086 

.29376 

.95588 

.31040 

.95061 

.32694 

.94504 

55 

6 

.26050 

.96547 

.27731 

.96078 

.29404 

.95579 

.31068 

.95052 

.32722 

.94495 

54 

7 

.26079 

.96540 

.27759 

.96070 

.29432 

.95571 

.31095 

.95043 

.32749 

.94485 

53 

8 

.26107 

.96532 

.27787 

.96062 

.29460 

.95562 

.31123 

.95033 

.32777 

.94476 

52 

9 

.26135 

.96524 

.27815 

.96054 

.29487 

.95554 

.31151 

.95024 

.32804 

.94466 

51 

10 

.26163 

.96517 

.27843 

.96046 

.29515 

.95545 

.31178 

.95015 

.32832 

.94457 

50 

11 

.26191 

.96509 

.27871 

.96037 

.29543 

.95536 

.31206 

.95006 

.32859 

.94447 

49 

12 

.26219 

.96502 

.27899 

.96029 

.29571 

.95528 

.31233 

.94997 

.32887 

.94438 

48 

13 

.26247 

.96494 

.27927 

.96021 

.29599 

.95519 

.31261 

.94988 

.32914 

.94428 

47 

14 

.26275 

.96486 

.27955 

.96013 

.29626 

.95511 

.31289 

.94979 

.32942 

.94418 

46 

15 

.26303 

.96479 

.27983 

.96005 

.29654 

.95502 

.31316 

.94970 

.32969 

.94409 

45 

16 

.26331 

.96471 

.28011 

.95997 

.29682 

.95493 

.31344 

.94961 

.32997 

.94399 

44 

17 

.26359 

.96463 

.28039 

.95989 

.29710 

.95485 

.31372 

.94952 

.33024 

.94390 

43 

18 

.26387 

.96456 

.28067 

.95981 

.29737 

.95476 

.31399 

.94943 

.33051 

.94380 

42 

19 

.26415 

.96448 

.28095 

.95972 

.29765 

.95467 

.31427 

.94933 

.33079 

.94370 

41 

20 

.26443 

.96440 

.28123 

.95964 

.29793 

.95459 

.31454 

.94924 

.33106 

.94361 

40 

21 

.26471 

.96433 

.28150 

.95956 

.29821 

.95450 

.31482 

.94915 

.33134 

.94351 

39 

22 

.26500 

.96425 

.28178 

.95948 

.29849 

.95441 

.31510 

.94906 

.33161 

.94342 

38 

23 

.26528 

.96417 

.28206 

.95940 

.29876 

.95433 

.31537 

.94897 

.33189 

.94332 

37 

24 

.26556 

.96410 

.28234 

.95931 

.29904 

.95424 

.31565 

.94888 

.33216 

.94322 

36 

25 

.26584 

.96402 

.28262 

.95923 

.29932 

.95415 

.31593 

.94878 

.33244 

.94313 

35 

26 

.26612 

.96394 

.28290 

.95915 

.29960 

.95407 

.31620 

.94869 

.33271 

.94303 

34 

27 

.26640 

.96386 

.28318 

.95907 

.29987 

.95398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.26668 

.96379 

.28346 

.95898 

.30015 

.95389 

.31675 

.94851 

.33326 

.94284 

32 

29 

.26696 

.96371 

.28374 

.95890 

.30043 

.95380 

.31703 

.94842 

.33353 

.94274 

31 

30 

.26724 

.96363 

28402 

.95882 

.30071 

.95372 

.31730 

.94832 

.33381 

.94264 

30 

31 

.26752 

.96355 

.28429 

.95874 

.30098 

.95363 

.31758 

.94823 

.33408 

.94254 

29 

32 

.26780 

.96347 

.28457 

.95865 

.30126 

.95354 

.31786 

.94814 

.33436 

.94245 

28 

33 

.26808 

.96340 

.28485 

.95857 

.30154 

.95345 

.31813 

.94805 

.33463 

.94235 

27 

34 

.26836 

.96332 

.28513 

.95849 

.30182 

.95337 

.31841 

.94795 

.33490 

.94225 

26 

35 

.26864 

.96324 

.28541 

.95841 

.30209 

.95328 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.96316 

.28569 

.95832 

.30237 

.95319 

.31896 

.94777 

.33545 

.94206 

24 

37 

.26920 

.96308 

.28597 

.95824 

.30265 

.95310 

.31923 

.94768 

.33573 

.94196 

23 

38 

.26948 

.96301 

.28625 

.95816 

.30292 

.95301 

.31951 

.94758 

.33600 

.94186 

22 

39 

.26976 

.96293 

.28652 

.95807 

.30320 

.95293 

.31979 

.94749 

.33627 

.94176 

21 

40 

.27004 

.96285 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.96277 

.28708 

.95791 

.30376 

.95275 

.32034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.28736 

.95782 

.30403 

.95266 

.32061 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.28764 

.95774 

.30431 

.95257 

' .32089 

.94712 

.33737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30459 

.95248 

.32116 

.94702 

.33764 

.94127 

16 

45 

.27144 

.96246 

.28820 

.95757 

.30486 

.95240 

.32144 

.94693 

.33792 

.94118 

15 

46 

.27172 

.96238 

.28847 

.95749 

.30514 

.95231 

.32171 

.94684 

.33819 

.94108 

14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222 

.32199 

.94674 

.33846 

.94098 

13 

48 

.27228 

.96222 

.28903 

.95732 

.30570 

.95213 

.32227 

.94665 

.33874 

.94088 

12 

49 

.27256 

.96214 

.28931 

.95724 

.30597 

.95204 

.32254 

.94656 

.33901 

.94078 

11 

50 

.27284 

.96206 

.28959 

.95715 

.30625 

.95195 

.32282 

.94646 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987 

.95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340 

.96190 

.29015 

.95698 

.30680 

.95177 

.32337 

.94627 

.33983 

.94049 

8 

53 

.27368 

.96182 

.29042 

.95690 

.30708 

.95168 

.32364 

.94618 

.34011 

.94039 

7 

54 

.27396 

.96174 

.29070 

.95681 

.30736 

.95159 

.32392 

.94609 

.34038 

.94029 

6 

55 

.27424 

.96166 

.29098 

.95673 

.30763 

.95160 

.32419 

.94599 

.34065 

.94019 

5 

56 

.27452 

.96158 

.29126 

.95664 

.30791 

.95142 

.32447 

.94590 

.34093 

.94009 

4 

57 

.27480 

.96150 

.29154 

.95656 

.30819 

.95133 

.32474 

.94580 

.34120 

.93999 

3 

58 

.27508 

.96142 

.29182 

.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

2 

59 

.27536 

.96134 

.29209 

.95639 

.30874 

.95115 

.32529 

.94561 

.34175 

.93979 

1 

60 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

.34202 

.93969 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

7 

4° 

78° 

72° 

71° 

70° 

\ 

/ 

NATURAL  SINES  AND  COSINES. 


459 


20° 

21° 

22° 

23° 

24° 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

o 

.34202 

.93969 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

60 

1 

.34229 

.93959 

.35864 

.93348 

.37488 

.92707 

.39100 

.92039 

.40700 

.91343 

59 

2 

.34257 

.93949 

.35891 

.93337 

.37515 

.92697 

.39127 

.92028 

.40727 

.91331 

58 

3 

.34284 

.93939 

.35918 

.93327 

.37542 

.92686 

.39153 

.92016 

.40753 

.91319 

57 

4 

.34311 

.93929 

.35945 

.93316 

.37569 

.92675 

.39180 

.92005 

.40780 

.91307 

56 

5 

.34339 

.93919 

.35973 

.93306 

.37595 

.92664 

.39207 

.91994 

.40806 

.91295 

55 

6 

.34366 

.93909 

.36000 

.93295 

.37622 

.92653 

.39234 

.91982 

.40833 

.91283 

54 

7 

.34393 

.93899 

.36027 

.93285 

.37649 

.92642 

.39260 

.91971 

.40860 

.91272 

53 

g 

.34421 

.93889 

.36054 

.93274 

.37676 

.92631 

.39287 

.91959 

.40886 

.91260 

52 

9 

.34448 

.93879 

.36081 

.93264 

.37703 

.92620 

.39314 

.91948 

.40913 

.91248 

51 

10 

.34475 

.93869 

.36108 

.93253 

.37730 

.92609 

.39341 

.91936 

.40939 

.91236 

50 

11 

.34503 

.93859 

.36135 

.93243 

.37757 

.92598 

.39367 

.91925 

.40966 

.91224 

49 

12 

.34530 

.93849 

.36162 

.93232 

.37784 

.92587 

.39394 

.91914 

.40992 

.91212 

48 

13 

.34557 

.93839 

.36190 

.93222 

.37811 

.92576 

.39421 

.91902 

.41019 

.91200 

47 

14 

.34584 

.93829 

.36217 

.93211 

.37838 

.92565 

.39448 

.91891 

.41045 

.91188 

46 

15 

.34612 

.93819 

.36244 

.93201 

.37865 

.92554 

.39474 

.91879 

.41072 

.91176 

45 

16 

.34639 

.93809 

.36271 

.93190 

.37892 

.92543 

.39501 

.91868 

.41098 

.91164 

44 

17 

.34666 

.93799 

.36298 

.93180 

.37919 

.92532 

.39528 

.91856 

.41125 

.91152 

43 

18 

.34694 

.93789 

.36325 

.93169 

.37946 

.92521 

.39555 

.91845 

.41151 

.91140 

42 

19 

.34721 

.93779 

.36352 

.93159 

.37973 

.92510 

.39581 

.91833 

.41178 

.91128 

41 

20 

.$4748 

.93769 

.36379 

.93148 

.37999 

.92499 

.39608 

.91822 

.41204 

.91116 

40 

21 

.34775 

.93759 

.36406 

.93137 

.38026 

.92488 

.39635 

.91810 

.41231 

.91104 

39 

22 

.34803 

.93748 

.36434 

.93127 

.38053 

.92477 

.39661 

.91799 

.41257 

.91092 

38 

23 

*.34830 

.93738 

.36461 

.93116 

.38080 

.92466 

.39688 

.91787 

.41284 

.91080 

37 

24 

.34857 

.93728 

.36488 

.93106 

.38107 

.92455 

.39715 

.91775 

.41310 

.91068 

36 

25 

.34884 

.93718 

.36515 

.93095 

.38134 

.92444 

.39741 

.91764 

.41337 

.91056 

35 

26 

.34912 

.93708 

.36542 

.93084 

.38161 

.92432 

.39768 

.91752 

.41363 

.91044 

34 

27 

.34939 

.93698 

.36569 

.93074 

.38188 

.92421 

.39795 

.91741 

.41390 

.91032 

33 

28 

.34966 

.93688 

.36596 

.93063 

.38215 

.92410 

.39822 

.91729 

.41416 

.91020 

32 

29 

.34993 

.93677 

.36623 

.93052 

.38241 

.92399 

.39848 

.91718 

.41443 

.91008 

31 

30 

.35021 

.93667 

.36650 

.93042 

.38268 

.92388 

.39875 

.91706 

.41469 

.90996 

30 

31  ' 

.35048 

.93657 

.36677 

.93031 

.38295 

.92377 

.39902 

.91694 

.41496 

.90984 

29 

32 

.35075 

.93647 

.36704 

.93020 

.38322 

.92366 

.39928 

.91683 

.41522 

.90972 

28 

33 

.35102 

.93637 

.36731 

.93010 

.38349 

.92355 

.39955 

.91671 

.41549 

.90960 

27 

34 

.35130 

.93626 

.36758 

.92999 

.38376 

.92343 

.39982 

.91660 

.41575 

.90948 

26 

35 

.35157 

.93616 

.36785 

.92988 

.38403 

.92332 

.40008 

.91648 

.41602 

.90936 

25 

36 

.35184 

.93606 

.36812 

.92978 

.38430 

.92321 

.40035 

.91636 

.41628 

.90924 

24 

37 

.35211 

.93596 

.36839 

.92967 

.38456 

.92310 

.40062 

.91625 

.41655 

.90911 

23 

38 

.35239 

.93585 

.36867 

*92956 

.38483 

.92299 

.40088 

.91613 

.41681 

.90899 

22 

39 

.35266 

.93575 

.36894 

.92945 

.38510 

.92287 

.40115 

.91601 

.41707 

.90887 

21 

40 

.35293 

.93565 

.36921 

.92935 

.38537 

.92276 

.40141 

.91590 

.41734 

.90875 

20 

41 

.35320 

.93555 

.36948 

.92924 

.38564 

.92265 

.40168 

.91578 

.41760 

.90863 

19 

42 

.35347 

.93544 

.36975 

.92913 

.38591 

.92254 

.40195 

.91566 

.41787 

.90851 

18 

43 

.35375 

.93534 

.37002 

.92902 

.38617 

.92243 

.40221 

.91555 

.41813 

.90839 

17 

44 

.35402 

.93524 

.37029 

.92892 

.38644 

.92231 

.40248 

.91543 

.41840 

.90826 

16 

45 

.35429 

.93514 

.37056 

.92881 

.38671 

.92220 

.40275 

.91531 

.41866 

.90814 

15 

46 

.35456 

.93502 

.37083 

.92870 

.38698 

.92209 

.40301 

.91519 

.41892 

.90802 

14 

47 

.35484 

.93493 

.37110 

.92859 

.38725 

.92198 

.40328 

.91508 

.41919 

.90790 

13 

48 

.35511 

.93483 

.37137 

.92849 

.38752 

.92186 

.40355 

.91496 

.41945 

.90778 

12 

49 

.35538 

.93472 

.37164 

.92838 

.38778 

.92175 

.40381 

.91484 

.41972 

.90766 

11 

50 

.35565 

.93462 

.37191 

.92827 

.38805 

.92164 

.40408 

.91472 

.41998 

.90753 

10 

51 

.35592 

.93452 

.37218 

.92816 

.38832 

.92152 

.40434 

.91461 

.42024 

.90741 

9 

52 

.35619 

.93441 

.37245 

.92805 

.38859 

.92141 

.40461 

.91449 

.42051 

.90729 

8 

53 

.35647 

.93431 

.37272 

.92794 

.38886 

.92130 

.40488 

.91437 

.42077 

.90717 

7 

54 

.35674 

.93420 

.37299 

.92784 

.38912 

.92119 

.40514 

.91425 

.42104 

.90704 

6 

55 

.35701 

.93410 

.37326 

.92773 

.38939 

.92107 

.40541 

.91414 

.42130 

.90692 

5 

56 

.35728 

.93400 

.37353 

.92762 

.38966 

.92096 

.40567 

.91402 

.42156 

.90680 

4 

57 

.35755 

.93389 

.37380 

.92751 

.38993 

.92085 

.40594 

.91390 

.42183 

.90668 

3 

58 

.35782 

.93379 

.37407 

.92740 

.39020 

.92073 

.40621 

.91378 

.42209 

.90655 

2 

59 

.35810 

.93368 

.37434 

.92729 

.39046 

.92062 

.40647 

.91366 

.42235 

.90643 

1 

60 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

.42262 

.90631 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

I 

69° 

68° 

67° 

66° 

65° 

f 

460 


natural  sines  and  cosines. 


25° 

26° 

27° 

28° 

29° 

/ 

I - 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 
87 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

.42262 

.42288 

.42315 

.42341 

.42367 

.42394 

.42420 

.42446 

.42473 

.42499 

.42525 

.42552 

.42578 

.42604 

.42631 

.42657 

.42683 

.42709 

.42736 

.42762 

.42788 

.42815 

.42841 

.42867 

.42894 

.42920 

.42946 

.42972 

.42999 

.43025 

.43051 

.43077 

.43104 

.43130 

.43156 

.43182 

.43209 

.43235 

.43261 

.43287 

.43313 

.43340 

.43366 

.43392 

.43418 

.43445 

.43471 

.43497 

.43523 

.43549 

.43575 

.43602 

.43628 

.43654 

.43680 

.43706 

.43733 

.43759 

.43785 

.43811 

.43837 

.90631 

.90618 

.90606 

.90594 

.90582 

.90569 

.90557 

.90545 

.90532 

.90520 

.90507 

.90495 

.90483 

.90470 

.90458 

.90446 

.90433 

.90421 

.90408 

.90396 

.90383 

.90371 

.90358 

.90346 

.90334 

.90321 

.90309 

.90296 

.90284 

.90271 

.90259 

.90246 

.90233 

.90221 

.90208 

.90196 

.90183 

.90171 

.90158 

.90146 

.90133 

.90120 

.90108 

.90095 

.90082 

.90070 

.90057 

.90045 

.90032 

.90019 

.90007 

.89994 

.89981 

.89968 

.89956 

.89943 

.89930 

.89918 

.89905 

.89892 

.89879 

.43837 

.43863 

.43889 

.43916 

.43942 

.43968 

.43994 

.44020 

.44046 

.44072 

.44098 

.44124 

.44151 

.44177 

.44203 

.44229 

.44255 

.44281 

.44307 

.44333 

.44359 

.44385 

.44411 

.44437 

.44464 

.44490 

.44516 

.44542 

.44568 

.44594 

.44620 

.44646 

.44672 

.44698 

.44724 

.44750 

.44776 

.44802 

.44828 

.44854 

.44880 

.44906 

.44932 

.44958 

.44984 

.45010 

.45036 

.45062 

.45088 

.45114 

.45140 

.45166 

.45192 

.45218 

.45243 

.45269 

.45295 

.45321 

.45347 

.45373 

.45399 

.89879 

.89867 

.89854 

.89841 

.89828 

.89816 

.89803 

.89790 

.89777 

.89764 

.89752 

.89739 

.89726 

.89713 

.89700 

.89687 

.89674 

.89662 

.89649 

.89636 

.89623 

.89610 

.89597 

.89584 

.89571 

.89558 

.89545 

.89532 

.89519 

.89506 

.89493 

.89480 

.89467 

.89454 

.89441 

.89428 

.89415 

.89402 

.89389 

.89376 

.89363 

.89350 

.89337 

.89324 

.89311 

.89298 

.89285 

.89272 

.89259 

.89245 

.89232 

.89219 

.89206 

.89193 

.89180 

.89167 

.89153 

.89140 

.89127 

.89114 

.89101 

.45399 

.45425 

.45451 

.45477 

.45503 

.45529 

.45554 

.45580 

.45606 

.45632 

.45658 

.45684 
.45710 
.45736 
.45762  | 
.45787 
.45813  | 
.45839  | 
.45865 
.45891  : 
.45917  j 

.45942 

.45968 

.45994 

.46020 

.46046 

.46072  ! 

.46097 

.46123 

.46149  | 

.46175 

.46201  ! 

.46226 

.46252 

.46278 

.46304 

.46330 

.46355 

.46381 

.46407 

.46433 

.46458 

.46484 

.46510 

.46536 

.46561 

.46587 

.46613 

.46639 

.46664 

.46690 

.46716 

.46742 

.46767 

.46793 

.46819 

.46844 

.46870 

.46896 

.46921 

.46947 

.89101 

.89087 

.89074 

.89061 

.89048 

.89035 

.89021 

.89008 

.88995 

.88981 

.88968 

.88955 

.88942 

.88928 

.88915 

.88902 

.88888 

.88875 

.88862 

.88848 

.88835 

.88822 

.88808 

.88795 

.88782 

.88768 

.88755 

.88741 

.88728 

.88715 

.88701 

! .88688 
.88674 
| .88661 
i .88647 
! .88634 
.88620 
.88607 
1 .88593 
.88580 
.88566 

.88553 
.88539 
! .88526 
.88512 
! .88499 
! .88485 
1 .88472 
1 .88458 
1 .88445 
: .88431 

! .88417 
1 .88404 
i .88390 
I .88377 
1 .88363 
' .88349 
.88336 
! .88322 
| .88308 
.88295 

.46947 

.46973 

.46999 

.47024 

.47050 

.47076 

.47101 

.47127 

.47153 

.47178 

.47204 

.47229 

.47255 

.47281 

.47306 

.47332 

.47358 

.47383 

.47409 

.47434 

.47460 

.47486 

.47511 

.47537 

.47562 

.47588 

.47614 

.47639 

.47665 

.47690 

.47716 

.47741 

.47767 

.47793 

.47818 

.47844 

.47869 

.47895 

.47920 

.47946 

.47971 

.47997 

.48022 

.48048 

.48073 

.48099 

.48124 

.48150 

.48175 

.48201 

.48226 

.48252 

.48277 

.48303 

.48328 

.48354 

.48379 

.48405 

.48430 

.48456 

.48481 

.88295 

.88281 

.88267 

.88254 

.88240 

.88226 

.88213 

.88199 

.88185 

.88172 

.88158 

.88144 

.88130 

.88117 

.88103 

.88089 

.88075 

.88062 

.88048 

.88034 

.88020 

.88006 

.87993 

.87979 

.87965 

.87951 

.87937 

.87923 

.87909 

.87896 

.87882 

.87868 

.87854 

.87840 

.87826 

.87812 

.87798 

.87784 

.87770 

.87756 

.87743 

.87729 

.87715 

.87701 

.87687 

.87673 

.87659 

.87645 

.87631 

.87617 

.87603 

.87589 

.87575 

.87561 

.87546 

.87532 

.87518 

.87504 

.87490 

.87476 

.87462 

.48481 

.48506 

.48532 

.48557 

.48583 

.48608 

.48634  ! 

.48659  j 

.48684  | 

.48710 

.48735 

.48761 

.48786 

.48811 

.48837 

.48862 

.48888 

.48913 

.48938 

.48964  | 

.48989 

.49014 

.49040 

.49065 

.49090 

.49116 

.49141 

.49166 

.49192 

.49217 

.49242 

.49268 

.49293 

.49318 

.49344 

.49369 

.49394 

.49419 

.49445 

.49470 

.49495 

.49521 

.49546 

.49571 

.49596 

.49622 

.49647 

.49672 

.49697 

.49723 

.49748 

.49773 

.49798 

.49824 

.49849 

.49874 

.49899 

.49924 

.49950 

.49975 

.50000 

.87462 

.87448 

.87434 

.87420 

.87406 

.87391 

.87377 

.87363 

.87349 

.87335 

.87321 

.87306 

.87292 

.87278 

.87264 

.87250 

.87235 

.87221 

.87207 

.87193 

.87178 

.87164 

.87150 

.87136 

.87121 

.87107 

.87093 

.87079 

.87064 

.87050 

.87036 

.87021 

.87007 

.86993 

.86978 

.86964 

.86949 

.86935 

.86921 

.86906 

.86892 

.86878 

.86863 

.86849 

.86834 

.86820 

.86805 

.86791 

.86777 

.86762 

.86748 

,.86733 

.86719 

.86704 

.86690 

.86675 

.86661 

.86646 

.86632 

.86617 

.86603 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

Cosine 

Sine 

Cosine 

| Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

/ 

64° 

63° 

62° 

61° 

60° 

NATURAL  SINES  AND  COSINES. 


461 


30° 

31° 

32° 

33° 

34° 

/ 

t 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

.50000 

.50025 

.50050 

.50076 

.50101 

.50126 

.50151 

.50176 

.50201 

.50227 

.50252 

.50277 

.50302 

.50327 

.50352 

.50377 

.50403 

.50428 

.50453 

.50478 

.50503 

.50528 

.50553 

.50578 

.50603 

.50628 

.50654 

.50679 

.50704 

.50729 

.50754 

.50779 

.50804 

.50829 

.50854 

.50879 

.50904 

.50929 

.50954 

.50979 

.51004 

.51029 

.51054 

.51079 

.51104 

.51129 

.51154 

.51179 

.51204 

.51229 

.51254 

.51279 

.51304 

.51329 

.51354 

.51379 

.51404 

.51429 

.51454 

.51479 

.51504 

.86603 

.86588 

.86573 

.86559 

.86544 

.86530 

.86515 

.86501 

.86486 

.86471 

.86457 

.86442 

.86427 

.86413 

.86398 

.86384 

.86369 

.86354 

.86340 

.86325 

.86310 

.86295 

.86281 

.86266 

.86251 

.86237 

.86222 

.86207 

.86192 

.86178 

.86163 

.86148 

.86133 

.86119 

.86104 

.86089 

.86074 

.86059 

.86045 

.86030 

.86015 

.86000 

.85985 

.85970 

.85956 

.85941 

.85926 

.85911 

.85896 

.85881 

.85866 

.85851 

.85836 

.85821 

.85806 

.85792 

.85777 

.85762 

.85747 

.85732 

.85717 

.51504 

.51529 

.51554 

.51579 

.51604 

.51628 

.51653 

.51678 

.51703 

.51728 

.51753 

.51778 

.51803 

.51828 

.51852 

.51877 

.51902 

.51927 

.51952 

.51977 

.52002 

.52026 

.52051 

.52076 

.52101 

.52126 

.52151 

.52175 

.52200 

.52225 

.52250 

.52275 

.52299 

.52324 

.52349 

.52374 

.52399 

.52423 

.52448 

.52473 

.52498 

.52522 

.52547 

.52572 

.52597 

.52621 

.52646 

.52671 

.52696 

.52720 

.52745 

.52770 

.52794 

.52819 

.52844 

.52869 

.52893 

.52918 

.52943 

.52967 

.52992 

.85717 

.85702 

.85687 

.85672 

.85657 

.85642 

.85627 

.85612 

.85597 

.85582 

.85567 

.85551 

.85536 

.85521 

.85506 

.85491 

.85476 

.85461 

.85446 

.85431 

.85416 

.85401 

.85385 

.85370 

.85355 

.85340 

.85325 

.85310 

.85294 

.85279 

.85264 

.85249 

.85234 

.85218 

.85203 

.85188 

.85173 

.85157 

.85142 

.85127 

.85112 

.85096 

.85081 

.85066 

.85051 

.85035 

.85020 

.85005 

.84989 

.84974 

.84959 

.84943 

.84928 

.84913 

.84897 

.84882 

.84866 

.84851 

.84836 

.84820 

.84805 

.52992 

.53017 

.53041 

.53066 

.53091 

.53115 

.53140 

.53164 

.53189 

.53214 

.53238 

.53263 

.53288 

.53312 

.53337 

.53361 

.53386 

.53411 

.53435 

.53460 

.53484 

.53509 

.53534 

.53558 

.53583 

.53607 

.53632 

.53656 

.53681 

.53705 

.53730 

.53754 
.53779 
.53804 
.53828 
.53853 
. .53877 
.53902 
.53926 
.53951 
.53975 

.54000 

.54024 

.54049 

.54073 

.54097 

.54122 

.54146 

.54171 

.54195 

.54220 

.54244 

.54269 

.54293 

.54317 

.54342 

.54366 

.54391 

.54415 

.54440 

.54464 

.84805 

.84789 

.84774 

.84759 

.84743 

.84728 

.84712 

.84697 

.84681 

.84666 

.84650 

.84635 

.84619 

.84604 

.84588 

.84573 

.84557 

.84542 

.84526 

.84511 

.84495 

.84480 

.84464 

.84448 

.84433 

.84417 

.84402 

.84386 

.84370 

.84355 

.84339 

.84324 

.84308 

.84292 

.84277 

.84261 

.84245 

.84230 

.84214 

.84198 

.84182 

.84167 

.84151 

.84135 

.84120 

.84104 

.84088 

.84072 

.84057 

.84041 

.84025 

.84009 

.83994 

.83978 

.83962 

.83946 

.83930 

.83915 

.83899 

.83883 

.83867 

.54464 

.54488 

.54513 

.54537 

.54561 

.54586 

.54610 

.54635 

.54659 

.54683 

.54708 

.54732 

.54756 

.54781 

.54805 

.54829 

.54854 

.54878 

.54902 

.54927 

.54951 

.54975 

.54999 

.55024 

.55048 

.55072 

.55097 

.55121 

.55145 

.55169 

.55194 

.55218 

.55242 

.55266 

.55291 

.55315 

.55339 

.55363 

.55388 

.55412 

.55436 

.55460 

.55484 

.55509 

.55533 

.55557 

.55581 

.55605 

.55630 

.55654 

.55678 

.55702 

.55726 

.55750 

.55775 

.55799 

.55823 

.55847 

.55871 

.55895 

.55919 

.83867 

.83851 

.83835 

.83819 

.83804 

.83788 

.83772 

.83756 

.83740 

.83724 

.83708 

.83692 

.83676 

.83660 

.83645 

.83629 

.83613 

.83597 

.83581 

.83565 

.83549 

.83533 

.83517 

.83501 

.83485 

.83469 

.83453 

.83437 

.83421 

.83405 

.83389 

.83373 

.83356 

.83340 

.83324 

.83308 

.83292 

.83276 

.83260 

.83244 

.83228 

.83212 

.83195 

.83179 

.83163 

.83147 

.83131 

.83115 

.83098 

.83082 

.83066 

.83050 

.83034 

.83017 

.83001 

.82985 

.82969 

.82953 

.82936 

.82920 

.82904 

.55919 

.55943 

.55968 

.55992 

.56016 

.56040 

.56064 

.56088 

.56112 

.56136 

.56160 

.56184 

.56208 

.56232 

.50256 

.56280 

.56305 

.56329 

.56353 

.56377 

.56401 

.56425 

.56449 

.56473 

.56497 

.56521 

.56545 

.56569 

.56593 

.56617 

.56641 

.56665 

.56689 

.56713 

.56736 

.56760 

.56784 

.56808 

.56832 

.56856 

.56880 

.56904 

.56928 

.56952 

.56976 

.57000 

.57024 

.57047 

.57071 

.57095 

.57119 

.57143 

.57167 

.57191 

.57215 

.57238 

.57262 

.57286 

.57310 

.57334 

.57358 

.82904 

.82887 

.82871 

.82855 

.82839 

.82822 

.82806 

.82790 

.82773 

.82757 

.82741 

.82724 

.82708 

.82692 

.82675 

.82659 

.82643 

.82626 

.82610 

.82593 

.82577 

.82561 

.82544 

.82528 

.82511 

.82495 

.82478 

.82462 

.82446 

.82429 

.82413 

.82396 

.82380 

.82363 

.82347 

.82330 

.82314 

.82297 

.82281 

.82264 

.82248 

.82231 

.82214 

.82198 

.82181 

.82165 

.82148 

.82132 

.82115 

.82098 

.82082 

.82065 

.82048 

.82032 

.82015 

.81999 

.81982 

.81965 

.81949 

.81932 

.81915 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 
28 
27 
26 
25 
24 
23 
22 
21  , 
20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

/ 

Cosine 

i Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

59° 

58° 

i 57° 

56° 

55° 

f 

462 


NATURAL  SINES  AND  COSINES. 


35° 

36° 

37° 

38° 

39° 

f 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.57358 

.81915 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

60 

1 

.57381 

.81899 

.58802 

.80885 

.60205 

.79846 

.61589 

.78783 

.62955 

.77696 

59 

2 

.57405 

.81882 

.58826 

.80867 

.60228 

.79829 

.61612 

.78765 

.62977 

.77678 

58 

3 

.57429 

.81865 

.58849 

.80850 

.60251 

.79811 

.61635 

.78747 

.63000 

.77660 

57 

4 

.57453 

.81848 

.58873 

.80833 

.60274 

.79793 

.61658 

.78729 

.63022 

.77641 

56 

5 

.57477 

.81832 

.58896 

.80816 

.60298 

.79776 

.61681 

.78711 

.63045 

.77623 

55 

6 

.57501 

.81815 

.58920 

.80799 

.60321 

.79758 

.61704 

.78694 

.63068 

.77605 

54 

7 

.57524 

.81798 

.58943 

.80782 

.60344 

.79741 

.61726 

.78676 

.63090 

.77586 

53 

8 

.57548 

.81782 

.58967 

.80765 

.60367 

.79723 

.61749 

.78658 

.63113 

.77568 

52 

9 

.57572 

.81765 

.58990 

.80748 

.60390 

.79706 

.61772 

.78640 

.63135 

.77550 

51 

10 

.57596 

.81748 

.59014 

.80730 

.60414 

.79688 

.61795 

.78622 

.63158 

.77531 

50 

11 

.57619 

.81731 

.59037 

.80713 

.60437 

.79671 

.61818 

.78604 

.63180 

.77513 

49 

12 

.57643 

.81714 

.59061 

.80696 

.60460 

.79653 

.61841 

.78586 

.63203 

.77494 

48 

13 

.57667 

.81698 

.59084 

.80679 

.60483 

.79635 

.61864 

.78568 

.63225 

.77476 

47 

14 

.57691 

.81681 

.59108 

.80662 

.60506 

.79618 

.61887 

.78550 

.63248 

.77458 

46 

15 

.57715 

.81664 

.59131 

.80644 

.60529 

.79600 

.61909 

.78532 

.63271 

.77439 

45 

16 

.57738 

.81647 

.59154 

.80627 

.60553 

.79583 

.61932 

.78514 

.63293 

.77421 

44 

17 

.57762 

.81631 

.59178 

.80610 

.60576 

.79565 

.61955 

.78496 

.63316 

.77402 

43 

18 

.57786 

.81614 

.59201 

.80593 

.60599 

.79547 

.61978 

.78478 

.63338 

.77384 

42 

19 

.57810 

.81597 

.59225 

.80576 

.60622 

.79530 

.62001 

.78460 

.63361 

.77366 

41 

20 

.57833 

.81580 

.59248 

.80558 

.60645 

.79512 

.62024 

.78442 

.63383 

.77347 

40 

21 

.57857 

.81563 

.59272 

.80541 

.60668 

.79494 

.62046 

.78424 

.63406 

.77329 

39 

22 

.57881 

.81546 

.59295 

.80524 

.60691 

.79477 

.62069 

.78405 

.63428 

.77310 

38 

23 

.57904 

.81530 

.59318 

.80507 

.60714 

.79459 

.62092 

.78387 

.63451 

.77292 

37 

24 

.57928 

.81513 

.59342 

.80489 

.60738 

.79441 

.62115 

.78369 

.63473 

.77273 

36 

25 

.57952 

.81496 

.59365 

.80472 

.60761 

.79424 

.62138 

.78351 

.63496 

.77255 

35 

26 

.57976 

.81479 

.59389 

.80455 

.60784 

.79406 

.62160 

.78333 

.63518 

.77236 

34 

27 

.57999 

.81462 

.59412 

.80438 

.60807 

.79388 

.62183 

.78315 

.63540 

.77218 

33 

28 

.58023 

.81445 

.59436 

.80420 

.60830 

.79371 

.62206 

.78297 

.63563 

.77199 

32 

29 

.58047 

.81428 

.59459 

.80403 

.60853 

.79353 

.62229 

.78279 

.63585 

.77181 

31 

30 

.58070 

.81412 

.59482 

.80386 

.60876 

.79335 

.62251 

.78261 

.63608 

.77162 

30 

31 

.58094 

.81395 

.59506 

.80368 

.60899 

.79318 

.62274 

.78243 

.63630 

.77144 

29 

32 

.58118 

.81378 

.59529 

.80351 

.60922 

.79300 

.62297 

.78225 

.63653 

.77125 

28 

33 

.58141 

.81361 

.59552 

.80334 

.60945 

.79282 

.62320 

.78206 

.63675 

.77107 

27 

34 

.58165 

.81344 

.59576 

.80316 

.60968 

.79264 

.62342 

.78188 

.63698 

.77088 

26 

35 

.58189 

.81327 

.59599 

.80299 

.60991 

.79247 

.62365 

.78170 

.63720 

.77070 

25 

36 

.58212 

.81310 

.59622 

.80282 

.61015 

.79229 

.62388 

.78152 

.63742 

.77051 

24 

37 

.58236 

.81293 

.59646 

.80264 

.61038 

.79211 

.62411 

.78134 

.63765 

.77033 

23 

38 

.58260 

.81276 

.59669 

.80247 

.61061 

.79193 

.62433 

.78116 

.63787 

.77014 

22 

39 

.58283 

.81259 

.59693 

.80230 

.61084 

.79176 

.62456 

.78098 

.63810 

.76996 

21 

40 

.58307 

.81242 

.59716 

.80212 

.61107 

.79158 

.62479 

.78079 

.63832 

.76977 

20 

41 

.58330 

.81225 

.59739 

.80195 

.61130 

.79140 

.62502 

.78061 

.63854 

.76959 

19 

42 

.58354 

.81208 

.59763 

.80178 

.61153 

.79122 

.62524 

.78043 

.63877 

.76940 

18 

43 

.58378 

.81191 

.59786 

.80160 

.61176 

.79105 

.62547 

.78025 

.63899 

.76921 

17 

44 

.58401 

.81174 

.59809 

.80143 

.61199 

.79087 

.62570 

.78007 

.63922 

.76903 

16 

45 

.58425 

.81157 

.59832 

.80125 

.61222 

.79069 

.62592 

.77988 

.63944 

.76884 

15 

46 

.58449 

.81140 

.59856 

.80108 

.61245 

.79051 

.62615 

.77970 

.63966 

.76866 

14 

47 

.58472 

.81123 

.59879 

.80091 

.61268 

.79033 

.62638 

.77952 

.63989 

.76847 

13 

48 

.58496 

.81106 

.59902 

.80073 

.61291 

.79016 

.62660 

.77934 

.64011 

.76828 

12 

49 

.58519 

.§1089 

.59926 

.80056 

.61314 

.78998 

.62683 

.77916 

.64033 

.76810 

11 

50 

.58543 

.81072 

.59949 

.80038 

.61337 

.78980 

.62706 

.77897 

.64056 

.76791 

10 

51 

.58567 

.81055 

.59972 

.80021 

.61360 

.78962 

.62728 

.77879  ■ 

.64078 

.76772 

9 

52 

.58590 

.81038 

.59995 

.80003 

.61383 

.78944 

.62751 

.77861 

.64100 

.76754 

8 

53 

.58614 

.81021 

.60019 

.79986 

.61406 

.78926 

.62774 

.77843 

.64123 

.76735 

7 

54 

.58637 

.81004 

.60042 

.79968 

.61429 

.78908 

.62796 

.77824 

.64145 

.76717 

6 

55 

.58661 

.80978 

.60065 

.79951 

.61451 

.78891 

.62819 

.77806 

.64167 

.76698 

5 

56 

.58684 

.80970 

.60089 

.79934 

.61474 

.78873 

.62842 

.77788 

.64190 

.76679 

4 

57 

.58708 

.80953 

.60112 

.79916 

.61497 

.78855 

.62864 

.77769 

.64212 

.76661 

3 

58 

.58731 

.80936 

.60135 

.79899 

.61520 

.78837 

.62887 

.77751 

.64234 

.76642 

2 

59 

.58755 

.80919 

.60158 

.79881 

.61543 

.78819 

.62909 

.77733 

.64256 

.76623 

1 

60 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

.64279 

.76604 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

54° 

; 53° 

52° 

51° 

50° 

/ 

NATURAL  SINES  AND  COSINES. 


463 


40° 

41° 

42° 

43° 

44° 

/ 

/ - 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine  i 

Cosine 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 
. 49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

.64279 

.64301 

.64323 

.64346 

.64368 

.64390 

.64412 

.64435 

.64457 

.64479 

.64501 

.64524 

.64546 

.64568 

.64590 

.64612 

.64635 

.64657 

.64679 

.64701 

.64723 

.64746 

.64768 

.64790 

.64812 

.64834 

.64856 

.64878 

.64901 

.64923 

.64945 

.64967 

.64989 

.65011 

.65033 

.65055 

.65077 

.65100 

.65122 

.65144 

.65166 

.65188 

.65210 

.65232 

.65254 

.65276 

.65298 

.65320 

.65342 

.65364 

.65386 

.65408 

.65430 

.65452 

.65474 

.65496 

.65518 

.65540 

.65562 

.65584 

.65606 

.76604 

.76586 

.76567 

.76548 

.76530 

.76511 

.76492 

.76473 

.76455 

.76436 

.76417 

.76398 

.76380 

.76361 

.76342 

.76323 

.76304 

.76286 

.76267 

.76248 

.76229 

.76210 

.76192 

.76173 

.76154 

.76135 

.76116 

.76097 

.76078 

.76059 

.76041 

.76022 

.76003 

.75984 

.75965 

.75946 

.75927 

.75908 

.75889 

.75870 

.75851 

.75832 

.75813 

.75794 

.75775 

.75756 

.75738 

.75719 

.75700 

.75680 

.75661 

.75642 

.75623 

.75604 

.75585 

.75566 

.75547 

.75528 

.75509 

.75490 

.75471 

.65606 

.65628 

.65650 

.65672 

.65694 

.65716 

.65738 

.65759 

.65781 

.65803 

.65825 

' 

.65847 

.65869 

.65891 

.65913 

.65935 

.65956 

.65978 

.66000 

.66022 

.66044 

.66066 

.66088 

.66109 

.66131 

.66153 

.66175 

.66197 

.66218 

.66240 

.66262 

.66284 

.66306 

.66327 

.66349 

.66371 

.66393 

.66414 

.66436 

.66458 

.66480 

.66501 
.66523 
.66545 
.66566 
.66588 
.66610 
.66632 
.66653 
.66675 
- .66697 

.66718 

.66740 

.66762 

.66783 

.66805 

.66827 

.66848 

.66870 

.66891 

.66913 

.75471 

.75452 

.75433 

.75414 

.75395 

.75375 

.75356 

.75337 

.75318 

.75299 

.75280 

.75261 

.75241 

.75222 

.75203 

.75184 

.75165 

.75146 

.75126 

.75107 

.75088 

.75069 

.75050 

.75030 

.75011 

.74992 

.74973 

.74953 

.74934 

.74915 

.74896 

.74876 

.74857 

.74838 

.74818 

.74799 

.74780 

.74760 

.74741 

.74722 

.74703 

.74683 

.74664 

.74644 

.74625 

.74606 

.74586 

.74567 

.74548 

.74528 

.74509 

.74489 

.74470 

.74451 

.74431 

.74412 

.74392 

.74373 

.74353 

.74334 

.74314 

.66913 

.66935 

.66956 

.66978 

.66999 

.67021 

.67043 

.67064 

.67086 

.67107 

.67129 

.67151 

.67172 

.67194 

.67215 

.67237 

.67258 

.67280 

.67301 

.67323 

.67344 

.67366 

.67387 

.67409 

.67430 

.67452 

.67473 

.67495 

.67516 

.67538 

.67559 

.67580 

.67602 

.67623 

.67645 

.67666 

.67688 

.67709 

.67730 

.67752 

.67773 

.67795 

.67816 

.67837 

.67859 

.67880 

.67901 

.67923 

.67944 

.67965 

.67987 

.68008 

.68029 

.68051 

.68072 

.68093 

.68115 

.68136 

.68157 

.68179 

.68200 

.74314 

.74295 

.74276 

.74256 

.74237 

.74217 

.74198 

.74178 

.74159 

.74139 

.74120 

.74100 

.74080 

.74061 

.74041 

.74022 

.74002 

.73983 

.73963 

.73944 

.73924 

.73904 

.73885 

.73865 

.73846 

.73826 

.73806 

.73787 

.73767 

.73747 

.73728 

.73708 

.73688 

.73669 

.73649 

.73629 

.73610 

.73590 

.73570 

.73551 

.73531 

.73511 

.73491 

.73472 

.73452 

.73432 

.73413 

.73393 

.73373 

.73353 

.73333 

.73314 

.73294 

.73274 

.73254 

.73234 

.73215 

.73195 

.73175 

.73155 

.73135 

.68200 

.68221 

.68242 

.68264 

.68285 

.68306 

.68327 

.68349 

.68370 

.68391 

.68412 

.68434 

.68455 

.68476 

.68497 

.68518 

.68539 

.68561 

.68582 

.68603 

.68624 

.68645 

.68666 

.68688 

.68709 

.68730 

.68751 

.68772 

.68793 

.68814 

.68835 

.68857 

.68878 

.68899 

.68920 

.68941 

.68962 

.68983 

.69004 

.69025 

.69046 

.69067 

.69088 

.69109 

.69130 

.69151 

.69172 

.69193 

.69214 

.69235 

.69256 

.69277 

.69298 

.69319 

.69340 

.69361 

.69382 

.69403 

.69424 

.69445 

.69466 

.73135 

.73116 

.73096 

.73076 

.73056 

.73036 

.73016 

.72996 

.72976 

.72957 

.72937 

.72917 

.72897 

.72877 

.72857 

.72837 

.72817 

.72797 

.72777 

.72757 

.72737 

.72717 

.72697 

.72677 

.72657 

.72637 

.72617 

.72597 

.72577 

.72557 

.72537 

.72517 

.72497 

.72477 

.72457 

.72437 

.72417 

.72397 

.72377 

.72357 

.72337 

.72317 

.72297 

.72277 

.72257 

.72236 

.72216 

.72196 

.72176 

.72156 

.72136 

.72116 

.72095 

.72075 

.72055 

.72035 

.72015 

.71995 

.71974 

.71954 

.71934 

.69466 

.69487 

.69508 

.69529 

.69549 

.69570 

.69591 

.69612 

.69633 

.69654 

.69675 

.69696 

.69717 

.69737 

.69758 

.69779 

.69800 

.69821 

.69842 

.69862 

.69883 

.69904 

.69925 

.69946 

.69966 

.69987 

.70008 

.70029 

.70049 

.70070 

.70091 

.70112 

.70132 

.70153 

.70174 

.70195 

.70215 

.70236 

.70257 

.70277 

.70298 

.70319 

.70339 

.70360 

.70381 

.70401 

.70422 

.70443 

.70463 

.70484 

.70505 

.70525 

.70546 

.70567 

.70587 

.70608 

.70628 

.70649 

.70670 

.70690 

.70711 

.71934 

.71914 

.71894 

.71873 

.71853 

.71833 

.71813 

.71792 

.71772 

.71752 

.71732 

.71711 

.71691 

.71671 

.71650 

.71630 

.71610 

.71590 

.71569 

.71549 

.71529 

.71508 

.71488 

.71468 

.71447 

.71427 

.71407 

.71386 

.71366 

.71345 

.71325 

.71305 

.71284 

.71264 

.71243 

.71223 

.71203 

.71182 

.71162 

.71141 

.71121 

.71100 

.71080 

.71059 

.71039 

.71019 

.70998 

.70978 

.70957 

.70937 

.70916 

.70896 

.70875 

.70855 

.70834 

.70813 

.70793 

.70772 

.70752 

.70731 

.70711 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

T 

6 

5 

4 

3 

2 

1 

0 

/ 

Cosine 

s Sine 

1 

Cosine 

} Sine 

Cosine 

: Sine 

Cosine 

; Sine 

Cosine 

! Sine 

r 

49° 

48° 

47° 

46° 

45° 

464  NATURAL  TANGENTS  AND  COTANGENTS. 


0° 

1° 

2° 

3° 

4° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.00000 

Infin. 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

60 

1 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

.07022 

14.2411 

59 

2 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

.07051 

14.1821 

58 

3 

.00087 

1145.92 

.01833 

54.5613 

.03579 

27.9372 

.05328 

18.7678 

.07080 

14.1235 

57 

4 

.00116 

859.436 

.01862 

53.7086 

.03609 

27.7117 

.05357 

18.6656 

.07110 

14.0655 

56 

5 

.00145 

687.549 

.01891 

52.8821 

.03638 

27.4899 

.05387 

18.5645 

.07139 

14.0079 

55 

6 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

.07168 

13.9507 

54 

7 

.00204 

491.106 

.01949 

51.3032 

.03696 

27.0566 

.05445 

18.3655 

.07197 

13.8940 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2677 

.07227 

13.8378 

52 

9 

.00262 

381.971 

.02007 

49.8157 

.03754 

26.6367 

.05503 

18.1708 

.07256 

13.7821 

51 

10 

.00291 

343.774 

.02036 

49.1039 

.03783 

26.4316 

.05533 

18.0750 

.07285 

13.7267 

50 

11 

.00320 

312.521 

.02066 

48.4121 

.03812 

26.2296 

.05562 

17.9802 

.07314 

13.6719 

49 

12 

.00349 

286.478 

.02095 

47.7395 

.03842 

26.0307 

.05591 

17.8863 

.07344 

13.6174 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

.07373 

13.5634 

47 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

.07402 

13.5098 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6106 

.07431 

13.4566 

45 

16 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

.07461 

13.4039 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

.07490 

13.3515 

43 

18 

.00524 

190.984 

.02269 

44.0661 

.04016 

24.8978 

.05766 

17.3432 

.07519 

13.2996 

42 

19 

.00553 

180.932 

.02298 

43  5081 

.04046 

24.7185 

.05795 

17.2558 

.07548 

13.2480 

41 

20 

.00582 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1693 

.07578 

13.1969 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.3675 

.05854 

17.0837 

.07607 

13.1461 

39 

22 

.00640 

156.259 

.02386 

41.9158 

.04133 

24.1957 

.05883 

16.9990 

.07636 

13.0958 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

.07665 

13.0458 

37 

24 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05941 

16.8319 

.07695 

12.9962 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

.07724 

12.9469 

35 

26 

.00756 

132.219 

.02502 

39.9655 

.04250 

23.5321 

.05999 

16.6681 

.07753 

12.8981 

34 

27 

.00785 

127.321 

.02531 

39.5059 

.04279 

23.3718 

.06029 

16.5874 

.07782 

12.8496 

33 

28 

.00815 

122.774 

.02560 

39.0568 

.04308 

23.2137 

.06058 

16.5075 

.07812 

12.8014 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04337 

23.0577 

.06087 

16.4283 

.07841 

12.7536 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.9038 

.06116 

16.3499 

.07870 

12.7062 

30 

31 

.00902 

110.892 

.02648 

37.7686 

.04395 

22.7519 

.06145 

16.2722 

.07899 

12.6591 

29 

32 

.00931 

107.426 

.02677 

37.3579 

.04424 

22.6020 

.06175 

16.1952 

.07929 

12.6124 

28 

33 

.00960 

104.171 

.02706 

36.9560 

.04454 

22.4541 

.06204 

16.1190 

.07958 

12.5660 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

.07987 

12.5199 

26 

35 

.01018 

98.2179 

.02764 

36.1776 

.04512 

22.1640 

.06262 

15.9687 

.08017 

12.4742 

25 

36 

.01047 

95.4895 

.02793 

35.8006 

.04541 

22.0217 

.06291 

15.8945 

.08046 

12.4288 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

.08075 

12.3838 

23 

38 

.01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06350 

15.7483 

.08104 

12.3390 

22 

39 

.01135 

88.1438 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

.08134 

12.2946 

21 

40 

.01164 

85.9398 

.02910 

34.3678 

.04658 

21.4704 

.06408 

15.6048 

.08163 

12.2505 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.3369 

.06437 

15.5340 

.08192 

12.2067 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04716 

21,2049 

.06467 

15.4638 

.08221 

12.1632 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

.08251 

12.1201 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20.9460 

.06525 

15.3254 

.08280 

12.0772 

16 

45 

.01309 

76.3900 

.03055 

32.7303 

.04803 

20.8188 

.06554 

15.2571 

.08309 

12.0346 

15 

46 

.01338 

74.7292 

.03084 

32.4213 

.04833 

20.6932 

.06584 

15.1893 

.08339 

11.9923 

14 

47 

.01367 

73.1390 

.03114 

32.1181 

.04862 

20  5691 

.06613 

15.1222 

.08368 

11.9504 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06642 

15.0557 

.08397 

11.9087 

12 

49 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

.08427 

11.8673 

11 

50 

.01455 

68.7501 

.03201 

31.2416 

.04949 

20.2056 

.06700 

14.9244 

.08456 

11.8262 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

.08485 

11.7853 

9 

52 

.01513 

66.1055 

.03259 

30.6833 

.05007 

19.9702 

.06759 

14.7954 

.08514 

11.7448 

8 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

.08544 

11.7045 

7 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

.08573 

11.6645 

6 

55 

.01600 

62.4992 

.03346 

29.8823 

.05095 

19.6273 

.06847 

14.6059 

.08602 

11.6248 

5 

56 

.01629 

61.3829 

.03376 

29.6245 

.05124 

19.5156 

.06876 

14.5438 

.08632 

11.5853 

4 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.4051 

.06905 

14.4823 

.08661 

11.5461 

3 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.4212 

.08690 

11.5072 

2 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

.08720 

11.4685 

1 

60 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

.08749 

11.4301 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

1 

Tang 

Cotang 

Tang 

89° 

88° 

87° 

86° 

85° 

/ 

NATURAL  TANGENTS  AND  COTANGENTS. 


465 


5° 

6° 

7° 

8° 

9° 

/ 

f 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

.08749 

.08778 

.08807 

.08837 

.08866 

.08895 

.08925 

.08954 

.08983 

.09013 

.09042 

.09071 

.09101 

.09130 

.09159 

.09189 

.09218 

.09247 

.09277 

.09306 

.09335 

.09365 

.09394 

.09423 

.09453 

.09482 

.09511 

.09541 

.09570 

.09600 

.09629 

.09658 

.09688 

.09717 

.09746 

.09776 

.09805 

.09834 

.09864 

.09893 

.09923 

.09952 

.09981 

.10011 

.10040 

.10069 

.10099 

.10128 

.10158 

.10187 

.10216 

.10246 

.10275 

.10305 

.10334 

.10363 

.10393 

.10422 

.10452 

.10481 

.10510 

11.4301 
11.3919 
11.3540 
11.3163 
11.2789 
11.2417 
11 .2048 
11.1681 
11.1316 
11.0954 
11.0594 

11.0237 

10.9882 

10.9529 

10.9178 

10.8829 

10.8483 

10.8139 

10.7797 

10.7457 

10.7119 

10.6783 

10.6450 

10.6118 

10.5789 

10.5462 

10.5136 

10.4813 

10.4491 

10.4172 

10.3854 

10.3538 

10.3224 

10.2913 

10.2602 

10.2294 

10.1988 

10.1683 

10.1381 

10.1080 

10.0780 

10.0483 

10.0187 

9.98931 

9.96007 

9.93101 

9.90211 

9.87338 

9.84482 

9.81641 

9.78817 

9.76009 

9.73217 

9.70441 

9.67680 

9.64935 

9.62205 

9.59490 

9.56791 

9.54106 

9.51436 

.10510 

.10540 

.10569 

.10599 

.10628 

.10657 

.10687 

.10716 

.10746 

.10775 

.10805 

.10834 

.10863 

.10893 

.10922 

.10952 

.10981 

.11011 

.11040 

.11070 

.11099 

.11128 

.11158 

.11187 

.11217 

.11246 

.11276 

.11305 

.11335 

.11364 

.11394 

.11423 

.11452 

.11482 

.11511 

.11541 

.11570 

.11600 

.11629 

.11659 

.11688 

.11718 

.11747 

.11777 

.11806 

.11836 

.11865 

.11895 

.11924 

.11954 

.11983 

.12013 

.12042 

.12072 

.12101 

.12131 

.12160 

.12190 

.12219 

.12249 

.12278 

9.51436 

9.48781 

9.46141 

9.43515 

9.40904 

9.38307 

9.35724 

9.33155 

9.30599 

9.28058 

9.25530 

9.23016 

9.20516 

9.18028 

9.15554 

9.13093 

9.10646 

9.08211 

9.05789 

9.03379 

9.00983 

8.98598 

8.96227 

8.93867 

8.91520 

8.89185 

8.86862 

8.84551 

8.82252 

8.79964 

8.77689 

8.75425 

8.73172 

8.70931 

8.68701 

8.66482 

8.64275 

8.62078 

8.59893 

8.57718 

8.55555 

8.53402 

8.51259 

8.49128 

8.47007 

8.44896 

8.42795 

8.40705 

8.38625 

8.36555 

8.34496 

8.32446 

8.30406 

8.28376 

8.26355 

8.24345 

8.22344 

8.20352 

8.1837C 

8.16398 

8.1443c 

.12278 

.12308 

.12338 

.12367 

.12397 

.12426 

.12456 

.12485 

.12515 

.12544 

.12574 

.12603 

.12633 

.12662 

.12692 

.12722 

.12751 

.12781 

.12810 

.12840 

.12869 

.12899 

.12929 

.12958 

.12988 

.13017 

.13047 

.13076 

.13106 

.13136 

.13165 

.13195 

.13224 

.13254 

.13284 

.13313 

.13343 

.13372 

.13402 

.13432 

.13461 

.13491 

.13521 

.13550 

.13580 

.13609 

.13639 

.13669 

.13698 

.13728 

.13758 

.13787 
.13817 
.13846 
i .13876 
i .13906 
: .13935 

! .13965 

1 .13995 

! .14024 

i .ll054 

8.14435 

8.12481 

8.10536 

8.08600 

8.06674 

8.04756 

8.02848 

8.00948 

7.99058 

7.97176 

7.95302 

7.93438 

7.91582 

7.89734 

7.87895 

7.86064 

7.84242 

7.82428 

7.80622 

7.78825 

7.77035 

7.75254 

7.73480 

7.71715 

7.69957 

7.68208 

7.66466 

7.64732 

7.63005 

7.61287 

7.59575 

7.57872 

7.56176 

7.54487 

7.52806 

7.51132 

7.49465 

7.47806 

7.46154 

7.44509 

7.42871 

7.41240 

7.39616 

7.37999 

7.36389 

7.34786 

7.33190 

7.31600 

7.30018 

7.28442 

7.26873 

7.25310 

7.23754 

7.22204 

7.20661 

7.19125 

7.17594 

7.16071 

7.14553 

7.13042 

7.11537 

.14054 

.14084 

.14113 

.14143 

.14173 

.14202 

.14232 

.14262 

.14291 

.14321 

.14351 

.14381 

.14410 

.14440 

.14470 

.14499 

.14529 

.14559 

.14588 

.14618 

.14648 

.14678 

.14707 

.14737 

.14767 

.14796 

.14826 

.14856 

.14886 

.14915 

.14945 

.14975 

.15005 

.15034 

.15064 

.15094 

.15124 

.15153 

.15183 

.15213 

.15243 

.15272 

.15302 

.15332 

.15362 

.15391 

.15421 

.15451 

.15481 

.15511 

.15540 

.15570 

.15600 

.15630 

.15660 

.15689 

.15719 

.15749 

.15779 

.15809 

.15838 

7.11537 

7.10038 

7.08546 

7.07059 

7.05579 

7.04105 

7.02637 

7.01174 

6.99718 

6.98268 

6.96823 

6.95385 

6.93952 

6.92525 

6.91104 

6.89688 

6.88278 

6.86874 

6.85475 

6.84082 

6.82694 

6.81812 

6.79936 

6.78564 

6.77199 

6.75838 

6.74483 

6.73133 

6.71789 

6.70450 

6.69116 

6.67787 

6.66463 

6.65144 

6.63831 

6.62523 

6.61219 

6.59921 

6.58627 

6.57339 

6.56055 

6.54777 

6.53503 

6.52234 

6.50970 

6.49710 

6.48456 

6.47206 

6.45961 

6.44720 

6.43484 

6.42253 

6.41026 

6.39804 

6.38587 

6.37374 

6.36165 

6.34961 

6.33761 

6.32566 

6.31375 

.15838 

.15868 

.15898 

.15928 

.15958 

.15988 

.16017 

.16047 

.16077 

.16107 

.16137 

.16167 

.16196 

.16226 

.16256 

.16286 

.16316 

.16346 

.16376 

.16405 

.16435 

.16465 

.16495 

.16525 

.16555 

.16585 

.16615 

.16645 

.16674 

.16704 

.16734 

.16764 

.16794 

.16824 

.16854 

.16884 

.16914 

.16944 

.16974 

.17004 

.17033 

.17063 

.17093 

.17123 

.17153 

.17183 

.17213 

.17243 

.17273 

.17303 

.17333 

.17363 

.17393 

.17423 

.17453 

.17483 

.17513 

.17543 

.17573 

.17603 

.17633 

6.31375 

6.30189 

6.29007 

6.27829 

6.26655 

6.25486 

6.24321 

6.23160 

6.22003 

6.20851 

6.19703 

6.18559 

6.17419 

6.16283 

6.15151 

6.14023 

6.12899 

6.11779 

6.10664 

6.09552 

6.08444 

6.07340 

6.06240 

6.05143 

6.04051 

6.02962 

6.01878 

6.00797 

5.99720 

5.98646 

5.97576 

5.96510 

5.95448 

5.94390 

5.93335 

5.92283 

5.91236 

5.90191 

5.89151 

5.88114 

5.87080 

5.86051 

5.85024 

5.84001 

5.82982 

5.81966 

5.80953 

5.79944 

5.78938 

5.77936 

5.76937 

5.75941 

5.74949 

5.73960 

5.72974 

5.71992 

5.71013 

5.70037 

5.69064 

5.68094 

5.67128 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

Cotang 

; Tang 

Cotang 

; Tang 

Cotang 

; Tang 

Cotang 

; Tang 

Cotang 

' Tang 

84° 

83° 

82° 

81° 

80° 

486  NATURAL  TANGENTS  AND  COTANGENTS. 


10° 

11° 

12° 

18° 

14° 

f 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.17633 

5.67128 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

60 

1 

.17663 

5.66165 

.19468 

5.13658 

.21286 

4.69791 

.23117 

4.32573 

.24964 

4.00582 

59 

2 

.17693 

5.65205 

.19498 

5.12862 

.21316 

4.69121 

.23148 

4.32001 

.24995 

4.00086 

58 

3 

.17723 

5.64248 

.19529 

5.12069 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

57 

4 

.17753 

5.63295 

.19559 

5.11279 

.21377 

4.67786 

.23209 

4.30860 

.25056 

3.99099 

56 

5 

.17783 

5.62344 

.19589 

5.10490 

.21408 

4.67121 

.23240 

4.30291 

.25087 

3.98607 

55 

6 

.17813 

5.61397 

.19619 

5.09704 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

54 

7 

.17843 

5.60452 

.19649 

5.08921 

.21469 

4.65797 

.23301 

4.29159 

.25149 

3.97627 

53 

8 

.17873 

5.59511 

.19680 

5.08139 

.21499 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

52 

9 

.17903 

5.58573 

.19710 

5.07360 

.21529 

4.64480 

.23363 

4.28032 

.25211 

3.96651 

51 

10 

.17933 

5.57638 

.19740 

5.06584 

.21560 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

50 

11 

.17963 

5.56706 

.19770 

5.05809 

.21590 

4.63171 

.23424 

4.26911 

.25273 

3.95680 

49 

12 

.17993 

5.55777 

.19801 

5.05037 

.21621 

4.62518 

.23455 

4.26352 

.25304 

3.95196 

48 

13 

.18023 

5.54851 

.19831 

5.04267 

.21651 

4.61868 

.23485 

4.25795 

.25335 

3.94713 

47 

14 

.18053 

5.53927 

.19861 

5.03499 

.21682 

4.61219 

.23516 

4.25239 

.25366 

3.94232 

46 

.18083 

5.53007 

.19891 

5.02734 

.21712 

4.60572 

.23547 

4.24685 

.25397 

3.93751 

45 

16 

.18113 

5.52090 

.19921 

5.01971 

.21743 

4.59927 

.23578 

4.24132 

.25428 

3.93271 

44 

17 

.18143 

5.51176 

.19952 

5.01210 

.21773 

4.59283 

.23608 

4.23580 

.25459 

3.92793 

43 

18 

.18173 

5.50264 

.19982 

5.00451 

.21804 

4.58641 

.23639 

4.23030 

.25490 

3.92316 

42 

19 

.18203 

5.49356 

.20012 

4.99695 

.21834 

4.58001 

.23670 

4.22481 

.25521 

3.91839 

41 

20 

.18233 

5.48451 

.20042 

4.98940 

.21864 

4.57363 

.23700 

4.21933 

.25552 

3.91364 

40 

21 

.18263 

5.47548 

.20073 

4.98188 

.21895 

4.56726 

.23731 

4.21387 

.25583 

3.90890 

39 

22 

.18293 

5.46648 

.20103 

4.97438 

.21925 

4.56091 

.23762 

4.20842 

.25614 

3.90417 

38 

23 

.18323 

5.45751 

.20133 

4.96690 

.21956 

4.55458 

.23793 

4.20298 

.25645 

3.89945 

37 

24 

.18353 

5.44857 

.20164 

4.95945 

.21986 

4.54826 

.23823 

4.19756 

.25676 

3.89474 

36 

25 

.18384 

5.43966 

.20194 

4.95201 

.22017 

4.54196 

.23854 

4.19215 

.25707 

3.89004 

35 

26 

.18414 

5.43077 

.20224 

4.94460 

.22047 

4.53568 

.23885 

4.18675 

.25738 

3.88536 

34 

27 

.18444 

5.42192 

.20254 

4.93721 

.22078 

4.52941 

.23916 

4.18137 

.25769 

3.88068 

33 

28 

.18474 

5.41309 

.20285 

4.92984 

.22108 

4.52316 

.23946 

4.17600 

.25800 

3.87601 

32 

29 

.18504 

5.40429 

.20315 

4.92249 

.22139 

4.51693 

.23977 

4.17064 

.25831 

3.87136 

31 

30 

.18534 

5.39552 

.20345 

4.91516 

.22169 

4.51071 

.24008 

4.16530 

.25862 

3.86671 

30 

31 

.18564 

5.38677 

.20376 

4.90785 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.86208 

29 

32 

.18594 

5.37805 

.20406 

4.90056 

.22231 

4.49832 

.24069 

4.15465 

.25924 

3.85745 

28 

33 

.18624 

5.36936 

.20436 

4.89330 

.22261 

4.49215 

.24100 

4.1'4934 

.25955 

3.85284 

27 

34 

.18654 

5.36070 

.20466 

4.88605 

.22292 

4.48600 

.24131 

4.14405 

.25986 

3.84824 

26 

35 

.18684 

5.35206 

.20497 

4.87882 

.22322 

4.47986 

.24162 

4.13877 

.26017 

3.84364 

25 

36 

.18714 

5.34345 

.20527 

4.87162 

.22353 

4.47374 

.24193 

4.13350 

.26048 

3.83906 

24 

87 

.18745 

5.33487 

.20557 

4.86444 

.22383 

4.46764 

.24223 

4.12825 

.26079 

3.83449 

23 

38 

.18775 

5.32631 

.20588 

4.85727 

.22414 

4.46155 

.24254 

4.12301 

.26110 

3.82992 

22 

39 

.18805 

5.31778 

.20618 

4.85013 

.22444 

4.45548 

.24285 

4.11778 

.26141 

3.82537 

21 

40 

.18835 

5.30928 

.20648 

4.84300 

.22475 

4.44942 

.24316 

4.11256 

.26172 

3.82083 

20 

41 

.18865 

5.30080 

.20679 

4.83590 

.22505 

4.44338 

.24347 

4.10736 

.26203 

3.81630 

19 

42 

.18895 

5.29235 

.20709 

4.82882 

.22536 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

18 

43 

.18925 

5.28393 

.20739 

4.82175 

.22567 

4.43134 

.24408 

4.09699 

.26266 

3.80726 

17 

44 

.18955 

5.27553 

.20770 

4.81471 

.22597 

4.42534 

.24439 

4.09182 

.26297 

3.80276 

16 

45 

.18986 

5.26715 

.20800 

4.80769 

.22628 

4.41936 

.24470 

4.08666 

.26328 

3.79827 

15 

46 

.19016 

5.25880 

.20830 

4.80068 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

14 

47 

.19046 

5.25048 

.20861 

4.79370 

.22689 

4.40745 

.24532 

4.07639 

.26390 

3.78931 

13 

48 

.19076 

5.24218 

.20891 

4.78673 

.22719 

4.40152 

.24562 

4.07127 

.26421 

3.78485 

12 

49 

.19106 

5.23391 

.20921 

4.77978 

.22750 

4.39560 

.24593 

4 06616 

.26452 

3.78040 

11 

50 

.19136 

5.22566 

.20952 

4.77286 

.22781 

4.38969 

.24624 

4.06107 

.26483 

3.77595 

10 

51 

.19166 

5.21744 

.20982 

4.76595 

.22811 

4.38381 

.24655 

4.05599 

.26515 

3.77152 

9 

52 

.19197 

5.20925 

.21013 

4.75906 

.22842 

4.37793 

.24686 

4.05092 

.26546 

3.76709 

8 

53 

.19227 

5.20107 

.21043 

4.75219 

.22872 

4.37207 

.24717 

4.04586 

.26577 

3.76268 

7 

54 

.19257 

5.19293 

.21073 

4.74534 

.22903 

4.36623 

.24747 

4.04081 

.26608 

3.75828 

6 

55 

.19287 

5.18480 

.21104 

4.73851 

.22934 

4.36040 

.24778 

4.03578 

.26639 

3.75388 

5 

56 

.19317 

5.17671 

.21134 

4.73170 

.22964 

4.35459 

.24809 

4.03076 

.26670 

3.74950 

4 

57 

.19347 

5.16863 

.21164 

4.72490 

.22995 

4.34879 

.24840 

4.02574 

.26701 

3,74512 

3 

58 

.19378 

5.16058 

.21195 

4.71813 

.23026 

4.34300 

.24871 

4.02074 

.26733 

3.74075 

2 

59 

.19408 

5.15256 

.21225 

4.71137 

.23056 

4.3J5723 

.24902 

4.01576 

.26764 

3.73640 

1 

60 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

f 

79° 

78° 

77° 

76° 

75° 

NATURAL  TANGENTS  AND  COTANGENTS. 


467 


15° 

16° 

17° 

18° 

19° 

/ - 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

o 

.26795 

3.73205 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

60 

26826 

3.72771 

.28706 

3.48359 

.30605 

3.26745 

.32524 

3.07464 

.34465 

2.90147 

59 

26857 

3.72338 

.28738 

3.47977 

.30637 

3.26406 

.32556 

3.07160 

.34498 

2.89873 

58 

3 

.26888 

3.71907 

.28769 

3.47596 

.30669 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

57 

26920 

3.71476 

.28800 

3.47216 

.30700 

3.25729 

.32621 

3.06554 

.34563 

2.89327 

56 

.26951 

3.71046 

.28832 

3.46837 

.30732 

3.25392 

.32653 

3.06252 

.34596 

2.89055 

55 

.26982 

3.70616 

.28864 

3.46458 

.30764 

3.25055 

.32685 

3.05950 

.34628 

2.88783 

54 

7 

.27013 

3.70188 

.28895 

3.46080 

.30796 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

53 

.27044 

3.69761 

.28927 

3.45703 

.30828 

3.24383 

.32749 

3.05349 

.34693 

2.88240 

52 

9 

.27076 

3.69335 

.28958 

3.45327 

.30860 

3.24049 

.32782 

3.05049 

.34726 

2.87970 

51 

10 

.27107 

3.68909 

.28990 

3.44951 

.30891 

3.23714 

.32814 

3.04749 

.34758 

2.87700 

50 

27138 

3.68485 

.29021 

3.44576 

.30923 

3.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.27169 

3.68061 

.29053 

3.44202 

.30955 

3.23048 

.32878 

3.04152 

.34824 

2.87161 

48 

13 

.27201 

3.67638 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34856 

2.86892 

47 

14 

.27232 

3.67217 

.29116 

3.43456 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

27263 

3.66796 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3.03260 

.34922 

2 .86356 

45 

16 

27294 

3.66376 

.29179 

3.42713 

.31083 

3.21722 

.33007 

3.02963 

.34954 

2.86089 

44 

17 

27326 

3.65957 

.29210 

3.42343 

.31115 

3.21392 

.33040 

3.02667 

.34987 

2.85822 

43 

18 

.27357 

3.65538 

.29242 

3.41973 

.31147 

3.21063 

.33072 

3.02372 

.35020 

2.85555 

42 

19 

.27388 

3.65121 

.29274 

3.41604 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.27419 

3.64705 

.29305 

3.41236 

.31210 

3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

27451 

3.64289 

.29337 

3.40869 

.31242 

3.20079 

.33169 

3.01489 

.35118 

2.84758 

39 

27482 

3.63874 

.29368 

3.40502 

.31274 

3.19752 

.33201 

3.01196 

.35150 

2.84494 

38 

23 

27513 

3.63461 

.29400 

3.40136 

.31306 

3.19426 

.33233 

3.00903 

.35183 

2.84229 

37 

27545 

3.63048 

.29432 

3.39771 

.31338 

3.19100 

.33266 

3.00611 

.35216 

2.83965 

36 

25 

27576 

3.62636 

.29463 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

35 

27607 

3.62224 

.29495 

3.39042 

.31402 

3 18451 

.33330 

3.00028 

.35281 

2.83439 

34 

27638 

3.61814 

.29526 

3.38679 

.31434 

3.18127 

.33363 

2.99738 

.35314 

2.83176 

33 

28 

.27670 

3.61405 

.29558 

3.38317 

.31466 

3.17804 

.33395 

2.99447 

.35346 

2.82914 

32 

29 

.27701 

3.60996 

.29590 

3.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

31 

30 

.27732 

3.60588 

.29621 

3.37594 

.31530 

3.17159 

.33460 

2.98868 

.35412 

2.82391 

30 

31 

.27764 

3.60181 

.29653 

3.37234 

.31562 

3.16838 

.33492 

2.98580 

.35445 

2.82130 

29 

32 

.27795 

3.59775 

.29685 

3.36875 

.31594 

3.16517 

.33524 

2.98292 

.35477 

2.81870 

28 

33 

'.27826 

3.59370 

.29716 

3.36516 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2.81610 

27 

34 

.27858 

3.58966 

.29748 

3.36158 

.31658 

3.15877 

.33589 

2.97717 

.35543* 

2.81350 

26 

35 

.27889 

3.58562 

.29780 

3.35800 

.31690 

3.15558 

.33621 

2.97430 

.35576 

2.81091 

25 

36 

.27921 

3.58160 

.29811 

3.35443 

.31722 

3.15240 

.33654 

2.97144 

.35608 

2.80833 

24 

37 

.27952 

3.57758 

.29843 

3.35087 

.31754 

3.14922 

.33686 

2.96858 

.35641 

2.80574 

23 

38 

.27983 

3.57357 

.29875 

3.34732 

.31786 

3.14605 

.33718 

2.96573 

<35674 

2.80316 

22 

39 

.28015 

3.56957 

.29906 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

!28046 

3.56557 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.28077 

3.56159 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.28109 

3.55761 

.30001 

3.33317 

.31914 

3.13341 

.33848 

2.95437 

.35805 

2.79289 

18 

43 

.28140 

3.55364 

.30033 

3.32965 

.31946 

3.13027 

.33881 

2.95155 

.35838 

2.79033 

17 

44 

.28172 

3.54968 

.30065 

3.32614 

.31978 

3.12713 

.33913 

2.94872 

.35871 

2.78778 

16 

45 

.28203 

3.54573 

.30097 

3.32264 

.32010 

3.12400 

.33945 

2.94591 

.35904 

2 .78523 

15 

46 

.28234 

3.54179 

.30128 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78269 

14 

47 

.28266 

3.53785 

.30160 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35969 

2.78014 

13 

48 

.28297 

3.53393 

.30192 

3.31216 

.32106 

3.11464 

.34043 

2.93748 

.36002 

2.77761 

12 

49 

.28329 

3.53001 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.93468 

.36035 

2 .77507 

11 

50 

.28360 

3.52609 

.30255 

3.30521 

.32171 

3.10842 

.34108 

2.93189 

.36068 

2.77254 

10 

51 

.28391 

3.52219 

.30287 

3.30174 

.32203 

3.10532 

.34140 

2.92910 

.36101 

2.77002 

9 

52 

.28423 

3.51829 

.30319 

3.29829 

.32235 

3.10223 

.34173 

2.92632 

.36134 

2.76750 

8 

53 

.28454 

3.51441 

.30351 

3.29483 

.32267 

3.09914 

.34205 

2.92354 

.36167 

2.76498 

7 

54 

.28486 

3.51053 

.30382 

3.29139 

.32299 

3.09606 

.34238 

2.92076 

.36199 

2.76247 

6 

55 

.28517 

3.50666 

.30414 

3.28795 

.32331 

3.09298 

.34270 

2.91799 

.36232 

2.75996 

5 

56 

.28549 

3.50279 

.30446 

3.28452 

.32363 

3.08991 

.34303 

2.91523 

.36265 

2.75746 

4 

57 

.28580 

3.49894 

.30478 

3.28109 

.32396 

3.08685 

.34335 

2.91246 

.36298 

2.75496 

3 

58 

.28612 

3.49509 

.30509 

3.27767 

.32428 

3.08379 

.34368 

2.90971 

.36331 

2.75246 

2 

59 

’*28643 

3.49125 

.30541 

3.27426 

.32460 

3.08073 

.34400 

2.90696 

.36364 

2.74997 

1 

60 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

.36397 

2.74748 

0 

Cotang 

; Tang 

Cotang 

; Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

j Tang 

f 

t 

74° 

73° 

72° 

71° 

70° 

468 


NATURAL  TANGENTS  AND  COTANGENTS. 


20° 

21° 

22° 

23° 

24° 

/ 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.36397 

2.74748 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

60 

1 

.36430 

2.74499 

.38420 

2.60283 

.40436 

2.47302 

.42482 

2.35395 

.44558 

2.24428 

59 

2 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2.47095 

.42516 

2.35205 

.44593 

2.24252 

58 

3 

.36496 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

.44627 

2.24077 

57 

4 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

.44662 

2.23902 

56 

5 

.36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.34636 

.44697 

2.23727 

55 

6 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

.44732 

2.23553 

54 

7 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

.44767 

2.23378 

53 

8 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

.42722 

2.34069 

.44802 

2.23204 

52 

9 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45655 

.42757 

2.33881 

.44837 

2.23030 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

.44872 

2.22857 

50 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

.44907 

2.22683 

49 

12 

.36793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42860 

2.33317 

.44942 

2.22510 

48 

13 

.36826 

2.71548 

.38821 

2.57593 

.40843 

2.44839 

.42894 

2.33130 

.44977 

2.22337 

47 

14 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.44636 

.42929 

2.32943 

.45012 

2.22164 

46 

15 

.36892 

2.71062 

.38888 

2.57150 

.40911 

2.44433 

.42963 

2.32756 

.45047 

2.21992 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

.45082 

2.21819 

44 

17 

.36958 

2.70577 

.38955 

2.56707 

.40979 

2.44027 

.43032 

2.32383 

.45117 

2.21647 

43 

18 

.36991 

2.70335 

.38988 

2.56487 

.41013 

2.43825 

.43067 

2.32197 

.45152 

2.21475 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

.43101 

2.32012 

.45187 

2.21304 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

.45222 

2.21132 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

.45257 

2.20961 

39 

22 

.37123 

2.69371 

.39122 

2.55608 

.41149 

2.43019 

43205 

2.31456 

.45292 

2.20790 

38 

23 

.37157 

2.69131 

.39156 

2.55389 

.41183 

2.42819 

.43230 

2.31271 

.45327 

2.20619 

37 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

.45362 

2.20449 

36 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2 42418 

.43308 

2.30902 

.45397 

2.20278 

35 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

.45432 

2.20108 

34 

27 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.43378 

2.30534 

.45467 

2.19938 

33 

28 

.37322 

2.67937 

.39324 

2.54299 

.41353 

2.41819 

.43412 

2.30351 

.45502 

2.19769 

32 

29 

.37355 

2.67700 

.39357 

2.54082 

.41387 

2.41620 

.43447 

2.30167 

.45538 

2.19599 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

.45573 

2.19430 

30 

31 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

.45608 

2.19261 

29 

32 

.37455 

2.66989 

.39458 

2.53432 

.41490 

2.41025 

.43550 

2.29619 

.45643 

2.19092 

28 

33 

.37488 

2.66752 

.39492 

2.53217 

.41524 

2.40827 

.43585 

2.29437 

.45678 

2.18923 

27 

34 

.37521 

•2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

.45713 

2.18755 

26 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

.45748 

2.18587 

25 

36 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

.45784 

2.18419 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

.45819 

2.18251 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41694 

2.39841 

.43758 

2.28528 

.45854 

2.18084 

22 

39 

.37687 

2.65342 

.39694 

2.51929 

.41728 

2.39645 

.43793 

2.28348 

.45889 

2.17916 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2.28167 

.45924 

2.17749 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

.45960 

2.17582 

19 

42 

.37787 

2.64642 

.39795 

2.51289 

.41831 

2.39058 

.43897 

2.27806 

.45995 

2.17416 

18 

43 

.37820 

2.64410 

.39829 

2.51076 

.41865 

2.38863 

.43932 

2.27626 

.46030 

2.17249 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

.41899 

2.38668 

.43966 

2.27447 

.46065 

2.17083 

16 

45 

.37887 

2.63945 

.39896 

2.50652 

.41933 

2.38473 

.44001 

2.27267 

.46101 

2.16917 

15 

46 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27088 

.46136 

2.16751 

14 

47 

.37953 

2.63483 

.39963 

2.50229 

.42002 

2.38084 

.44071 

2.26909 

.46171 

2.16585 

13 

48 

.37986 

2.63252 

.39997 

2.50018 

.42036 

2.37891 

.44105 

2.26730 

.46206 

2.16420 

12 

49 

.38020 

2.63021 

.40031 

2.49807 

.42070 

2.37697 

.44140 

2.26552 

.46242 

2.16255 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

.46277 

2.16090 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

.46312 

2.15925 

9 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

.44.244 

2.26018 

.46348 

2.15760 

8 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

.46383 

2.15596. 

7 

54 

.38186 

2.61874 

.40200 

2.48758 

.42242 

2.36733 

.44314 

2.25663 

.46418 

2.15432 

6 

55 

.38220 

2.61646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

.46454 

2.15268 

5 

56 

.38253 

2.61418 

.40267 

2.48340 

.42310 

2.36349 

.44384 

2.25309 

.46489 

2.15104 

4 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.36158 

.44418 

2.25132 

.46525 

2.14940 

3 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2.24956 

.46560 

2.14777 

2 

59 

.38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2.24780 

.46595 

2.14614 

1 

60 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

.46631 

2.14451 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotaug 

Tang 

Cotang 

Tang 

f 

69° 

68° 

67° 

66° 

65° 

NATURAL  TANGENTS  AND  COTANGENTS. 


469 


25° 

26° 

27° 

28° 

29° 

t 

t 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

o 

46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.55431 

1.80405 

60 

\ 

46666 

2.14288 

.48809 

2.04879 

.50989 

1.96120 

.53208 

1.87941 

.55469 

1.80281 

59 

46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

.53246 

1.87809 

.55507 

1.80158 

58 

3 

46737 

2.13963 

.48881 

2.04577 

.51063 

1.95838 

.53283 

1.87677 

.55545 

1.80034 

57 

4 

46772 

2.13801 

.48917 

2.04426 

.51099 

1.95698 

.53320 

1.87546 

.55583 

1.79911 

56 

46»n« 

2 13639 

.48953 

2.04276 

.51136 

1.95557 

.53358 

1.87415 

.55621 

1.79788 

55 

46R43 

2 13477 

.48989 

2.04125 

.51173 

1.95417 

.53395 

1.87283 

.55659 

1.79665 

54 

40R79 

2 13316 

.49026 

2.03975 

.51209 

1.95277 

.53432 

1.87152 

.55697 

1.79542 

53 

46914 

2 13154 

.49062 

2.03825 

.51246 

1.95137 

.53470 

1.87021 

.55736 

1.79419 

52 

g 

46950 

2.12993 

.49098 

2.03675 

.51283 

1.94997 

.53507 

1.86891 

.55774 

1.79296 

51 

10 

.46985 

2.12832 

.49134 

2.03526 

.51319 

1.94858 

.53545 

1.86760 

.55812 

1.79174 

50 

U 

47021 

2.12671 

.49170 

2.03376 

.51356 

1.94718 

.53582 

1.86630 

.55850 

1.79051 

49 

12 

47056 

2.12511 

.49206 

2.03227 

.51393 

1.94579 

.53620 

1.86499 

.55888 

1.78929 

48 

13 

47092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

.53657 

1.86369 

.55926 

1.78807 

47 

14 

47128 

2.12190 

.49278 

2.02929 

.51467 

1.94301 

.53694 

1.86239 

.55964 

1.78685 

46 

15 

47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

.53732 

1.86109 

.56003 

1.78563 

45 

16 

47199 

2.11871 

.49351 

2.02631 

.51540 

1.94023 

.53769 

1.85979 

.56041 

1.78441 

44 

17 

47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

.53807 

1.85850 

.56079 

1.78319 

43 

18 

47270 

2.11552 

.49423 

2.02335 

.51614 

1.93746 

.53844 

1.85720 

.56117 

1.78198 

42 

19 

47305 

2.11392 

.49459 

2.02187 

.51651 

1.93608 

.53882 

1.85591 

.56156 

1.78077 

41 

20 

.47341 

2.11233 

.49495 

2.02039 

.51688 

1.93470 

.53920 

1.85462 

.56194 

1.77955 

40 

21 

47377 

2 11075 

.49532 

2.01891 

.51724 

1.93332 

.53957 

1.85333 

.56232 

1.77834 

39 

22 

.47412 

2.10916 

.49568 

2.01743 

.51761 

1.93195 

.53995 

1.85204. 

.56270 

1.77713 

38 

23 

.47448 

2.10758 

.49604 

2.01596 

.51798 

1.93057 

.54032 

1.85075 

.56309 

1.77592 

37 

24 

.47483 

2.10600 

.49640 

2.01449 

.51835 

1.92920 

.54070 

1.84946 

.56347 

1.77471 

36 

25 

47519 

2.10442 

.49677 

2.01302 

.51872 

1.92782 

.54107 

1.84818 

.56385 

1.77351 

35 

26 

2.10284 

.49713 

2.01155 

.51909 

1.92645 

.54145 

1.84689 

.56424 

1.77230 

34 

27 

47590 

2.10126 

.49749 

2.01008 

.51946 

1.92508 

.54183 

1.84561 

.56462 

1.77110 

33 

28 

.47626 

2.09969 

.49786 

2.00862 

.51983 

1.92371 

.54220 

1.84433 

.56501 

1.76990 

32 

29 

.47662 

2.09811 

.49822 

2.00715 

.52020 

1.92235 

.54258 

1.84305 

.56539 

1.76869 

31 

30 

.47698 

2.09654 

.49858 

2.00569 

.52057 

1.92098 

.54296 

1.84177 

.56577 

1.76749 

30 

31 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

.54333 

1.84049 

.56616 

1.76629 

29 

32 

.47769 

2.09341 

.49931 

2.00277 

.52131 

1.91826 

.54371 

1.83922 

.56654 

1.76510 

28 

33 

.47805 

2.09184 

.49967 

2.00131 

.52168 

1.91690 

.54409 

1.83794 

.56693 

1.76390 

27 

34 

.47840 

2.09028 

.50004 

1.99986 

.52205 

1.91554 

.54446 

1.83667 

.56731 

1.76271 

26 

35 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91418 

.54484 

1.83540 

.56769 

1.76151 

25 

36 

.47912 

2.08716 

.50076 

1.99695 

.52279 

1.91282 

.54522 

1.83413 

.56808 

1.76032 

24 

37 

.47948 

2.08560 

.50113 

1.99550 

.52316 

1.91147 

.54560 

1.83286 

.56846 

1.75913 

23 

38 

.47984 

2.08405 

.50149 

1.99406 

.52353 

1.91012 

.54597 

1.83159 

.56885 

1.75794 

22 

39 

• .48019 

2.08250' 

.50185 

1.99261 

.52390 

1.90876 

.54635 

1.83033 

.56923 

1.75675 

21 

40 

.48055 

2.08094 

.50222 

1.99116 

.52427 

1.90741 

.54673 

1.82906 

.56962 

1.75556 

20 

41 

.48091 

2.07939 

.50258 

1.98972 

.52464 

1.90607 

.54711 

1.82780 

.57000 

1.75437 

19 

42 

.48127 

2.07785 

.50295 

1.98828 

.52501 

1.90472 

.54748 

1.82654 

.57039 

1.75319 

18 

43 

.48163 

2.07630 

.50331 

1.98684 

.52538 

1.90337 

.54786 

1.82528 

.57078 

1.75200 

17 

44 

.48198 

2.07476 

.50368 

1.98540 

.52575 

1.90203 

.54824 

1.82402 

.57116 

1.75082 

16 

*5 

.48234 

2.07321 

.50404 

1.98396 

.52613 

1.90069 

.54862 

1.82276 

.57155 

1.74964 

15 

46 

.48270 

2.07167 

.50441 

1.98253 

.52650 

1.89935 

.54900 

1.82150 

.57193 

1.74846 

14 

47 

.48306 

2.07014 

.50477 

1.98110 

.52687 

1.89801 

.54938 

1.82025 

.57232 

1.74728 

13 

48 

.48342 

2.06860 

.50514 

1.97966 

.52724 

1.89667 

.54975 

1.81899 

.57271 

1.74610 

12 

49 

.48378 

2.06706 

.50550 

1.97823 

.52761 

1.89533 

.55013 

1.81774 

.57309 

1.74492 

11 

50 

.48414 

2.06553 

.50587 

1.97681 

.52798 

1.89400 

.55051 

1.81649 

.57348 

1.74375 

10 

51 

.48450 

2.06400 

.50623 

1.97538 

.52836 

1.89266 

.55089 

1.81524 

.57386 

1.74257 

9 

52 

.48486 

2 06247 

.50660 

1.97395 

.52873 

1.89133 

.55127 

1.81399 

.57425 

1.74140 

8 

53 

.48521 

2.06094 

.50696 

1.97253 

.52910 

1.89000 

.55165 

1.81274 

.57464 

1.74022 

7 

54 

.48557 

2.05942 

.50733 

1.97111 

.52947 

1.88867 

.55203 

1.81150 

.57503 

1.73905 

6 

55 

.48593 

2.05790 

.50769 

1.96969 

.52985 

1.88734 

.55241 

1.81025 

.57541 

1.73788 

5 

56 

.48629 

2.05637 

.50806 

1.96827 

.53022 

1.88602 

.55279 

1.80901 

.57580 

1.73671 

4 

57 

.48665 

2.05485 

.50843 

1.96685 

.53059 

1.88469 

.55317 

1.80777 

.57619 

1.73555 

3 

58 

.48701 

2.05333 

.50879 

1.96544 

.53096 

1.88337 

.55355 

1.80653 

.57657 

1.73438 

2 

59 

.48737 

2.05182 

.50916 

1.96402 

.53134 

1.88205 

.55393 

1.80529 

.57696 

1.73321 

1 

60 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1,88073 

.55431 

1.80405 

.57735 

1.73205 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

; Tang 

t 

64° 

I 

63° 

62° 

61° 

60° 

470 


NATURAL  TAX  GENTS  AND  COTANGENTS. 


30° 

31° 

32° 

33° 

2A° 

t 

Tang 

Cotang 

Tang  Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

1.73205 

.60086  1.66428 

.62487 

1.60033 

.64941 

1.53986 

.67451  ; 

1.48256  ' 

60 

1 ! 

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1.73089 

.60126  1.66318 

.62527 

1.59930 

.64982 

1.53888 

.67493  j 

1.48163 

59 

2 

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1.72973 

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1.59826 

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1.53791 

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1.48070  ! 

58 

3 1 

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1.72857 

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1.59723 

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1.53693 

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1.47977  j 

57 

4 | 

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1.72741 

.60245  1.65990 

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1.59620 

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1.53595 

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1.47885  ; 

56 

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1.72625 

.60284  1.65881 

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1.59517 

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1.53497 

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1.47792  ! 

55 

6 

.57968 

1.72509 

.60324  1.65772 

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1.59414 

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1.53400 

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1.47699  : 

54 

1.72393 

.60364  1.65663 

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1.59311 

.65231 

1.53302 

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1.47607  i 

53 

8 1 

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1.72278 

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1.59208 

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1.53205 

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1.47514  | 

52 

9 

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1.72163 

.60443  1.65445 

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1.59105 

.65314 

1.53107 

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1.47422 

51 

10  1 

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1.72047 

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1.59002 

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1.53010 

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1.47330  ! 

50 

11  ; 

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1.71932 

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1.52913 

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1.47238 

49 

12 

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1.71817 

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1.58797 

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1.52816 

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1.47146  ! 

48 

13  1 

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1.71702 

.60602  1.65011 

.63014  I 

1.58695 

.65480 

1.52719 

.68002 

1.47053  | 

47 

14  | 

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1.71588 

.60642  1.64903 

.63055 

1.58593 

.65521  1 

1.52622 

.68045 

1.46962 

46 

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1.71473 

.60681  1.64795 

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1.58490 

.65563  ! 

1.52525 

.68088  ! 

1.46870 

45 

16  j 

.58357 

1.71358 

.60721  1.64687 

.63136 

1.58388 

.65604 

1.52429 

.68130  1 

1.4677S  i 

44 

IT  1 

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1.71244 

.60761  1.64579 

.63177 

1.5S286 

.65646 

1.52332 

.68173  i 

1.46686 

43 

18  j 

.58435 

1.71129 

.60801  1.64471 

.63217 

1.58184 

.65688  j 

1.52235 

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1.46595  | 

42 

19 

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1.71015 

.60841  1.64363 

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1.58083 

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1.52139 

.68258 

1.46503  i 

41 

20  1 

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1.70901 

.60881  ! 1.64256 

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1.57981 

.65771  j 

1.52043 

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1.46411 

40 

21 

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1.70787 

.60921  1.64148 

.63340  . 

1.57879 

.65813  j 

1.51946 

.68343 

1.46320 

39 

22 

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1.70673 

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1.57778 

.65854  i 

1.51850 

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1.46229 

38 

23  j 

.58631 

1.70560 

.61000  1.63934 

.63421  | 

1 .57676 

.65896  ! 

1.51754 

.68429 

1.46137 

37 

24  1 

.58670 

1.70446 

.61040  1.63826 

.63462  ! 

1.5i575 

.65938 

1.51658 

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1.46046  I 

36 

25  1 

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1.70332 

.610S0  1.63719 

.63503 

1.57474 

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1.51562 

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1.45955 

26 

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1.70219 

.61120  1.63612 

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1.57372 

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1.51466 

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1.45864  1 

1 34 

27 

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1.70106 

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1.57271 

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1.51370 

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1.45773 

1 33 

28 

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1.69992 

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1.57170 

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1.51275 

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1.45682 

L 32 

29 

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1.69879 

.61240  1.63292 

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1.57069 

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J 1.51179 

.68685 

1.45592 

31 

30  1 

.58905 

1 1.69766 

.61280  1.63185 

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1 1.56969 

.66189 

1.51084 

.68728  1 

1.45501 

i 30 

3! 

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i 1.69653 

.61320  1 1.63079 

.63748^1.56868 

.66230  ! 

1.50988 

.68771 

| 1.45410 

: 29 

32 

.58983 

1.69541 

.61360  1.62972 

.63789  ! 

jl. 56767 

.66272  ! 

1.50893 

.68814 

! 1.45320 

-28 

33  1 

.59022 

1.69428 

.61400  1.62866 

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| 1.56667 

.66314 

1.50797 

.68857 

j 1.45229 

. 27 

34  | 

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1.69316 

.61440  1.62760 

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i 1.56566 

.66356 

! 1.50702 

.68900 

! 1.45139 

j 26 

35 

.59101 

j 1.69203 

.61480  1.62654 

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1 1.56466 

.66398 

: 1.50607 

.68942 

1 1.45049 

25 

36  i 

.59149 

; 1.69091 

.61520  1.62548 

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| 1.56366 

.66440 

1.50512 

.68985 

i 1.44958 

24 

37 

1 .59179 

1.68979 

.61561  | 1.62442 

.63994 

1.56265 

.66482 

1.50417 

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j 1.44868 

23 

38  I 

' .59218 

1.68S66 

.61601  j 1.62336 

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1 1.56165 

.66524 

1.50322 

.69071 

; 1.44778- 

22 

39 

| .59253 

1.68754 

.61641  1.62230 

.64076 

I 1.56065 

.66566 

1.50228 

.69114 

! 1.44688 

i 21 

40 

| .59297 

| 1.68643 

.61681  : 1.62125 

.64117 

J 1.55966 

.66608 

1.50133 

.69157 

j 1.44598 

20 

41 

.59336 

* 1.68531 

.61721  1.62019 

.64158 

! 1.55866 

.66650 

1.50038 

.69200 

! 1.4450S 

J* 

42 

! .59376 

1.68419 

.61761  1.61914 

.64199 

! 1.55766 

.66692 

1.49944 

.69243 

1 1.44418 

18 

43 

.59415 

1.68308 

.61801  1.61808 

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j 1.55666 

.66734 

1.49849 

.69286 

1.44329 

17 

44 

.59454 

1.68196 

.61842  1.61703 

.64281 

1.55567 

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1.49755 

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1.44239 

J® 

45 

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1.68085 

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.64322 

1.55467 

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1.49661 

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1.44149 

J3 

46 

j .59533 

1.67974 

.61922  1.61493 

.64363 

1.55368 

.66860 

1.49566 

.69416 

1.44060 

14 

47 

I .59573 

1.67863 

.61962  | 1.61388 

.64404 

1.55269 

.66902 

1.49472 

.69459 

! 1.43970 

! 13 

48 

.59612 

1.67752 

.62003  1.61283 

.64446 

1.55170 

.66944 

1.49378 

.69502 

1.43881 

49 

j .59651 

1.67641 

.62043  ! 1.61179 

.64487 

1.55071 

.66986 

1.49284 

.69545 

1.43792 

1 11 

50 

! .59691 

1.67530 

.62083  ! 1.61074 

.64528 

1.54972 

.67028 

1.49190 

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L. 43703 

i 10 

51 

.59730 

' 1.67419 

.62124  i 1.60970 

.64569 

1.54873 

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' 1.49097 

.69631 

1.43614 

9 

52 

i .59770 

1 1.67309 

.62164  1 1.60865 

.64610 

1.54774 

.67113 

I 1.49003 

.69675 

1.43525 

8 

53 

! .59809 

i 1.67198 

.62204  1.60761 

.64652 

1.54675 

.67155 

| 1.48909 

.69718 

1.43436 

7 

54 

j .59849 

1.67088 

.62245  , 1.60657 

.64693 

I 1.54576 

.67197 

' 1.48816 

.69761 

j 1.43347 

6 

55 

.59888 

1.66978 

.62285  ! 1.60553 

.64734 

1.54478 

.67239 

, 1.48722 

.69804 

| 1.43258 

5 

56 

' .59928 

1.66867 

.62325  1.60449 

.64775 

1.54379 

.67232 

1.48629 

.69847 

1.43169 

4 

57 

■ .59967 

1.66757 

.62366  ! 1 160345 

.64817 

1.54281 

.67324 

1 1.48536 

.69891 

1.43080 

3 

58 

.60007 

1.66647 

.62406  1.60241 

.64858 

1.54183 

.67366 

1 1.48442 

.69934 

1.42992 

2 

59 

.60046 

1.66538 

.62446  1.60137 

.64899 

1.54085 

.67409 

1.48349 

.69977 

1.42903 

1 

60 

.60086 

1.66428 

.62487  i 1.60033 

.64941 

1.53986 

.67451 

| 1.48256 

.70021 

1.42815 

0 

Cotang 

Tang 

Cotang  ] Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

r 

59° 

58° 

57° 

56° 

55° 

NATURAL  TANGENTS  AND  COTANGENTS. 


471 


35° 

36° 

37° 

38° 

39° 

/ 

f - 

Tang 

Cotang 

Tang 

Cotang 

Tang  < 

Cotang 

Tang  < 

Cotang 

Tang  1 

Cotang 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

.70021 

.70064 

.70107 

.70151 

.70194 

.70238 

.70281 

.70325 

.70368 

.70412 

.70455 

.70499 

.70542 

.70586 

.70629 

.70673 

.70717 

.70760 

.70804 

.70848 

.70891 

.70935 

.70979 

.71023 

.71066 

.71110 

.71154 

.71198 

.71242 

.71285 

.71329 

.71373 

.71417 

.71461 

.71505 

.71549 

.71593 

.71637 

.71681 

.71725 

.71769 

.71813 

.71857 

.71901 

.71946 

.71990 

.72034 

.72078 

.72122 

.72167 

.72211 

.72255 

.72299 

.72344 

.72388 

.72432 

.72477 

.72521 

.72565 

.72610 

.72654 

1.42815 
L. 42726 
L. 42638 
L. 42550 
1.42462 
1.42374 
1.42286 
1.42198 
1.42110 
1.42022 
1.41934 

1.41847 

1.41759 

1.41672 

1.41584 

1.41497 

1.41409 

1.41322 

1.41235 

1.41148 

1.41061 

1.40974 

1.40887 

1.40800 

1.40714 

1.40627 

1.40540 

1.40454 

1.40367 

1.40281 

1.40195 

1.40109 
1.40022 
1.39936 
1.39850 
1.39764 
1.39679 
1.39593 
1.39507 
1 .39421 
1.39336 

1.39250 

1.39165 

1.39079 

1.38994 

1.38909 

1.38824 

1.38738 

1.38653 

1.38568 

1.38484 

1.38399 

1.38314 

1.38229 

1.38145 

1.38060 

1.37976 

1.37891 

1.37807 

1.37722 

1.37638 

.72654 

.72699 

.72743 

.72788 

.72832 

.72877 

.72921 

.72966 

.73010 

.73055 

.73100 

.73144 

.73189 

.73234 

.73278 

.73323 

.73368 

.73413 

.73457 

.73502 

.73547 

.73592 

.73637 

.73681 

.73726 

.73771 

.73816 

.73861 

.73906 

.73951 

.73996 

.74041 

.74086 

.74131 

.74176 

.74221 

.74267 

.74312 

.74357 

.74402 

.74447 

.74492 

.74538 

.74583 

.74628 

.74674 

.74719 

.74764 

.74810 

.74855 

.74900 

.74946 
.74991 
.75037 
.75082 
.75128 
.75173 
.75219 
.75264 
! .75310 

1 .75355 

L. 37638 
.37554 
1.37470 
L. 37386 
1.37302 
1.37218 
1.37134 
1.37050 
1.36967 
1.36883 
1.36800 

1.36716 
1.36633 
1.36549 
1.36466 
1.36383 
1.36300 
1.36217 
1.36134 
1.36051 
1 35968 

1.35885 

1.35802 

1.35719 

1.35637 

1.35554 

1.35472 

1.35389 

1.35307 

1.35224 

1.35142 

1.35060 

1.34978 

1.34896 

1.34814 

1.34732 

1.34650 

1.34568 

1.34487 

1.34405 

1.34323 

1.34242 

1.34160 

1.34079 

1.33998 

1.33916 

1.33835 

1.33754 

1.33673 

1.33592 

1.33511 

1.33430 

1.33349 

1.33268 

1.33187 

1.33107 

1.33026 

1.32946 

1.32865 

1.32785 

1.32704 

.75355  ] 

.75401  : 

.75447  : 

.75492 

.75538 

.75584 

.75629 

.75675 

.75721 

.75767 

.75812 

.75858 

.75904 

.75950 

.75996 

.76042 

.76088 

.76134 

.76180 

.76226 

.76272 

.76318 

.76364 

.76410 

.76456 

.76502 

.76548 

.76594 

.76640 

.76686 

.76733 

.76779 

.76825 

.76871 

.76918 

.76964 

.77010 

.77057 

.77103 

.77149 

.77196 

.77242 

.77289 

.77335 

.77382 

.77428 

.77475 

.77521 

.77568 

.77615 

.77661 

.77708 
.77754 
.77801 
.77848 
.77895 
i .77941 
i .77988 
i .78035 
; .78082 

L .78129 

L. 32704 
L. 32624 
L. 32544 
1.32464 
1.32384 
1.32304 
1.32224 
1.32144 
1.32064 
1.31984 
1.31904 

1.31825 

1.31745 

1.31666 

1.31586 

1.31507 

1.31427 

1.31348 

1.31269 

1.31190 

1.31110 

1.31031 
1.30952 
1.30873 
1.30795 
1.30716 
1.30637 
1.30558 
1 .30480 
1.30401 
1.30323 

1.30244 
1.30166 
1.30087 
1.30009 
1.29931 
1.29853 
1.29775 
1 .29696 
1 .29618 
1.29541 

1.29463 

1.29385 

1.29307 

1.29229 

1.29152 

1.29074 

1.28997 

1.28919 

1.28842 

1.28764 

1.28687 
1 .28610 
1 .28533 
1.28456 
1.28379 
1.28302 
1.28225 
1.28148 
1.28071 
1.27994 

.78129  ] 

.78175  ] 

.78222  : 
.78269  : 

.78316  : 

.78363 
.78410 
.78457 
.78504 
.78551 
.78598 

.78645 

.78692 

.78739 

.78786 

.78834 

.78881 

.78928 

.78975 

.79022 

.79070 

.79117 

.79164 

.79212 

.79259 

.79306 

.79354 

.79401 

.79449 

.79496 

.79544 

.79591 

.79639 

.79686 

.79734 

.79781 

.79829 

.79877 

.79924 

.79972 

.80020 

.80067 

.80115 

.80163 

.80211 

.80258 

.80306 

.80354 

.80402 

.80450 

.80498 

.80546 
.80594 
.80642 
.80690 
.80738 
.80786 
i .80834 
l .80882 
. .80930 

r .80978 

L. 2 7994  , 

L. 27917  , 

L. 27841 

1.27764 

1.27688 

1.27611 

1.27535 

1.27458 

1.27382 

1.27306 

1.27230 

1.27153 
1.27077 
1.27001 
1 .26925 
1.26849 
1.26774 
1.26698 
1.26622 
1.26546 
1.26471 

1.26395 
1 .26319 
1.26244 
1 .26169 
1 .26093 
1 .26018 
1 .25943 
1.25867 
1.25792 
1.25717 

1.25642 

1.25567 

1.25492 

1.25417 

1.25343 

1.25268 

1.25193 

1.25118 

1.25044 

1.24969 

1.24895 

1.24820 

1.24746 

1.24672 

1.24597 

1.24523 

1.24449 

1.24375 

1.24301 

1.24227 

1.24153 
1 .24079 
1.24005 
1.23931 
1.23858 
1.23784 
1.23710 
1.23637 
1.23563 
1 .23490 

.80978  : 

.81027 
.81075  : 

.81123  : 

.81171 
.81220 
.81268 
.81316 
.81364 
.81413 
.81461 

.81510 

.81558 

.81606 

.81655 

.81703 

.81752 

.81800 

.81849 

.81898 

.81946 

.81995 

.82044 

.82092 

.82141 

.82190 

.82238 

.82287 

.82336 

.82385 

.82434 

.82483 

.82531 

.82580 

.82629 

.82678 

.82727 

.82776 

.82825 

.82874 

.82923 

.82972 

.83022 

.83071 

.83120 

.83169 

.83218 

.83268 

.83317 

.83366 

.83415 

.83465 
.83514 
.83564 
.83613 
.83662 
.83712 
i .83761 
.83811 
; .83860 

l .83910 

L. 23490 
1.23416 
1.23343 
1.23270 
1.23196 
1.23123 
1.23050 
1.22977 
1.22904 
1.22831 
1.22758 

1.22685 

1.22612 

1.22539 

1.22467 

1.22394 

1.22321 

1.22249 

1.22176 

1.22104 

1.22031 

1.21959 

1.21886 

1.21814 

1.21742 

1.21670 

1.21598 

1.21526 

1.21454 

1.21382 

1.21310 

1.21238 

1.21166 

1.21094 

1.21023 

1.20951 

1.20879 

1.20808 

1.20736 

1.20665 

1.20593 

1.20522 

1.20451 

1.20379 

1.20308 

1.20237 

1.20166 

1.20095 

1.20024 

1.19953 

1.19882 

1.19811 

1.19740 

1.19669 

1.19599 

1.19528 

1.19457 

1.19387 

1.19316 

1.19246 

1.19175 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

1 2 

; l 

, 0 

Cotan  j 

? Tang 

Cotan £ 

1 Tang 

Cotang 

l Tang 

Cotang 

; Tang 

Cotani 

g Tang 

t 

f 

54° 

53° 

i 

52° 

51° 

50° 

472 


NATURAL  TANGENTS  AND  COTANGENTS. 


40° 

41° 

42° 

43° 

440 

/ 

' 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.83910 

1.19175 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

.96569 

1.03553 

60 

1 

.83960 

1.19105 

.86980 

1.14969 

.90093 

1.10996 

.93306 

1.07174 

.96625 

1.03493 

59 

2 

.84009 

1.19035 

.87031 

1.14902 

.90146 

1.10931 

.93360 

1.07112 

.96681 

1.03433 

58 

3 

.84059 

1.18964 

.87082 

1.14834 

.90199 

1.10867 

.93415 

1.07049 

.96738 

1.03372 

57 

4 

.84108 

1.18894 

.87133 

1.14767 

.90251 

1.10802 

.93469 

1.06987 

.96794 

1.03312 

56 

5 

.84158 

1.18824 

.87184 

1.14699 

.90304 

1.10737 

.93524 

1.06925 

.96850 

1.03252 

55 

6 

.84208 

1.18754 

.87236 

1.14632 

.90357 

1.10672 

.93578 

1.06862 

.96907 

1.03192 

54 

7 

.84258 

1.18684 

.87287 

1.14565 

.90410 

1.10607 

.93633 

1.06800 

.96963 

1.03132 

53 

8 

.84307 

1.18614 

.87338 

1.14498 

.90463 

1.10543 

.93688 

1.06738 

.97020 

1.03072 

52 

9 

.84357 

1.18544 

.87389 

1.14430 

.90516 

1.10478 

.93742 

1.06676 

.97076 

1.03012 

51 

10 

.84407 

1.18474 

.87441 

1.14363 

.90569 

1.10414 

.93797 

1.06613 

.97133 

1.02952 

50 

n 

.84457 

1.18404 

.87492 

1.14296 

.90621 

1.10349 

.93852 

1.06551 

.97189 

1.02892 

49 

12 

.84507 

1.18334 

.87543 

1.14229 

.90674 

1.10285 

.93906 

1.06489 

.97246 

1.02832 

48 

13 

.84556 

1 .18264 

.87595 

1.14162 

.90727 

1.10220 

.93961 

1.06427 

.97302 

1.02772 

47 

14 

.84606 

1.18194 

.87646 

1.14095 

.90781 

1.10156 

.94016 

1.06365 

.97359 

1.02713 

46 

15 

.84656 

1.18125 

.87698 

1.14028 

.90834 

1.10091 

.94071 

1.06303 

.97416 

1.02653 

45 

16 

.84706 

1.18055 

.87749 

1.13961 

.90887 

1.10027 

.94125 

1.06241 

.97472 

1.02593 

44 

17 

.84756 

1.17986 

.87801 

1.13894 

.90940 

1.09963 

.94180 

1.06179 

.07529 

1.02533 

43 

18 

.84806 

1.17916 

.87852 

1.13828 

.90993 

1.09899 

.94235 

1.06117 

.97586 

1.02474 

42 

19 

.84856 

1.17846 

.87904 

1.13761 

.91046 

1.09834 

.94290 

1.06056 

.97643 

1.02414 

41 

20 

.84906 

1.17777 

.87955 

1.13694 

.91099 

1.09770 

.94345 

1.05994 

.97700 

1.02355 

40 

21 

.84956 

1.17708 

.88007 

1.13627 

.91153 

1.09706 

.94400 

1.05932 

.97756 

1.02295 

39 

22 

.85006 

1.17638 

.88059 

1.13561 

.91206 

1.09642 

.94455 

1.05870 

.97813 

1.02236 

38 

23 

.85057 

1.17569 

.88110 

1.13494 

.91259 

1.09578 

.94510 

1.05809 

.97870 

1.02176 

37 

24 

.85107 

1.17500 

.88162 

1.13428 

.91313 

1.09514 

.94565 

1.05747 

.97927 

1.02117 

36 

25 

.85157 

1.17430 

.88214 

1.13361 

.91366 

1.09450 

.94620 

1.05685 

.97984 

1.02057 

35 

26 

.85207 

1.17361 

.88265 

1.13295 

.91419 

1.09386 

.94676 

1.05624 

.98041 

1.01998 

34 

27 

.85257 

1.17292 

.88317 

1.13228 

.91473 

1.09322 

.94731 

1.05562 

.98098 

1.01939 

33 

28 

.85308 

1.17223 

.88369 

1.13162 

.91526 

1.09258 

.94786 

1.05501 

.98155 

1.01879 

32 

29 

.85358 

1.17154 

.88421 

1.13096 

.91580 

1.09195 

.94841 

1.05439 

.98213 

1.01820 

31 

30 

.85408 

1.17085 

.88473 

1.13029 

.91633 

1.09131 

.94896 

1.05378 

.98270 

1.01761 

30 

31 

.85458 

1.17016 

.88524 

1.12963 

.91687 

1.09067 

.94952 

1.05317 

.98327 

1.01702 

29 

32 

.85509 

1.16947 

.88576 

1.12897 

.91740 

1.09003 

.95007 

1.05255 

.98384 

1.01642 

28 

33 

.85559 

1.16878 

.88628 

1.12831 

.91794 

1.08940 

.95062 

1.05194 

.98441 

1.01583 

27 

34 

.85609 

1.16809 

.88680 

1.12765 

.91847 

1.08876 

.95118 

1.05133 

.98499 

1.01524 

26 

35 

.85660 

1.16741 

.88732 

1.12699 

.91901 

1.08813 

.95173 

1.05072 

.98556 

1.01465 

25 

36 

.85710 

1.16672 

.88784 

1.12633 

.91955 

1.08749 

.95229 

1.05010 

.98613 

1.01406 

24 

37 

.85761 

1.16603 

.88836 

1.12567 

.92008 

1.08686 

.95284 

1.04949 

.98671 

1.01347 

23 

38 

.85811 

1.16535 

.88888 

1.12501 

.92062 

1.08622 

.95340 

1.04888 

.98728 

1.01288 

22 

39 

.85862 

1.16466 

.88940 

1.12435 

.92116 

1.08559 

.95395 

1.04827 

.98786 

1.01229 

21 

40 

.85912 

1.16398 

.88992 

1.12369 

.92170 

1.08496 

.95451 

1.04766 

.98843 

1.01170 

20 

41 

.85963 

1.16329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

1.04705 

.98901 

1.01112 

19 

42 

.86014 

1.16261 

.89097 

1.12238 

.92277 

1.08369 

.95562 

1.04644 

.98958 

1.01053 

18 

43 

.86064 

1.16192 

.89149 

1.12172 

.92331 

1.08306 

.95618 

1.04583 

.99016 

1.00994 

17 

44 

.86115 

1.16124 

.89201 

1.12106 

.92385 

1.08243 

.95673 

1.04522 

.99073 

1.00935 

16 

45 

.86166 

1.16056 

.89253 

1.12041 

.92439 

1.08179 

.95729 

1.04461 

.99131 

1.00876 

15 

46 

.86216 

1.15987 

.89306 

1.11975 

.92493 

1.08116 

.95785 

1.04401 

.99189 

1.00818 

14 

47 

.86267 

1.15919 

.89358 

1.11909 

.92547 

1.08053 

.95841 

1.04340 

.99247 

1.00759 

13 

48 

.86318 

1.15851 

.89410 

1.11844 

.92601 

1.07990 

.95897 

1.04279 

.99304 

1.00701 

12 

49 

.86368 

1.15783 

.89463 

1.11778 

.92655 

1.07927 

.95952 

1.04218 

.99362 

1.00642 

11 

50 

.86419 

1.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

1.04158 

.99420 

1.00583 

10 

51 

.86470 

1.15647 

.89567 

1.11648 

.92763 

1.07801 

.96064 

1.04097 

.99478 

1.00525 

9 

52 

.86521 

1.15579 

.89620 

1.11582 

.92817 

1.07738 

.96120 

1.04036 

.99536 

1.00467 

8 

53 

.86572 

1.15511 

.89672 

1.11517 

.92872 

'1.07676 

.96176 

1.03976 

.99594 

1.00408 

7 

54 

.86623 

1.15443 

.89725 

1.11452 

.92926 

1.07613 

.96232 

1.03915 

.99652 

1.00350 

6 

55 

.86674 

1.15375 

.89777 

1.11387 

.92980 

1.07550 

.96288 

1.03855 

.99710 

1.00291 

5 

56 

.86725 

1.15308 

.89830 

1.11321 

.93034 

1.07487 

.96344 

1.03794 

.99768 

1.00233 

4 

57 

.86776 

1.15240 

.89883 

1.11256 

.93088 

1.07425 

.96400 

1.03734 

.99826 

1.00175 

3 

58 

.86827 

1.15172 

.89935 

1.11191 

.93143 

1.07362 

.96457 

1.03674 

.99884 

1.00116 

2 

59 

.86878 

1.15104 

.89988 

1.11126 

.93197 

1.07299 

.96513 

1.03613 

.99942 

1.00058 

1 

60 

.86929 

1.15037 

.90040 

1.11061 

.93352 

1.07237 

.96569 

1.03553 

1.00000 

1.00000 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

49° 

48° 

47° 

46° 

45° 

logarithmic  tables. 


473 


LOGARITHMIC  TABLES. 

rpmiPfth°andefolumn  headS  P(')i  opposite  'the  latter,  and  under  the  proper 
2l®  find  the  desired  logarithmic  sine,  cosine,  tangent,  or  cotangent. 

in  the  sine,  cosine,  tangent,  or  cotangent 

^TnTincfthe  L^MrUhmi^Rnictio^s^or  an  Angle  Containing  Degrees,  Minutes,  and 

c j Tt'ind  the  logarithm  for  the  degrees  and  minutes  in  the  manner  given 

Seconds.— Find  me  logantnm  , ded  ,?d take  the  number  next  below  the 

lo^Mithm^hus  fo^d-^Mer toda^tglumn^ea  e^  y 
prope^vate/n^  he  foun^^yJ^w^ating^etweeii^the^TOlues^gyra. 

ina+°CphSS"  ^4to%6°CtogTio7aC^  log  COtg  a 

log  tang  a + Cpl.  T.  _ — 

COMMON  LOGARITHMS  OF  NUMBERS. 


To. 

Log. 

No.! 

Log. 

No. 

Log. 

0 

— 00 

20 

30  103 

40 

60  206 

1 

00  000 

21 

32  222 

41 

61  278 

2 

30  103 

22 

34  242 

42 

62  325 

3 

47  712 

23 

36  173 

43 

63  347 

4 

60  206 

24 

38  021 

44 

64  345 

5 

69  897 

25 

39  794 

45 

65  321 

6 

77  815 

26 

41  497 

46 

66  276 

7 

84  510 

27 

43  136 

47 

67  210 

8 

90  309 

28 

44  716 

48 

68  124 

9 

95  424 

29 

46  240 

49 

69  020 

10 

00  000 

30 

47  712 

50 

69  897 

11 

04  139 

31 

49  136 

51 

70  757 

12 

07  918 

32 

50  515 

52 

71  600 

13 

11  394 

33 

51  851 

53 

72  428 

14 

14  613 

34 

53  148 

54 

73  239 

15 

17  609 

35 

54  407 

55 

74  036 

16 

20  412 

36 

55  630 

56 

74  819 

17 

23  045 

37 

56  820 

57 

75  587 

18 

25  527 

38 

57  978 

58 

76  343 

19 

27  875 

39 

59  106 

59 

77  085 

20 

30  103 

40 

60  206 

60 

77  815 

No. 


60 

61' 

62 

68 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 


Log. 


77  815 


78  533 

79  239 

79  934 

80  618 
81  291 

81  954 

82  607 

83  251 
83  885 


84  510 


85  126 

85  733 

86  332 

86  923 

87  506 

88  081 

88  649 

89  209 
89  763 


90  309 


No. 

Log. 

80 

90  309 

81 

90  849 

82 

91  381 

83 

91  908 

84 

92  428 

85 

92  942 

86 

93  450 

87 

93  952 

88 

94  448 

89 

94  939 

90 

95  424 

91 

95  904 

92 

96  379 

93 

96  848 

94 

97  313 

95 

97  772 

96 

98  227 

97 

98  677 

98 

99  123 

99 

99  564 

100 

00  000 

474 


LOGARITHMS. 


N. 

L.  0 

, 

T 

3 

4 

5 

6 

' 7 

8 

9 

P.  P. 

too 

00  000 

043 

087 

130 

173 

217 

260 

303 

346 

389 

101 

432 

475 

518 

561 

604 

647 

689 

732 

775 

817 

44 

43 

42 

102 

860 

903 

945 

988 

*030 

*072 

*115 

*157 

*199 

*242 

A A 

A S 

A 9 

103 

01  284 

326 

368 

410 

452 

494 

536 

578 

620 

662 

X 

2 

A. A 
8.8 

4.0 

8.6 

8.4 

104 

703 

745 

787 

828 

870 

912 

953 

995 

*036 

*078 

3 

13.2 

12.9 

12.6 

105 

02  119 

160 

202 

243 

284 

325 

366 

407 

449 

490 

4 

17.6 

17.2 

16.8 

106 

531 

572 

612 

653 

694 

735 

776 

816 

857 

898 

5 

22.0 

21.5 

21.0 

107 

938 

979 

*019 

*060 

*100 

*141 

*181 

*222 

*262 

*302 

6 

7 

26.4 
30  8 

25.8 

30.1 

25.2 
29  4 

108 

03  342 

383 

423 

463 

503 

543 

583 

623 

663 

703 

1 

8 

35^2 

34.4 

33^6 

109 

743 

■ 782 

822 

862 

902 

941 

981 

*021 

*060 

*100 

9 

39.6 

38.7 

37.8 

110 

04  139 

179 

218 

258 

297 

336 

376 

415 

454 

493 

111 

532 

571 

610 

650 

689 

727 

766 

805 

844 

883 

41 

40 

39 

112 

922 

961 

999 

*038 

*077 

*115 

*154 

*192 

*231 

*269 

A 1 

a n 

*»  Q 

113 

05  308 

346 

385 

423 

461 

500 

538 

576 

614 

652 

X 

2 

T.  1 
8.2 

8.0 

O.i/ 

7.8 

114 

690 

729 

767 

805 

843 

881 

918 

956 

994 

*032 

3 

12.3 

12.0 

11.7 

115 

06  070 

108 

145 

183 

221 

258 

296 

333 

371 

408 

4 

16.4 

16.0 

15.6 

116 

446 

483 

521 

558 

595 

633 

670 

707 

744 

781 

5 

20.5 

20.0 

19.5 

117 

819 

856 

893 

930 

967 

*004 

*041 

*078 

*115 

*151 

6 

7 

24.6 

28.7 

24.0 

28.0 

23.4 

27.3 

118 

07  188 

225 

262 

298 

335 

372 

408 

445 

482 

518 

1 

8 

32.8 

32.0 

31.2 

119 

555 

591 

628 

664 

700 

737 

773 

809 

846 

882 

9 

36.9 

36.0 

35.1 

120 

918 

954 

990 

*027 

*063 

*099 

*135 

*171 

*207 

*243 

121 

08  279 

314 

350 

386 

422 

458 

493 

529 

565 

600 

38 

37 

36 

122 

636 

672 

707 

743 

778 

814 

849 

884 

920 

955 

x 

3.8 

3.7 

3.6 

123 

991 

*026 

*061 

*096 

*132 

*167 

*202 

*237 

*272 

*307 

2 

7.6 

7!4 

7.2 

124 

09  342 

377 

412 

447 

482 

517 

552 

587 

621 

656 

3 

11.4 

11.1 

10.8 

125 

691 

726 

760 

795 

830 

864 

899 

934 

968 

*003 

4 

15.2 

14.8 

14.4 

126 

10  037 

072 

106 

140 

175 

209 

243 

278 

312 

346 

5 

19.0 

18.5 

18.0 

127 

380 

415 

449 

483 

517 

551 

585 

619 

653 

687 

6 

7 

22.8 

26.6 

22.2 

25.9 

21. (> 
25.2 

128 

721 

755 

789 

823 

857 

890 

924 

958 

992 

*025 

8 

30^4 

29  6 

28^ 

129 

11  059 

093 

126 

160 

193 

227 

261 

294 

327 

361 

9 

34.2 

33.3 

32.4 

130 

394 

428 

461 

494 

528 

561 

594 

628 

661 

694 

131 

727 

760 

793 

826 

860 

893 

926 

959 

992 

*024 

35 

34 

33 

132 

12  057 

090 

123 

156 

189 

222 

254 

287 

320 

352 

1 

3.5 

3.4 

3.3 

133 

385 

418 

450 

483 

516 

548 

581 

613 

646 

678 

2 

7!o 

6*8 

6^6 

134 

710 

743 

775 

808 

840 

872 

905 

937 

969 

*001 

3 

10.5 

10.2 

9.9 

135 

13  033 

066 

098 

130 

162 

194 

226 

258 

290 

322 

4 

14.0 

13.6 

13.2 

136 

354 

386 

418 

450 

481 

513 

545 

577 

609 

640 

5 

17.5 

17.0 

*)A  A 

16.5 

TOO 

137 

672 

704 

735 

767 

799 

830 

862 

893 

925 

956 

6 

7 

21.0 

24.5 

zU.4 

23.8 

19.0 

23.1 

138 

988 

*019 

*051 

*082 

*114 

*145 

*176 

*208 

*239 

*270 

8 

28^0 

27.2 

26^4 

139 

14  301 

333 

364 

395 

426 

457 

489 

520 

551 

582 

9 

31.5 

30.6 

29.7 

140 

613 

644 

675 

706 

737 

768 

799 

829 

860 

891 

141 

922 

953 

983 

*014 

*045 

*076 

*106 

*137 

*168 

*198 

32 

31 

30 

142 

15  229 

259 

290 

320 

351 

381 

412 

442 

473 

503 

1 

3.2 

3.1 

3.0 

143 

534 

564 

594 

625 

655 

685 

715 

746 

776 

806 

2 

6^4 

6^2 

6^0 

144 

836 

866 

897 

'927 

957 

987 

*017 

*047 

*077 

*107 

3 

9.6 

9.3 

9.0 

145 

16  137 

167 

197 

227 

256 

286 

316 

346 

376 

406 

4 

12.8 

12.4 

12.0 

146 

435 

465 

495 

524 

554 

584 

613 

643 

673 

702 

5 

16.0 

15.5 

15.0 

147 

732 

761 

791 

820 

850 

879 

909 

938 

967 

997 

6 

7 

19.2 

22.4 

18.6 

21.7 

18.0 

21.0 

148 

17  026 

056 

085 

114 

143 

173 

202 

231 

260 

289 

8 

25^6 

24^8 

24^0 

149 

319 

348 

377 

406 

435 

464 

493 

522 

551 

580 

9 

28.8 

27.9 

27.0 

150 

609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


475 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P 

• 

150  1 

7 609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

151 

898 

926 

955 

984  * 

<013  * 

<041  * 

*070  =< 

<099  * 

*127  * 

*156 

29 

28 

152 

.8  184 

213 

241 

270 

298 

327 

355 

384 

412 

441 

i 

2.9 

2.8 

153 

469 

498 

526 

554 

583 

611 

639 

667 

696 

724 

2 

5.8 

5.6 

154 

752 

780 

808 

837 

865 

893 

921 

949 

977  * 

*005 

3 

8.7 

8.4 

155 

L9  033 

061 

089 

117 

145 

173 

201 

229 

257 

285 

4 

11.6 
1 A 

11.2 

110 

156 

312 

340 

368 

396 

424 

451 

479 

507 

535 

562 

5 

6 

14.0 

17.4 

16.8 

157 

590 

618 

645 

673 

700 

728 

756 

783 

811 

838 

7 

20.3 

19.6 

158 

866 

893 

921 

948 

976 

*003  5 

*030  * 

*058  5 

*085  5 

*112 

8 

23.2 

22.4 

159 

20  140 

167 

194 

222 

249 

276 

303 

330 

358 

385 

9 

26.1 

25.2 

160 

412 

439 

466 

493 

520 

548 

575 

602 

629 

656 

161 

683 

710 

737 

763 

790 

817 

844 

871 

898 

925 

27 

26 

162 

952 

978 

*005 

*032 

*059 

*085  : 

*112  = 

*139  : 

*165  : 

*192 

1 

2.7 

2.6 

163 

21  219 

245 

272 

299 

325 

352 

378 

405 

431 

458 

2 

5.4 

5.2 

164 

484 

511 

537 

564 

590 

617 

643 

669 

696 

722 

3 

8.1 

7.8 

165 

748 

775 

801 

827 

854 

880 

906 

932 

958 

985 

4 

10.8 
IQ  C 

10.4 

IQ  ft 

166 

22  Oil 

037 

063 

089 

115 

141 

167 

194 

220 

246 

5 

6 

lo.D 

16.2 

lo.u 

15.6 

167 

272 

298 

324 

350 

376 

401 

427 

453 

479 

505 

7 

18.9 

18.2 

168 

531 

557 

583 

608 

634 

660 

686 

712 

737 

763 

8 

21.6 

20.8 

169 

789 

814 

840 

866 

891 

917 

943 

968 

994 

*019 

9 

24.3 

23,4 

170 

23  045 

070 

096 

121 

147 

172 

198 

223 

249 

274 

171 

300 

325 

350 

376 

401 

426 

452 

477 

502 

528 

25 

172 

553 

578 

603 

629 

654 

679 

704 

729 

754 

779 

1 

2.5 

173 

805 

830 

855 

880 

905 

930 

955 

980 

*005 

*030 

2 

5.0 

174 

24  055 

080 

105 

130 

155 

180 

204 

229 

254 

279 

3 

7.5 

175 

304 

329 

353 

378 

403 

428 

452 

477 

502 

527 

4 

10.0 
1o  K 

176 

551 

576 

601 

625 

650 

674 

699 

724 

748 

773 

O 

6 

LA.O 

15.0 

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797 

822 

846 

871 

895 

920 

944 

969 

993 

*018 

7 

17.5 

178 

25  042 

066 

091 

115 

139 

164 

188 

212 

237 

261 

8 

20.0 

179 

285 

310 

334 

358 

382 

406 

431 

455 

479 

503 

9 

22.5 

180 

527 

551 

575 

600 

624 

648 

672 

696 

720 

744 

181 

768 

792 

816 

840 

864 

888 

912 

935 

959 

983 

24 

23 

182 

26  007 

031 

055 

079 

102 

126 

150 

174 

198 

221 

1 

2.4 

2.3  ! 

183 

245 

269 

293 

316 

340 

364 

387 

411 

435 

458 

2 

4.8 

4.6 

184 

482 

505 

529 

553 

576 

600 

623 

647 

670 

694 

3 

7.2 

6.9 

185 

717 

741 

764 

788 

811 

834 

858 

881 

905 

928 

4 

K 

9.6 

9.2 

11.5 

186 

951 

975 

998 

*021 

*045 

*068 

*091 

*114 

*138 

*161 

o 

6 

LA  .v 

14.4 

13^8 

187 

27  184 

: 207 

231 

254 

277 

300 

323 

346 

370 

393 

7 

16.8 

16.1 

188 

416 

- 439 

462 

485 

508 

531 

554 

577 

600 

623 

8 

19.2 

18.4 

189 

646 

1 669 

692 

715 

738 

761 

784 

807 

830 

852 

9 

21.6 

20.7 

190 

875 

> 898 

921 

944 

967 

989 

*012 

*035 

*058 

*081 

191 

28  102 

; 126 

149 

171 

194 

217 

240 

262 

285 

307 

22 

2! 

192 

33C 

> 353 

375 

398 

421 

443 

466 

488 

511 

533 

1 

2.2 

2.1 

193 

| 55( 

> 578 

601 

623 

646 

668 

691 

713 

735 

758 

2 

4.4 

4.2 

194 

78C 

) 803 

825 

847 

870 

892 

914 

937 

959 

981 

3 

66 

6.3 

195 

29  002 

5 026 

048 

070 

092 

115 

137 

159 

181 

203 

4 

8.8 

11.0 

8.4 

10.5 

196 

226 

> 248 

270 

292 

314 

336 

358 

380 

403 

425 

o 

6 

13.2 

12.6 

197 

1 469 

491 

513 

535 

557 

579 

601 

623 

645 

7 

15.4 

14.7 

198 

66- 

1 688 

710 

732 

754 

776 

798 

820 

842 

863 

8 

17.6 

16.8 

199 

882 

> 907 

929 

951 

973 

994 

*016 

*038 

*060 

*081 

9 

19.8 

18.9 

200 

30  102 

J 125 

146 

168 

190 

211 

233 

255 

276 

298 

N. 

L.O 

1 

2 

3 

4 

5 

6 

1 

7 

8 

9 

P.  P. 

476 


LOGARITHMS . 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

200 

30  103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

22  21 

1 2.2  2.1 

2 4.4  4.2 

3 6.6  6.3 

4 8.8  8.4 

5 11.0  10.5 

- 6 13.2  12.6 

7 15.4  14.7 

8 17.8  16.8 

9 19.8  18.9 

20 

1 2.0 

2 4.0 

3 6.0 

4 8.0 

5 10.0 

6 12.0 

7 14.0 

8 16.0 

9 18.0 

19 

1 1.9 

2 3.8 

3 5.7 

4 7.6 

5 9.5 

6 11.4 

7 13.3 

8 15.2 

9 17.1 

18 

1 1.8 

2 3.6 

3 5.4 

4 7.2 

5 9.0 

6 10.8 

7 12.6 

8 14.4 

9 16.2 

17 

1 1.7 

2 34 

3 5.1 

4 6.8 

5 8.5 

6 10.2 

7 11.9 

! 8 13.6 

9 15.3 

201 

202 

203 

204 

205 

206 

207 

208 

209 

210 

320 

535 

750 

963 

31  175 
387 
597 
806 

32  015 

341 

557 

771 

984 

197 

408 

618 

827 

035 

363 

578 

792 

*006 

218 

429 

639 

848 

056 

384 

600 

814 

*027 

239 

450 

660 

869 

077 

406 

621 

835 

*048 

260 

471 

681 

890 

098 

428 

643 

856 

*069 

281 

492 

702 

911 

118 

449 

664 

878 

*091 

302 

513 

723 

931 

139 

471 

685 

899 

*112 

323 

534 

744 

952 

160 

492 

707 

920 

*133 

345 

555 

765 

973 

181 

514 

728 

942 

*154 

366 

576 

785 

994 

201 

222 

243 

263 

284 

305 

325 

346 

366 

387 

408 

211 

212 

213 

214 

215 

216 

217 

218 
219 

220 

221 

222 

223 

224 

225 

226 

227 

228 
229 

230 

231 

232 

233 

234 

235 

236 

237 

238 

239 

240 

241 

242 

243 

244 

245 

246 

247 

248 

249 

250 

428 

634 

838 

33  041 
244 
445 
646 
846 

34  044 

449 

654 

858 

062 

264 

465 

666 

866 

064 

469 

675 

879 

082 

284 

486 

686 

885 

084 

490 

695 

899 

102 

304 

506 

706 

905- 

104 

510 

715 

919 

122 

325 

526 

726 

925 

124 

531 

736 

940 

143 

345 

546 

746 

945 

143 

552 

756 

960 

163 

365 

566 

766 

965 

163 

572 

777 

980 

183 

385 

586 

786 

985 

183 

593 

797 

*001 

203 

405 

606 

806 

*005 

203 

613 

818 

*021 

224 

425 

626 

826 

*025 

223 

242 

262 

282 

301 

321 

341 

361 

380 

400 

420 

439 
635 
830 
35  025 
218 
411 
603 
793 
984 

459 

655 

850 

044 

238 

430 

622 

813 

*003 

479 

674 

869 

064 

257 

449 

641 

832 

*021 

498 

694 

889 

083 

276 

468 

660 

851 

*040 

518 

713 

908 

102 

295 

488 

679 

870 

*059 

537 

733 

928 

122 

315 

507 

698 

889 

*078 

557 

753 

947 

141 

334 

526 

717 

908 

*097 

577 

772 

967 

160 

353 

545 

736 

927 

*116 

596 

792 

986 

180 

372 

564 

755 

946 

*135 

616 

811 

*005 

199 

392 

583 

774 

965 

*154 

36  173 

192 

211 

229 

248 

267 

286 

305 

324 

342 

361 
549 
736 
922 
37  107 
291 
475 
658 
840 

380 

568 

754 

940 

125 

310 

493 

676 

858 

399 

586 

773 

959 

144 

328 

511 

694 

876 

418 

605 

791 

977 

162 

346 

530 

712 

894 

436 

624 

810 

996 

181 

365 

548 

731 

912 

455 

642 

829 

*014 

199 

383 

566 

749 

931 

474 

661 

847 

*033 

218 

401 

585 

767 

949 

493 

680 

866 

*051 

236 

420 

603 

785 

967 

511 

698 

884 

*070 

254 

438 

621 

803 

985 

530 

717 

903 

*088 

273 

457 

639 

822 

*003 

38  021 

039 

057 

075 

093 

112 

130 

148 

166 

184 

202 
382 
561 
739 
917 
39  094 
270 
445 
! 62C 

! 220 
; 399 
578 
i 757 
934 
111 
» 287 
> 463 
1 637 

238 

417 

596 

775 

952 

129 

305 

480 

655 

256 

435 

614 

792 

970 

146 

322 

498 

672 

274 

453 

632 

810 

987 

164 

340 

515 

690 

292 

471 

650 

828 

*005 

182 

358 

533 

707 

310 
489 
■ 668 
846 
*023 
199 
375 
550 
724 

328 

507 

686 

863 

*041 

217 

393 

568 

742 

346 

525 

703 

881 

*058 

235 

410 

585 

759 

364 

543 

721 

899 

*076 

252 

428 

602 

777 

794 

t 811 

829 

846 

863 

881 

898 

915 

933 

950 

K. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMS. 


477 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

250  : 

251 

252 

253 

254 

255 

256 

257 

258 

259 

260 

261 

262 

263 

264 

265 

266 

267 

268 
269 

270 

271 

272 

273 

274 

275 

276 
•‘277 

278 

279 

280 

281 

282 

283 

284 

285 

286 

287 

288 
289 

290 

291 

292 

293 

294 

295 

296 

297 

298 

299 

300 

59  794 

811 

829 

846 

863 

881 

898 

915 

933 

950 

18 

1 1.8 

2 3.6 

3 5.4 

4 7.2 

5 9.0 

6 10.8 
7 12.6 

8 14.4 

9 16.2 

17 

1 1.7 

2 3.4 

3 5.1 

4 6.8 

5 8.5 

6 10.2 

7 11.9 

8 13.6 

9 15.3 

16 

1 1.6 

2 3.2 

3 4.8 

4 6.4 

5 8.0 

6 9.6 

7 11.2 

8 12.8 

9 14.4 

15 

1 1.5 

2 3.0 

3 4.5 

4 6.0 

5 7,5 

6 9.0 

7 10.5 

8 12.0 

9 13.5 

14 

1 1.4 

2 2 8 

3 4.2 

4 5.6 

5 7.0 

6 8.4 

7 9.8 

8 11.2 

9 12.6 

967 
10  140 
312 
483 
654 
824 
993 
41  162 
330 

985 

157 

329 

500 

671 

841 

*010 

179 

347 

*002 

175 

346 

518 

688 

858 

*027 

196 

363 

*019 

192 

364 

535 

705 

875 

*044 

212 

380 

*037 

209 

381 

552 

722 

892 

*061 

229 

397 

*054  5 
226 
398 
569 
739 
909 
*078  : 
246 
414 

*071  5 
243 
415 
586 
756 
926 
*095  ; 
263 
430 

*088  s 
261 
432 
603 
773 
943 
*111  : 
280 
447 

*106  5 
278 
449 
620 
790 
960 
*128  ; 
296 
464 

*123 

295 

466 

637 

807 

976 

*145 

313 

481 

497 

514 

531 

547 

564 

581 

597 

614 

631 

647 

664 
830 
996 
42  160 
325 
488 
651 
813 
975 

681  | 
847 
*012 
177 
341 
504 
667 
830 
991 

697 

863 

*029 

193 

357 

521 

684 

846 

*008 

714 

880 

*045 

210 

374 

537 

700 

862 

*024 

731 

896 

*062 

226 

390 

553 

716 

878 

*040 

747 

913 

*078 

243 

406 

570 

732 

894 

*056 

764 

929 

*095 

259 

423 

586 

749 

911 

*072 

780 

946 

*111 

275 

439 

602 

765 

927 

*088 

797 

963 

*127 

292 

455 

619 

781 

943 

*104 

814 

979 

*144 

308 

472 

635 

797 

959 

*120 

43  136 

152 

169 

185 

201 

217 

233 

249 

265 

281 

297 
457 
616 
775 
933 
44  091 
248 
404 
560 

313 

473 

632 

791 

949 

107 

264 

420 

576 

329 

489 

648 

807 

965 

122 

279 

436 

592 

345 

505 

664 

823 

981 

138 

295  • 

451 

607 

361 

521 

680 

838 

996 

154 

311 

467 

623 

377 

537 

696 

854 

*012 

170 

326 

483 

638 

393 

553 

712 

870 

*028 

185 

342 

498 

654 

409 

569* 

727 

886 

*044 

201 

358 

514 

669 

425 

584 

743 

902 

*059 

217 

373 

529 

685 

441 

600 

759 

917 

*075 

232 

389 

545 

700 

716 

731 

747 

762 

778 

793 

809 

824 

840 

855 

871 

45  025 
179 
332 
484 
637 
788 
939 

46  090 

886 
040 
194 
347 
500 
652 
803 
954 
i 105 

902 

056 

209 

362 

515 

667 

818 

969 

120 

917 

071 

225 

378 

530 

682 

834 

984 

135 

932 

086 

240 

393 

545 

697 

849 

*000 

150 

948 

102 

255 

408 

561 

712 

864 

*015 

165 

963 

117 

271 

423 

576 

728 

879 

*030 

180 

979 

133 

286 

439 

591 

743 

894 

*045 

195 

994 

148 

301 

454 

606 

758 

909 

*060 

210 

*010 

163 

317 

469 

621 

773 

924 

*075 

225 

240 

i 255 

270 

285 

300 

315 

330 

345 

359 

374 

380 

538 

m 

835 
982 
47  120 
27 1 
422 
567 

> 404 
i 553 
' 702 

> 850 
5 997 
) 144 
5 290 

> 436 
I 582 

419 

568 

716 

864 

*012 

159 

305 

451 

596 

434 

583 

731 

879 

*026 

173 

319 

465 

611 

449 

598 

746 

894 

*041 

188 

334 

480 

625 

464 

613 

761 

909 

*056 

202 

349 

494 

640 

479 

627 

776 

923 

*070 

217 

363 

509 

654 

494 

642 

790 

938 

*085 

232 

378 

524 

669 

509 

657 

805 

953. 

*100 

246 

392 

538 

683 

523 

672 

820 

967 

*114 

261 

407 

553 

698 

712 

2 727 

741 

756 

770 

784 

799 

813 

828 

842 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

478 


LOGARITHMS. 


N. 

L.oj 

1 

2 

3 

4 

5 

6 

7 

8 

9 

p. 

P. 

300 

47  712 

727 

741 

756 

770 

784 

799 

813 

828 

842 

301 

857 

871 

885 

900 

914 

929 

943 

958 

972 

986 

302 

48  001 

015 

029 

044 

058 

073 

087 

101 

116 

130 

303 

144 

159 

173 

187 

202 

216 

230 

244 

259 

273 

304 

287 

302 

316 

330 

344 

359 

373 

387 

401 

416 

15 

305 

430 

444 

458 

473 

487 

501 

515 

530 

544 

558 

306 

572 

586 

601 

615 

629 

643 

657 

671 

686 

700 

1 

1.5 

307 

714 

728 

742 

756 

770 

785 

799 

813 

827 

841 

2 

3.0 

308 

855 

869 

883 

897 

911 

926 

940 

954 

968 

982 

3 

A 

4.5 
a n 

309 

996 

*010 

*024 

*038 

*052 

*066 

*080 

*094 

*108 

*122 

4 

5 

o.u 

7.5 

310 

49  136 

150 

104 

178 

192 

206 

220 

234 

248 

262 

7 | 

9.0 

10.5 

311 

276 

290 

304 

318 

332 

346 

360 

374 

388 

402 

8 

9 j 

12.0 

13.5 

312 

415 

429 

443 

457 

471 

485 

499 

513 

527 

541 

313 

554 

568 

582 

596 

610 

624 

638 

651 

665 

679 

314 

693 

707 

721 

734 

748 

762 

776 

790 

803 

817 

315 

831 

845 

859 

872 

886 

900 

914 

927 

941 

955 

14 

316 

969 

982 

996 

*010 

*024 

*037 

*051 

*065 

*079 

*092 

317 

50  106 

120 

133 

147 

161 

174 

188 

202 

215 

229 

1 

1.4 

318 

243 

256 

270 

284 

297 

311 

325 

338 

352 

365 

2 

2.8 

319 

379 

393 

406 

420 

433 

447 

461 

474 

488 

501 

3 

4 

4.2 

5.6 

320 

515 

529 

542 

556 

569 

583 

596 

610 

623 

| 637 

5 

6 

7.0 

8.4 

321 

651 

664 

678 

691 

705 

718 

732 

745 

759 

772 

7 

g 

9.8 

11.2 

322 

786 

799 

813 

S2& 

840 

853 

866 

880 

893 

907 

9 

12^ 

1 \ - 

323 

920 

934 

947 

961 

974 

987 

*001 

*014 

*028 

*041 

324 

51  0551 

068 

081 

095 

108 

121 

135 

148 

162 

175 

325 

188 

202 

215 

228 

242 

255 

268 

282 

295 

308 

326 

322 

335 

348 

362 

375 

388 

402 

415 

428 

441 

13 

327 

455 

468 

481 

495 

508 

521 

534 

548 

561 

574 

328 

587 

601 

614 

627 

640 

654 

667 

680 

693 

706 

1 

1.3 

329 

720 

733 

746 

759 

772 

786 

799 

812 

825 

838 

2 

3 

2.6 

3.9 

330 

851 

865 

878 

891 

904 

917 

930 

943 

957 

970 

4 

5 

5 2 
6.5 

331 

983 

996 

*009 

*022 

*035 

*048 

*061 

*075 

*088 

*101 

6 

7.8 

Q 1 

332 

52  114 

127 

140 

153 

166 

179 

192 

205 

218 

231 

7 

g 

10.4 

333 

244 

257 

270 

284 

297 

310 

323 

336 

349 

362 

9 

11.7 

334 

375 

388 

401 

414 

427 

440 

453 

466 

479 

492 

335 

504 

517 

530 

543 

556 

569 

582 

595 

608 

621 

336 

634 

S 647 

660 

673 

686 

699 

711 

724 

737 

750 

337 

763 

; 776 

789 

802 

815 

827 

840 

853 

866 

879 

12 

338 

892:  905 

917 

930 

943 

956 

969 

982 

994 

*007 

339 

53  020 

| 033 

046 

058 

071 

084 

097 

| 110 

122 

135 

1 

t) 

1.2 

O I 

340 

148 

1 161 

173 

186 

199 

212 

224 

237 

250 

263 

L 

3 

i 

A.T 

3.6 

A W 

311 

275 

| 288 

301 

314 

326 

339 

352 

364 

377 

390 

4 

5 

4.0 

6.0 

342 

403 

! 415 

428 

441 

453 

466 

479 

491 

504 

517 

6 

7.2 

343 

529 

! 542 

555 

567 

580 

593 

605. 

618 

631 

m 

7 

g 

8.4 

9.6 

344 

656 

; 668 

681 

694 

706 

719 

732 

744 

757 

769 

9 

10.8 

345 

782 

794 

807 

820 

832 

845 

857 

870 

882 

895 

346 

908 

920 

933 

945 

958 

970 

983 

995 

*008 

*020 

347 

54  033 

045 

058 

070 

083 

095 

108 

120 

133 

145 

348 

158 

170 

183 

195 

208 

220 

233 

245 

258 

270 

349 

283 

295 

307 

320 

332 

345 

357 

370 

382 

394 

350 

407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

N. 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


479 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

350 

351 

352 

353 

354 

355 

356 

357 

358 

359 

360 

361 

362 

363 

364 

365 

366 

367 

368 

369 

370 

371 

372 

373 

374 

375 

376 

377 

378 

379 

380 

381 

382 

383 

384 

385 

386 

387 

388 

389 

390 

391 

392 

393 

394 

395 

396 

397 

398 

399 

400 

54  407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

13 

1 1.3 

2 2.6 

3 3.9 

4 5.2 

5 6.5 

6 7.8  ' 

7 9.1 

8 10.4 

9 11.7 

12 

1 1.2 

2 2.4 

3 3.6 

4 4.8 

5 6.0 

6 7,2 

7 8.4 

8 9.6 

9 10.8 

II 

1 1.1 
2 2.2 

3 3.3 

4 4.4 

5 5.5 

6 6.6 

7 7.7 

8 8.8 

9 9.9 

10 

1 1.0 
2 2,0 

3 3.0 

4 4.0 

5 5.0 

6 6.0 

7 7.0 

8 8.0 

9 9.0 

531 
654 
777 
900 
55  023 
145 
267 
388 
509 

543 

667 

790 

913 

035 

157 

279 

400 

522 

555 

679 

802 

925 

047 

169 

291 

413 

534 

568 

691 

814 

937 

060 

182 

303 

425 

546 

580 

704 

827 

949 

072 

194 

315 

437 

558 

593 

716 

839 

962 

084 

206 

328 

449 

570 

605 

728 

851 

974 

096 

218 

340 

461 

582 

617 

741 

864 

986 

108 

230 

352 

473 

594 

630 
753 
876 
998  ! 
121 
242 
364 
485 
606 

642 

765 

888 

*011 

133 

255 

376 

497 

618 

630 

642 

654 

666 

678 

691 

703 

715 

727 

739 

751 
871 
991 
56  110 
229 
348 
467 
585 
703 

763 

883 

*003 

122 

241 

360 

478 

597 

714 

775 

895 

*015 

134 

253 

372 

490 

608 

726 

787 

907 

*027 

146 

265 

384 

502 

620 

738 

799 

919 

*038 

158 

277 

396 

514 

632 

750 

811 

931 

*050 

170 

289 

407 

526 

644 

761 

823 

943 

*062 

182 

301 

419 

538 

656 

773 

835 

955 

*074 

194 

312 

431 

549 

667 

785 

847 

967 

*086 

205 

324 

443 

561 

679 

797 

859 

979 

*098 

217 

336 

455 

573 

691 

808 

820 

832 

844 

855 

867 

879 

891 

902 

914 

926 

937 
57  054 
171 
287 
* 403 

519 
634 
749 
864 

949 

066 

183 

299. 

415 

530 

646 

761 

875 

961 

078 

194 

310 

426 

542 

657 

772 

887 

972 

089 

206 

322 

438 

553 

669 

784 

898 

984 

101 

217 

334 

449 

565 

680 

795 

910 

996 

113 

229 

345 

461 

576 

692 

807 

921 

*008 

124 

241 

357 

473. 

588 

703 

818 

933 

*019 

136 

252 

368 

484 

600 

715 

830 

944 

*031 

148 

264 

380 

496 

611 

726 

841 

955 

*043 

159 

276 

392 

507 

623 

738 

852 

967 

978 

990 

*001 

*013 

*024 

*035 

*047 

*058 

*070 

*081 

58  092 
206 
320 
433 
546 
659 
771 
883 
995 

104 

218 

331 

444 

557 

670 

782 

894 

*006 

115 

229 

343 

456 

569 

•681 

794 

906 

*017 

127 

240 

354 

467 

580 

692 

805 

917 

*028 

138 

252 

365 

478 

591 

704 

816 

928 

*040 

149 

263 

377 

490 

602 

715 

827 

939 

*051 

161 

274 

388 

501 

614 

726 

838 

950 

*062 

172 

286 

399 

512 

625 

737 

850 

961 

*073 

184 

297 

410 

524 

636 

749 

861 

973 

*084 

195 

309 

422 

535 

647 

760 

872 

984 

*095 

59  106 

118 

129 

140 

151 

162 

173 

184 

195 

207 

218 

329 

439 

55C 

66C 

77C 

87? 

m 

60 

229 
340 
450 
l 561 
1 671 
1 780 
) 890 
5 999 
’ 108 

240 

351 

461 

572 

682 

791 

901 

*010 

119 

251 

362 

472 

583 

693 

802 

912 

*021 

130 

262 

373 

483 

594 

704 

813 

923 

*032 

141 

273 

384 

494 

605 

715 

824 

934 

*043 

152 

284 

395 

506 

616 

726 

835 

945 

*054 

163 

295 

406 

517 

627 

737 

846 

956 

*065 

173 

306 

417 

528 

638 

748 

857 

966 

*076 

184 

318 

428 

539 

649 

759 

868 

977 

*086 

195 

20( 

3 217 

228 

239 

249 

260 

271 

282 

293 

304 

N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

480 


LOGARITHMS. 


N. 

L 0 

| 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

400 

50  206 

217 

228. 

239 

249 

260 

271 

282 

293 

304 

401 

314 

325 

336 

347 

358 

369 

379 

390 

401 

412 

402 

423 

433 

444 

455 

466 

477 

487 

498 

509 

520 

403 

531 

541 

552 

563 

574 

584 

595 

606 

617 

627 

404 

638 

649 

660 

670 

681 

692 

703 

713 

724 

735 

405 

746 

756 

767 

778 

788 

799 

810 

821 

831 

842 

406 

853 

863 

874 

885 

895 

906 

917 

927 

938 

949 

H 

407 

959 

970 

981 

991 

*002 

*013 

*023 

*034 

*045 

*055 

408 

61  066 

077 

087 

098 

109 

119 

130 

140 

151 

162 

l 

i.i 

409 

172 

183 

194 

204 

215 

225 

236 

247 

257 

268 

2 

3 

2.2 

3.3 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

4 

5 

4.4 

5.5 

411 

384 

395 

405 

416 

426 

437 

448 

458 

469 

479 

6 

6.6 

412 

490 

500 

511 

521 

532 

542 

553 

563 

574 

584 

7 

g 

7.7 

8.8 

413 

595 

606 

616 

627 

637 

648 

658 

669 

679 

690 

9 

9!9 

414 

700 

711 

721 

731 

742 

752 

763 

773 

784 

794 

415 

805 

815 

826 

836 

847 

857 

868 

878 

888 

899 

416 

909 

920 

930 

941 

951 

962 

972 

982 

993 

*003 

417 

62  014 

024 

034 

045 

055 

066 

076 

086 

097 

107 

418 

118 

128 

138 

149 

159 

170 

180 

190 

201 

211 

419 

221 

232 

242 

252 

263 

273 

284 

294 

304 

315 

420 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 

10 

421 

428 

439 

449 

459 

469 

480 

490 

500 

511 

521 

1 

422 

531 

542 

552 

562 

572 

583 

593 

603 

613 

624 

1 ! 

o ! 

1.0 

423 

634 

644 

655 

665 

675 

685 

696 

706 

716 

726 

3 

z .u 
3.0 

424 

737 

747 

757 

767 

778 

788  | 

798 

808 

818 

829 

4.0 

425 

839 

849 

859 

87C 

880 

890 

| 900 

910 

921 

931 

5 

5.0 

426 

941 

951 

961 

972 

982 

992 

*002 

*012 

*022 

*033 

6 

: 6.0 

427 

63  043 

053 

063 

073 

083 

094 

104 

114 

124 

134 

7 

Q 

i 7.0 

Q A 

428 

144 

155 

165 

175 

185 

195 

205 

215 

225 

236 

O 

9 

j o.U 

! 9.0 

429 

246 

256 

266 

276 

286 

296 

306 

317 

327 

337 

1 

430 

347 

357 

367 

377 

387 

397 

407 

417 

428 

438 

431 

448 

458 

468 

478 

488 

498 

508 

518 

528 

538 

432 

548 

558 

568 

579 

589 

599 

609 

619 

629 

639 

433 

649 

659 

669 

679 

689 

699 

709 

719 

729 

739 

434 

749 

759 

769 

779 

789 

799 

809 

819 

829 

839 

435 

849 

859 

869 

879 

889 

899 

909 

919 

929 

939 

Q 

436 

949 

959 

969 

979 

988 

998 

*008 

*018 

*028 

*038 

437 

64  048 

058 

068 

078 

088 

098 

108 

118 

J.28 

137 

i 

0.9 

438 

147 

157 

167 

177 

187 

197 

207 

217 

227 

237 

2 

1.8 

439 

246 

256 

266 

276 

286 

296 

306 

316 

326 

335 

3 

A 

2.7 

q 

440 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

* 

5 

A 

0.0 

4.5 

K A 

441 

444 

454 

464 

473 

483 

493 

503 

513 

523 

532 

D 

7 

O.T 

6.3 

442 

542 

; 552 

562 

572 

582 

591 

601 

611 

621 

631 

8 

Q 

7.2 

Q 1 

443 

640 

1 650 

660 

670 

680 

689 

699 

709 

719 

729 

0.1 

444 

738 

, 748 

758 

768 

777 

787 

797 

807 

816 

826 

445 

836 

I 846 

856 

865 

875 

885 

895 

904 

914 

924 

446 

933 

; 943 

953 

963 

972 

982 

992 

*002 

*011 

*021 

447 

65  031 

040 

050 

060 

070 

079 

089 

099 

108 

118 

448 

128 

1 137 

147 

157 

167 

176 

186 

196 

205 

215 

449 

225 

> 234 

244 

254 

263 

273 

283 

292 

302 

312 

450 

321 

. 331 

341 

350 

360 

369 

379 

389 

398 

408 

N. 

L.  0 

1 

2 

3 

4 

5 

6 

t-r 

i 

8 

9 

p.  p. 

LOGARITHMS . 


481 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

450 

451 

452 

453 

454 

455 

456 

457 

458 

459 

460 

461 

462 

463 

464 

465 

466 

467 

468 

469 

470 

471 

472 

473 

474 

475 

476 

477 

478 

479 

480 

481 

482 

483 

484 

485 

486 

487 

488 

489 

490 

491 

492 

493 

494 

495 

496 

497 

498 

499 

500 

35  321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

10 

1 1.0 
2 2.0 

3 3.0 

4 4.0 

5 5.0 

6 6.0 

7 7.0 

8 8.0 

9 9.0 

9 

1 0.9 

2 1.8 

3 2.7 

4 3.6 

5 4.5 

6 5.4 

7 6.3 

8 7.2 

9 8.1 

8 

1 0.8 
2 1.6 

3 2.4 

4 3.2 

5 4.0 

6 4.8 

j 7 5.6 

8 6.4 

9 7.2 

418 
514 
610 
706 
801 
896 
992 
36  087 
181 

427 

523 

619 

715 

811 

906 

*001 

096 

191 

437 

533 

629 

725 

820 

916 

*011 

106 

200 

447 

543 

639 

734 

830 

925 

*020 

115 

210 

456 

552 

648 

744 

839 

935 

*030 

124 

219 

466 

562 

658 

753 

849 

944 

*039 

134 

229 

475 
571 
667 
763 
858 
954 
*049  : 
143 
238 

485 

581 

677 

772 

868 

963 

*058 

153 

247 

495 

591 

686 

782 

877 

973 

*068 

162 

257 

504 

600 

696 

792 

887 

982 

*077 

172 

266 

276 

285 

295 

304 

314 

323 

332 

342 

351 

361 

370 
464 
558 
652 
745 
839 
932 
67  025 
117 

380 

474 

567 

661 

755 

848 

941 

034 

127 

389 

483 

577 

671 

764 

857 

950 

043 

136 

398 

492 

586 

680 

773 

867 

960 

052 

145 

408 

502 

596 

689 

783 

876 

969 

062 

154 

417 

511 

605 

699 

792 

885 

978 

071 

164 

427 

521 

614 

708 

801 

894 

987 

080 

173 

436 

530 

624 

717 

811 

904 

997 

089 

182 

445 

539 

633 

727 

820 

913 

*006 

099 

191 

455 

549 

642 

736 

829 

922 

*015 

108 

201 

210 

219 

228 

237 

247 

256 

265 

274 

284 

293 

302 
394 
486 
578 
669 
761 
852 
943 
68  034 

311 

403 

495 

587 

679 

770 

861 

952 

043 

321 

413 

504 

596 

688 

779 

870 

961 

052 

330 

422 

514 

605 

697 

788 

879 

970 

061 

339 

431 

523 

614 

706 

797 

888 

979 

070 

348 

440 

532 

624 

715 

806 

897 

988 

079 

357 

449 

541 

633 

724 

815 

906 

997 

088 

367 

459 

550 

642 

733 

825 

916 

*006 

097 

376 

468 

560 

651 

742 

834 

925 

*015 

106 

385 

477 

569 

660 

752 

843 

934 

*024 

115 

124 

133 

142 

151 

160 

169 

178 

187 

196 

205 

215 

305 

395 

485 

574 

664 

753 

842 

931 

224 

314 

404 

494 

583 

673 

762 

851 

940 

233 

323 

413 

502 

592 

681 

771 

860 

949 

242 

332 

422 

511 

601 

690 

780 

869 

958 

251 

341 

431 

520 

610 

699 

789 

878 

966 

260 

350 

440 

529 

619 

708 

797 

886 

975 

269 

359 

449 

538 

628 

717 

806 

895 

984 

278 

368 

458 

547 

637 

726 

815 

904 

993 

287 

377 

467 

556 

646 

735 

824 

913 

*002 

296 

386 

476 

565 

655 

744 

833 

922 

*011 

69  020 

028 

037 

046 

055 

064 

073 

082 

090 

099 

108 

197 

285 

373 

461 

548 

636 

722 

81C 

117 
205 
294 
; 381 
469 
l 557 
i 644 
; 732 
1 819 

126 

214 

302 

390 

478 

566 

653 

740 

827 

135 

223 

311 

399 

487 

574 

662 

749 

836 

144 

232 

320 

408 

496 

583 

671 

758 

845 

152 

241 

329 

417 

504 

592 

679 

767 

854 

161 

249 

338 

425 

513 

601 

688 

775 

862 

170 

258 

346 

434 

522 

609 

697 

784 

871 

179 

267 

355 

443 

531 

618 

705 

793 

880 

188 

276 

364 

452 

539 

627 

714 

801 

888 

897 

r 906 

914 

923 

932 

940 

949 

958 

966 

975 

N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

482 


LOGARITHMS. 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

500 

>9  897 

906 

914 

923  1 

932 

940 

949 

958  1 

966 

975 

9 

1 0.9 

2 i 1.8 

3 2.7 

4 3.6 

5 | 4.5 

6 1 5.4 

7 I 6.3 

8 7.2 
9 | 8.1 

8 

1 0.8 
2 1.6 

3 2.4 

4 3.2 

5 4.0 

6 4.8 

7 5.6 

8 6.4 

9 7.2 

7 

| 

1 0.7 

2 1.4 

3 2.1 

4 2.8 

501 

502 

503 

504 

505 

506 

507 

508 

509 

984 
'0  070 
157 
243 
329 
415 
501 
586 
672 

992 

079 

165 

252 

338 

424 

509 

595 

680 

*001 

088 

174 

260 

346 

432 

518 

603 

689 

*010 

096 

183 

269 

355 

441 

526 

612 

697 

*018 

105 

191 

278 

364 

449 

535 

621 

706 

*027  : 
114 
200 
286 
372 
458 
544 
629 
714 

*036  : 
122 
209 
295 
381 
467 
552 
638 
723 

*044  : 
131 
217 
303 
389 
475 
561 
646 
731 

*053  : 
140 
226 
312 
398 
484 
569 
655 
740 

*062 

148 

234 

321 

406 

492 

578 

663 

749 

510 

511 

512 

513 

514 

515 

516 

517 

518 

519 

520 

521 

522 

523 

524 

525 

526 

527 

528 

529 

530 

531 

532 

533 

534 

535 

536 

537 

538 

539 

540 

541 

542 

543 

544 

545 

546 

547 

548 

549 

550 

757 

766 

774 

783 

791 

800 

808 

817 

825 

834 

842 
927 
71  012 
096 
181 
265 
349 
433 
517 

851 

935 

020 

105 

189 

273 

357 

441 

525 

859 

944 

029 

113 

198 

282 

366 

450 

533 

868 

952 

037 

122 

206 

290 

374 

458 

542 

876 

961 

046 

130 

214 

299 

383 

466 

550 

885 

969 

054 

139 

223 

307 

391 

475 

559 

893 

978 

063 

147 

231 

315 

399 

483 

567 

902 

986 

071 

155 

240 

324 

408 

492 

575 

910 

995 

079 

164 

248 

332 

416 

500 

584 

919 

*003 

088 

172 

257 

341 

425 

508 

592 

600 

609 

617 

625 

634 

642 

650 

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539 

546 

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670 

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176 

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211 

219 

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233 

240 

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140 

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209 

216 

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277 

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171 

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198 

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238 

245 

251 

258 

265 

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311 

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485 


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411 

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425 

431 

438 

445 

451 

458 

465 

471 

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653 

491 

498 

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511 

518 

525 

531 

538 

544 

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654 

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564 

571 

578 

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611 

617 

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657 

664 

671 

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656 

690 

697 

704 

710 

717 

723 

730 

737 

743 

750 

657 

757 

763 

770 

776 

783 

790 

796 

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809 

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658 

823 

829 

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862 

869 

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659 

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915 

921 

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961 

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105 

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119 

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151 

158 

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171 

178 

184 

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217 

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282 

289 

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315 

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360 

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549 

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737 

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782 

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814 

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104 

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123 

129 

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142 

149 

155 

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168 

174 

181 

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187 

193 

200 

206 

213 

219 

225 

232 

238 

245 

680 

251 

257 

264 

270 

276 

283 

289 

296 

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308 

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681 

315 

321 

327 

334 

340 

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359 

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378 

385 

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398 

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410 

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423 

429 

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765 

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784 

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822 

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872 

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973 

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105 

111 

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136 

142 

148 

155 

161 

167 

173 

180 

186 

192 

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198 

205 

211 

217 

223 

230 

236 

242 

248 

255 

696 

261 

267 

273 

280 

286 

292 

298 

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311 

317 

697 

323 

330 

336 

342 

348 

354 

361 

367 

373 

379 

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! 386 

392 

398 

404 

410 

417 

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429 

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699 

448 

454 

460 

466 

473 

479 

485 

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497 

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700 

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516 

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528 

535 

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P.  P. 

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704 

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6 

1 1 0.6 

2 I 1.2 

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6 3.6 

7 4.2 

8 4.8 

9 | 5.4 

5 

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572 
634 
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770 

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720 

782 

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107 

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052 

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628 

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120 

126 

132 

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144 

150 

156 

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175 

181 

187 

248 

309 

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254 

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205 

266 

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570 

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211 

272 

333 

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217 

278 

339 

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643 

703 

224 

285 

345 

406 

467 

528 

588 

649 

709 

230 

291 

352 

412 

473 

534 

594 

655 

715 

236 

297 

358 

418 

479 

540 

600 

661 

721 

242 

303 

364 

425 

485 

546 

606 

667 

727 

733 

739 

745 

751 

757 

818 

878 

938 

998 

058 

118 

177 

237 

297 

763 

769 

775 

781 

788 

794 
854 
914 
974 
86  034 
094 
153 
213 
273 

800 

860 

920 

980 

040 

100 

159 

219 

279 

806 

866 

926 

986 

016 

106 

165 

225 

285 

812 

872 

932 

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052 

112 

171 

231 

291 

824 

884 

944 

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064 

124 

183 

243 

303 

830 

890 

950 

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070 

130 

189 

249 

308 

836 

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956 

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076 

136 

195 

255 

314 

842 

902 

962 

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082 

141 

201 

261 

320 

848 

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968 

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088 

147 

207 

267 

326 

332 

338 

344 

350 

356 

362 

368 

374 

380 

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510 

570 

629 

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747 

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864 

398 

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812 

870 

404 

463 

522 

581 

641 

700 

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817 

876 

410 

469 

528 

587 

646 

705 

764 

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415 

475 

534 

593 

652 

711 

770 

829 

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421 

481 

540 

599 

658 

717 

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427 

487 

546 

605 

664 

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841 

900 

433 

493 

552 

611 

670 

729 

788 

847 

906 

439 

499 

558 

617 

676 

735 

794 

853 

911 

445 

504 

564 

623 

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741 

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859 

917 

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958 

964 

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976^ 

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332 
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l 046 
l 105 
r 163 
i 221 
L 280 
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l 454 

994 

052 

111 

169 

227 

286 

344 

402 

460 

999 

058 

116 

175 

233 

291 

349 

408 

466 

*005 

064 

122 

181 

239 

297 

355 

413 

471 

*011 

070 

128 

186 

245 

303 

361 

419 

477 

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075 

134 

192 

251 

309 

367 

425 

483 

*023 

081 

140 

198 

256 

315 

373 

431 

489 

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087 

146 

204 

262 

320 

379 

437 

495 

*035 

093 

151 

210 

268 

326 

384 

442 

500 

50( 

5 512 

518 

523 

529 

535 

541 

547 

552 

558 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMS. 


48  7 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

750 

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512 

518 

523 

529 

535 

541 

547 

552 

558 

751 

564 

570 

576 

581 

587 

593 

599 

604 

610 

616 

752 

622 

628 

633 

639 

645 

651 

656 

662 

668 

674 

753 

679 

685 

691 

697 

703 

708 

714 

720 

726 

731 

754 

737 

743 

749 

754 

760 

766 

772 

777 

783 

789 

755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 

756 

852 

858 

864 

869 

875 

881 

887 

892 

898 

904 

757 

910 

915 

921 

927 

933 

938 

944 

950 

955 

961 

758 

967 

973 

978 

984 

990 

996 

*001 

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759 

88  024 

030 

036 

041 

047 

053 

058 

064 

070 

076 

760 

081 

087 

093 

098 

104 

110 

116 

121 

127 

133 

6 

761 

138 

144 

150 

156 

161 

167 

173 

178 

184 

190 

762 

195 

201 

207- 

213 

218 

224 

230 

235 

241 

247 

1 

2 

0.6 
1 2 

763 

252 

258 

264 

270 

275 

281 

287 

292 

298 

304 

3 

1.8 

764 

309 

315 

321 

326 

332 

338 

343 

349 

355 

360 

4 

2.4 

765 

366 

372 

377 

383 

389 

395 

400 

406 

412 

417 

5 

3.0 

766 

423 

429 

434 

440 

446 

451 

457 

463 

468 

474 

6 

3.6 

767 

480 

485 

491 

497 

502 

508 

513 

519 

525 

530 

7 

g 

4.2 

4.8 

768 

536 

542 

547 

553 

559 

564 

570 

576 

581 

587 

9 

5^4 

769 

593 

598 

604 

610 

615 

621 

627 

632 

638 

643 

770 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 

771 

705 

711 

717 

722 

728 

734 

739 

745 

750 

756 

772 

762 

767 

773 

779 

784 

790 

795 

801 

807 

812 

773 

818 

824 

829 

835 

840 

846 

852 

857 

863 

868 

774 

874 

880 

885 

891 

897 

902 

908 

913 

919 

925 

775 

930 

936 

941 

947 

953 

958 

964 

969 

975 

981 

776 

986 

992 

997 

*003 

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*025 

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777 

89  042 

048 

053 

059 

064 

070 

076 

081 

087 

092 

778 

098 

104 

109 

115 

120 

126 

131 

137 

143 

148 

779 

154 

159 

165 

170 

176 

182 

187 

193 

198 

204 

780 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

5 

781 

265 

271 

276 

282 

287 

293 

298 

304 

310 

315 

1 

0.5 

782 

321 

326 

332 

337 

343 

348 

354 

360 

365 

37  L 

2 

1.0 

783 

376 

382 

387 

393 

398 

404 

409 

415 

421 

426 

3 

1.5 

784 

432 

437 

443 

448 

454 

459 

465 

470 

476 

481 

4 

2.0 

785 

487 

492 

498 

504 

509 

515 

520 

526 

531 

537 

5 

« 

2.5 

3.0 

786 

542 

548 

553 

559 

564 

570 

575 

581 

586 

592 

| D 

7 

3.5 

787 

597 

603 

609 

614 

620 

625 

631 

636 

642 

647 

8 

4.0 

788 

653 

658 

664 

669 

675 

680 

686 

691 

697 

702 

9 

4.5 

789 

708 

713 

719 

724 

730 

735 

741 

746 

752 

757 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

791 

818 

. 823 

829 

834 

840 

845 

851 

856 

862 

867 

792 

873 

878 

883 

889 

894 

900 

905 

911 

916 

922 

793 

927 

933 

938 

944 

949 

955 

960 

966 

971 

977 

794 

982 

: 988 

993 

998 

*004 

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*015 

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*026 

*031 

795 

90  037 

042 

048 

053 

059 

064 

069 

075 

080 

086 

796 

091 

097 

102 

108 

113 

119 

124 

129 

135 

140 

797 

146 

l 151 

157 

162 

168 

173 

179 

184 

189 

195 

798 

; 200 

i 206 

211 

217 

222 

227 

233 

238 

244 

249 

799 

255 

> 260 

266 

271 

276 

282 

287 

293 

298 

304 

800 

30S 

1 314 

320 

325 

331 

336 

342 

347 

352 

358 

N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

488 


LOGARITHMS. 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

800 

90  309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

801 

363 

369 

374 

380 

385 

390 

396 

401 

407 

412 

802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

803 

472 

477 

482 

488 

493 

499 

504 

509 

515 

520 

804 

526 

531 

536 

542 

547 

553 

558 

563 

569 

574 

805 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 

806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

807 

687 

693 

698 

703 

709 

714 

720 

725 

730 

736 

808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 

809 

795 

800 

806 

811 

816 

822 

827 

832 

838 

843 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

6 

811 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 

812 

956 

961 

966 

972 

977 

982 

988 

993 

998 

*004 

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o 

0.6 
1 0 

813 

91  009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

L 

3 

Y.L 

1.8 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

110 

4 

2.4 

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116 

121 

126 

132 

137 

142 

148 

153 

158 

164 

5 

3.0 

816 

169 

174 

180 

185 

190 

196 

201 

206 

212 

217 

6 

3.6 

817 

222 

228 

233 

238 

243 

249 

254 

259 

265 

270 

7 

Q 

4.2 
± a 

818 

275 

281 

286 

291 

297 

302 

307 

312 

318 

323 

O 

9 

5.4 

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328 

334 

339 

344 

350 

355 

360 

365 

371 

376 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

821 

434 

440 

445 

450 

455 

461 

466 

471 

477 

482 

822 

487 

492 

498 

503 

508 

514 

519 

524 

529 

535 

823 

540 

545 

551 

556 

561 

566 

572 

577 

582 

587 

824 

593 

598 

603 

609 

614 

619 

624 

630 

635 

640 

825 

645 

651 

656 

661 

666 

672 

677 

682 

687 

693 

826 

698 

703 

709 

714 

719 

724 

730 

735 

740 

745 

827 

751 

756 

761 

766 

772 

777 

782 

787 

793 

798 

828 

803 

808 

814 

819 

824 

829 

834 

840 

845 

850 

829 

855 

861 

866 

871 

876 

882 

887 

892 

897 

903 

830 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 

5 

831 

960 

965 

971 

976 

981 

986 

991 

997 

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1 

0.5 

832 

92  012 

018 

023 

028 

033 

038 

044 

049 

054 

059 

2 

1.0 

833 

065 

070 

075 

080 

085 

091 

096 

101 

106 

111 

3 

1.5 

834 

117 

122 

127 

132 

137 

143 

148 

153 

158 

163 

4 

2.0 

835 

169 

174 

179 

184 

189 

195 

200 

205 

210 

215 

5 

c 

2.5 
9 n 

836 

221 

226 

231 

236 

241 

247 

252 

257 

262 

267 

D 

7 

o.u 

3.5 

837 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

8 

4.0 

838 

324 

330 

335 

340 

345 

350 

355 

361 

366 

371 

9 

4.5 

839 

376 

381 

387 

392 

397 

402 

407 

412 

418 

423 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 

841 

480 

485 

490 

495 

500 

505 

511 

516 

521 

526 

842 

531 

536 

542 

547 

552 

557. 

562 

567 

572 

578 

843 

583 

588 

593 

598 

603 

609 

614 

619 

624 

629 

844 

634 

639 

645 

650 

655 

660 

665 

670 

675 

681 

845 

586 

; 691 

696 

701 

706 

711 

716 

722 

727 

732 

846 

737 

742 

747 

752 

758 

763 

768 

773 

778 

783 

847 

78£ 

; 793 

799 

804 

809 

814 

819 

824 

829 

834 

848 

84C 

1 845 

850 

855 

860 

865 

870 

875 

881 

886 

849 

891 

. 896 

901 

906 

911 

916 

921 

927 

932 

937 

850 

942 

1 947 

952 

957 

962 

967 

973 

978 

983 

988 

N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

I 

\ P. 

LOGARITHMS. 


483 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

850  1 

851 

852 

853 

854 

855 

856 

857 

858 

859 

860 

861 

862 

863 

864 

865 

866 

867 

868 
869 

870 

871 

872 

873 

874 

875 

876 

877 

878 

879 

880 

881 

882 

883 

884 

885 

886 

887 

888 
889 

890 

891  ‘ 

892 

893 

894 

895 

896 

897 

898 

899 

900 

12  942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

6 

1 0.6 
2 1.2 

3 1.8 

4 2.4 

5 3.0 

6 3.6 

7 4.2 

8 4.8 

9 5.4 

5 

1 0.5 

2 1.0 

3 1.5 

4 2.0 

5 2,5 

6 3.0 

7 3.5 

8 4.0 

9 4.5 

4 

1 0.4 

2 0.8 

3 1.2 

4 1.6 

5 2.0 

6 2.4 

7 2.8 

8 3.2 

9 3.6 

993 
33  044 
095 
146 
197 
247 
298 
349 
399 

998 

049 

100 

151 

202 

252 

303 

354 

404 

*003 

054 

105 

156 

207 

258 

308 

359 

409 

*008 

059 

110 

161 

212 

263 

313 

364 

414 

*013 

064 

115 

166 

217 

268 

318 

369 

420 

*018  : 
069 
120 
171 
222 
273 
323 
374 
425 

*024  : 
075 
125 
176 
227 
278 
328 
379 
430 

*029  : 
080 
131 
181 
232 
283 
334 
384 
435 

*034  : 
085 
136 
186 
237 
288 
339 
389 
440 

*039 

090 

141 

192 

242 

293 

344 

394 

445 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

500 

551 

601 

651 

702 

752 

802 

852 

902 

505 

556 

606 

656 

707 

757 

807 

857 

907 

510 

561 

611 

661 

712 

762 

812 

862 

912 

515 

566 

616 

666 

717 

767 

817 

867 

917 

520 

571 

621 

671 

722 

772 

822 

872 

922 

526 

576 

626 

676 

727 

777 

827 

877 

927 

531 

581 

631 

682 

732 

782 

832 

882 

932 

536 

586 

636 

687 

737 

787 

837 

887 

937 

541 

591 

641 

692 

742 

792 

842 

892 

942 

546 

596 

646 

697 

747 

797 

847 

897 

947 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

94  002 
052 
101 
151 
201 
250 
300 
349 
399 

007 

057 

106 

156 

206 

255 

305 

354 

404 

012 

062 

111 

161 

211 

260 

310 

359 

409 

017 

067 

116 

166 

216 

265 

315 

364 

414 

022 

072 

121 

171 

221 

270 

320 

369 

419 

027 

077 

126 

176 

226 

275 

325 

374 

424 

032 

082 

131 

181 

231 

280 

330 

379 

429 

037 

086 

136 

186 

236 

285 

335 

384 

433 

042 

091 

141 

191 

240 

290 

340 

389 

438 

047 

096 

146 

196 

245 

295 

345 

394 

443 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

498 

547 

596 

645 

694 

743 

792 

841 

890 

503 

552 

601 

650 

699 

748 

797 

846 

895 

507 

557 

606 

655 

704 

753 

802 

851 

900 

512 

562 

611 

660 

709 

758 

807 

856 

905 

517 

567 

616 

665 

714 

763 

812 

861 

910 

522 

571 

621 

670 

719 

768 

817 

866 

915 

527 

576 

626 

675 

724 

773 

822 

871 

919 

532 

581 

630 

680 

729 

778 

827 

876 

924 

537 

586 

635 

685 

734 

783 

832 

880 

929 

542 

591 

640 

689 

738 

787 

836 

885 

934 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

988 
95  036 
085 
134 
182 
231 
279 
328 
37€ 

993 
041 
090 
139 
i 187 
236 
' 284 
1 332 
i 381 

998 

046 

095 

143 

192 

240 

289 

337 

386 

*002 

051 

100 

148 

197 

245 

294 

342 

390 

*007 

056 

105 

153 

202 

-250 

299 

347 

395 

*012 

061 

109 

158 

207 

255 

303 

352 

400 

*017 

066 

114 

163 

211 

260 

308 

357 

405 

*022 

071 

119 

168 

216 

265 

313 

361 

410 

*027 

075 

124 

173 

221 

270 

318 

366 

415 

*032 

080 

129 

177 

226 

274 

323 

371 

419 

424 

t 429 

434 

439 

444 

448 

453 

458 

463 

468 

N.  * 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

490 


LOGARITHMS . 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

soo 

901 

902 

903 

904 

905 

906 

907 

908 

909 

910 

911 

912 

913 

914 

915 

916 

917 

918 

919 

920 

921 

922 

923 

924 

925 

926 

927 

928 

929 

930 

931 

932 

933 

934 

935 

936 

937 

938 

939 

940 

941 

942 

943 

944 

945 

946 

947 

948 

949 

950 

& 424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

5 

1 0.5 

2 1.0 

3 1.5 

4 2.0 

5 2.5 

6 3.0 

7 3.5 

8 4.0 

9 4.5 

4 

1 0.4 

2 0.8 

3 1.2 

4 1.6 

5 2.0 

6 2.4 

7 2.8 

8 3.2  | 

9 3.6 

472 

521 

569 

617 

665 

713 

761 

809 

856 

477 

525 

574 

622 

670 

718 

766 

813 

861 

482 

530 

578 

626 

674 

722 

770 

818 

866 

487 

535 

583 

631 

679 

727 

775 

823 

871 

492 

540 

588 

636 

684 

732 

780 

828 

875 

497 

545 

593 

641 

689 

737 

785 

832 

880 

501 

550 

598 

646 

694 

742 

789 

837 

885 

506 

554 

602 

650 

698 

746 

794 

842 

890 

511 

559 

607 

655 

703 

751 

799 

847 

895 

516 

564 

612 

660 

708 

756 

804 

852 

899 

904 

909 

914 

918 

923 

928 

933 

938 

942 

947 

952 
999 
96  047 
095 
142 
190 
237 
284 
332 

957 

*004 

052 

099 

147 

194 

242 

289 

336 

961 

*009 

057 

104 

152 

199 

246 

294 

341 

966 

*014 

061 

109 

156 

204 

251 

298 

346 

971 

*019 

066 

114 

161 

209 

256 

303 

350 

976 

*023 

071 

118 

166 

213 

261 

308 

355 

980 

*028 

076 

123 

171 

218 

265 

313 

360 

985 

*033 

080 

128 

175 

223 

270 

317 

365 

990 

*038 

085 

133 

180 

227 

275 

322 

369 

995 

*042 

090 

137 

185 

232 

280 

327 

374 

379 

384 

388 

393 

398 

402 

407 

412 

417 

421 

426 

473 

520 

567 

614 

661 

708 

755 

802 

431 

478 

525 

572 

619 

666 

713 

759 

806 

435 

483 

530 

577 

624 

670 

717 

764 

811 

440 

487 

534 

581 

628 

675 

722 

769 

.816 

445 

492 

539 

586 

633 

680 

727 

774 

820 

450 

497 

544 

591 

638 

685 

731 

778 

825 

454 

501 

548 

595 

642 

689 

736 

783 

830 

459 

506 

553 

600 

647 

694 

741 

788 

834 

464 

511 

558 

605 

652 

699 

745 

792 

839 

468 

515 

562 

609 

656 

703 

750 

797 

844 

848 

853 

858 

862 

867 

872 

876 

881 

886 

890 

895 
942 
988 
97  035 
081 
128 
174 
220 
267 

900 

946 

993 

039 

086 

132 

179 

225 

271 

904 

951 

997 

044 

090 

137 

183 

230 

276 

909 

956 

*002 

049 

095 

142 

188 

234 

280 

914 

960 

*007 

053 

100 

146 

192 

239 

285 

918 

965 

*011 

058 

104 

151 

197 

243 

290 

923 

970 

*016 

063 

109 

155 

202 

248 

294 

928 

974 

*021 

067 

114 

160 

206 

253 

299 

932 

979 

*025 

072 

118 

165 

211 

257 

304 

937 

984 

*030 

077 

123 

169 

216 

262 

308 

313 

317 

322 

327 

331 

336 

340 

345 

350 

354 

359 
405 
451 
I 497 
543 
589 
635 
681 
727 

364 
410 
456 
502 
, 548 
i 594 
> 640 
685 
' 731 

368 

414 

460 

506 

552 

598 

644 

690 

736 

373 

419 

465 

511 

557 

603 

649 

695 

740 

377 

424 

470 

516 

562 

607 

653 

699 

745 

382 

428 

474 

520 

566 

612 

658 

704 

749 

387 

433 

479 

525 

571 

617 

663 

708 

754 

391 

437 

483 

529 

575 

621 

667 

713 

759 

396 

442 

488 

534 

580 

626 

672 

717 

763 

400 

447 

493 

539 

585 

630 

676 

722 

768 

772 

\ 777 

782 

786 

791 

795 

800 

804 

809 

813 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS 


491 


1 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

950 

Y7  772 ' 

777 

782 

786 

791 

795 

800 

804 

809 

813 

5 

1 0.5 

2 1.0 

3 1.5 

4 2.0 

5 2.5 

6 3.0 

7 3.5 

8 4.0 

9 4.5 

4 

1 0.4 

2 0.8 

3 1.2 

4 1.6 

5 2.0 

6 2.4 

7 2.8 

8 3.2 

9 3.6 

951 

952 

953 

954 

955 

956 

957 

958 

959 

960 

961 

962 

963 

964 

965 

966 

967 

968 

969 

970 

971 

972 

973 

974 

975 

976 

977 
978. 
979 

980 

981 

982 

983 

984 

985 

986 

987 

988 

989 

990 

991 

992 

993 

994 

995 

996 

997 

998 

999 

I00C 

818 
864 
909 
955 
)8  000 
046 
091 
137 
182 

823 

868 

914 

959 

005 

050 

096 

141 

186 

827 

873 

918 

964 

009 

055 

100 

146 

191 

832 

877 

923 

968 

014 

059 

105 

150 

195 

836 

882 

928 

973 

019 

064 

109 

155 

200 

841 

886 

932 

978 

023 

068 

114 

159 

204 

845 

891 

937 

982 

028 

073 

118 

164' 

209 

850 

896 

941 

987 

032 

078 

123 

168 

214 

855 

900 

946 

991 

037 

082 

127 

173 

218 

859 

905 

950 

996 

041 

087 

132 

177 

223 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

272 

318 

363 

408 

453 

498 

543 

588 

632 

277 

322 

367 

412 

457 

502 

547 

592 

637 

281 

327 

372 

417 

462 

507 

552 

597 

641 

286 

331 

376 

421 

466 

511 

556 

601 

646 

290 

336 

381 

426 

471 

516 

561 

605 

650 

295 

340 

385 

430 

475 

520 

565 

610 

655 

299 

345 

390 

435 

480 

525 

570 

614 

659 

304 

349 

394 

439 

484 

529 

574 

619 

664 

308 

354 

399 

444 

489 

534 

579 

623 

668 

313 

358 

403 

448 

493 

538 

583 

628 

673 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

722 
767 
811 
856 
900 
945 
989 
99  034 
078 

726 

771 

816 

860 

905 

949 

994 

038 

083 

731 

776 

820 

865 

909 

954 

998 

043 

087 

735 

780 

825 

869 

914 

958 

*003 

047 

092 

740 

784 

829 

874 

918 

963 

*007 

052 

096 

744 

789 

834 

878 

923 

967 

*012 

056 

100 

749 

793 

838 

883 

927 

972 

*016 

061 

105 

753 

798 

843 

887 

932 

976 

*021 

065 

109 

758 

802 

847 

892 

936 

981 

*025 

069 

114 

762 

807 

851 

896 

941 

985 

*029 

074 

118 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

167 

211 

255 

300 

344 

388 

432 

476 

52C 

171 
216 
260 
304 
348 
i 392 
! 436 
i 480 
1 524 

176 

220 

264 

308 

352 

396 

441 

484 

528 

180 

224 

269 

313 

357 

401 

445 

489 

533 

185 

229 

273 

317 

361 

405 

449 

493 

537 

189 

233 

277 

322 

366 

410 

454 

498 

542 

193 

238 

282 

326 

370 

414 

458 

502 

546 

198 

242 

286 

330 

374 

4ia 

463 

506 

550 

202 

247 

291 

335 

379 

423 

467 

511 

555 

207 

251 

295 

339 

383 

427 

471 

515 

559 

56 4 

t 568 

572 

577 

581 

585 

590 

594 

599 

603 

607 
651 
69 1 
73< 
782 
'82( 
87( 
91; 
95' 

? 612 
[ 656 
> 699 
) 743 
1 787 
3 830 
) 874 
3 917 
7 961 

616 

660 

704 

747 

791 

835 

878 

922 

965 

621 

664 

708 

752 

795 

839 

883 

926 

970 

625 

669 

712 

756 

800 

843 

887 

930 

974 

629 

673 

717 

760 

804 

848 

891 

935 

978 

634 

677 

721 

765 

808 

852 

896 

939 

983 

638 

682 

726 

769 

813 

856 

900 

944 

987 

642 

686 

730 

774 

817 

861 

904 

948 

991 

647 

691 

734 

778 

822 

865 

909 

952 

996 

| 00  001 

1 004 

009 

013 

017 

022 

026 

030 

035 

039 

N. 

L.O 

1 1 

2 

3 

I4 

5 

6 

7 

8 

9 

P.  P. 

492 


LOGAixsm^  nv  TRIGONOMETRIC  FUNCTIONS. 


0° 


// 

~ o 
60 
120 
180 
240 

/ 

L.  Sin.  1 d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang.j  d.  c. 

. L.  Cotg. 

L.  Cos. 

0 

1 

2 

3 

4 

6.46373 

6.76476 

6.94085 

7.06579 

30103 

17609 

12494 

9691 

7918 

6694 

5800 

5115 

4576 

4139 

3779 

3476 

3218 

2997 

2802 

2633 

2483 

2348 

2227 

2119 

2021 

1930 

1848 

1773 

1704 

1639 

1579 

1524 

1472 

1424 

1379 

1336 

1297 

1259 

1223 

1190 

1158 

1128 

1100 

1072 

1046 

1022 

999 

976 

954 

934 

914 

896 

877 

860 

843 

827 

812 

797 

782 

769 

755 

743 

730 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

6.46373 

6.76476 

6.94085 

7.06579 

30103 

17609 

12494 

9691 

7918 

6694 

5800 

5115 

4576 

4139 

3779 

3476 

3219 

2996 

2803 

2633 

2482 

2348 

2228 

2119 

2020 

1931 

1848 

1773 

1704 

1639 

1579 

1524 

1473 

1424 

1379 

1336 

1297 

1259 

1223 

1190 

1159 

1128 

1100 

1072 

1047 

1022 

998 

976 

955 

934 

915 

895 

878 

860 

843 

828 

812 

797 

782 

769 

756 

742 

730 

3.53627 

3.23524 

3.05915 

2.93421 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

60 

59 

58 

57 

56 

300 

360 

420 

480 

540 

5 

6 

7 

8 
9 

7.16270 

7.24188 

7.30882 

7.36682 

7.41797 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.16270 

7.24188 

7.30882 

7.36682 

7.41797 

2.83730 

2.75812 

2.69118 

2.63318 

2.58203 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

55 

54 

53 

52 

51 

600 

660 

720 

780 

840 

10 

11 

12 

13 

14 

7.46373 

7.50512 

7.54291 

7.57767 

7.60985 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.46373 

7.50512 

7.54291 

7.57767 

7.60986 

2.53627 

2.49488 

2.45709 

2.42233 

2.39014 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

50 

49 

48 

47 

46 

900 

960 

1020 

1080 

1140 

15 

16 

17 

18 
19 

7.63982 

7.66784 

7.69417 

7.71900 

7.74248 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.63982 

7.66785 

7.69418 

7.71900 

7.74248 

2.36018 

2.33215 

2.30582 

2.28100 

2.25752 

0.00000 

0.00000 

9.99999 

9.99999 

9.99999 

45 

44 

43 

42 

41 

1200 

1260 

1320 

1380 

1440 

20 

21 

22 

23 

24 

7.76475 

7.78594 

7.80615 

7.82545 

7.84393 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.76476 

7.78595 

7.80615 

7.82546 

7.84394 

2.23524 

2.21405 

2.19385 

2.17454 

2.15606 

9.99999 

9.99999 

9.99999 

9.99999 

9.99999 

40 

39 

38 

37 

36 

1500 

1560 

1620 

1680 

1740 

25 

26 

27 

28 
29 

7.86166 

7.87870 

7.89509 

7.91088 

7.92612 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31441 

7.86167 

7.87871 

7.89510 

7.91089 

7.92613 

2.13833 

2.12129 

2.10490 

2.08911 

2.07387 

9.99999 

9.99999 

9.99999 

9.99999 

9.99998 

35 

34 

33 

32 

31 

1800 

1860 

1920 

1980 

2040 

30 

31 

32 

33 

34 

7.94084 

7.95508 

7.96887 

7.98223 

7.99520 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31441 

5.31441 

5.31441 

5.31441 

5.31441 

7.94086 

7.95510 

7.96889 

7.98225 

7.99522 

2.05914 

2.04490 

2.03111 

2.01775 

2.00478 

9.99998 

9.99998 

9.99998 

9.99998 

9.99998 

30 

29 

28 

27 

26 

2100 

2160 

2220 

2280 

2340 

35 

36 

37 

38 

39 

8.00779 

8.02002 

8.03192 

8.04350 

8.05478 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31441 

5.31441 

5.31441 

5.31441 

5.31441 

8.00781 

8.02004 

8.03194 

8.04353 

8.05481 

1.99219 

1.97996 

1.96806 

1.95647 

1.94519 

9.99998 

9.99998 

9.99997 

9.99997 

9.99997 

25 

24 

23 

22 

21 

2400 

2460 

2520 

2580 

2640 

40 

41 

42 

43 

44 

8.06578 

8.07650 

8.08696 

8.09718 

8.10717 

5.31443 

5.31444 
5.31444 
5.31444 
5.31444 

5.31441 

5.31440 

5.31440 

5.31440 

5.31440 

8.06581 

8.07653 

8.08700 

8.09722 

8.10720 

1.93419 

1.92347 

1.91300 

1.90278 

1.89280 

9.99997 

9.99997 

9.99997 

9.99997 

9.99996 

20 

19 

18 

17 

16 

2700 

2760 

2820 

2880 

2940 

45 

46 

47 

48 

49 

8.11693 

8.12647 

8.13581 

8.14495 

8.15391 

5.31444 

5.31444 

5.31444 

5.31444 

5.31444 

5.31440 

5.31440 

5.31440 

5.31440 

5.31440 

8.11696 

8.12651 

8.13585 

8.14500 

8.15395 

1.88304 

1.87349 

1.86415 

1.85500 

1.84605 

9.99996 

9.99996 

9.99996 

9.99996 

9.99996 

15 

14 

13 

12 

11 

3000 

3060 

3120 

3180 

3240 

50 

51 

52 

53 

54 

8.16268 

8.17128 

8.17971 

8.18798 

8.19610 

5.31444 

5.31444 

5.31444 

5.31444 

5.31444 

5.31439 

5.31439 

5.31439 

5.31439 

5.31439 

8.16273 

8.17133 

8.17976 

8.18804 

8.19616 

1.83727 

1.82867 

1.82024 

1.81196 

1.80384 

9.99995 

9.99995 

9.99995 

9.99995 

9.99995 

10 

9 

8 

7 

6 

3300 

3360 

3420 

3480 

3540 

55 

56 

57 

58 

59 

8.20407 

8.21189 

8.21958 

8.22713 

8.23456 

5.31444 

5.31444 

5.31445 
5.31445 
5.31445 

5.31439 

5.31439 

5.31439 

5.31438 

5.31438 

8.20413 

8.21195 

8.21964 

8.22720 

8.23462 

1.79587 

1.78805 

1.78036 

1.77280 

1.76538 

9.99994 

9.99994 

9.99994 

9.99994 

9.99994 

5 

4 

3 

2 

1 

3600 

60 

8.24186 

5.31445 

5.31438 

8.24192 

1.75808 

9.99993 

0 

L.  Cos.  1 d. 

L.  Cotg. 

d.  c. 

L.  Tang. 

L.  Sin. 

/ 

89° 


493 


LOGARITHMS  OF  TRIGONOMETRIC  FTT 


1v 


n 

/ 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T.  I 

j.  Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

3600 

3660 

3720 

3780 

3840 

0 

1 

2 

3 

4 

8.24186 

8.24903 

8.25609 

8.26304 

8.26988 

717 

706 

695 

684 

5.31445 

5.31445 

5.31445 

5.31445 

5.31445 

5.31438 

5.31438 

5.31438 

5.31438 

5.31437 

8.24192 

8.24910 

8.25616 

8.26312 

8.26996 

718 
706 
696 
684 
673  - 

1.75808  ' 

1.75090 

1.74384 

1.73688 

1.73004 

9.99993 

9.99993 

9.99993 

9.99993 

9.99992 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

3900 

3960 

4020 

4080 

4140 

5 

6 

7 

8 
9 

8.27661 

8.28324 

8.28977 

8.29621 

8.30255 

673 

663 

653 

644 

634 

624 

616 

608 

599 

590 

583 

575 

568 

560 

553 

547 

539 

533 

526 

520 

514 

508 

502 

496 

491 

485 

480 

474 

470 

464 

459 

455 

450 

445 

441 

436 

433 

427 

424 

419 

5.31445 

5.31445 

5.31445 

5.31445 

5.31445 

5.31437 

5.31437 

5.31437 

5.31437 

5.31437 

8.27669 

8.28332 

8.28986 

8.29629 

8.30263 

663 
654 
643 
634 
625  - 

1.72331 

1.71668 

1.71014 

1.70371 

1.69737 

9.99992 

9.99992 

9.99992 

9.99992 

9.99991 

4200 

4260 

4320 

4380 

4440 

10 

11 

12 

13 

14 

8.30879 

8,31495 

8.32103 

8.32702 

8.33292 

5.31446 

5.31446 

5.31446 

5.31446 

5.31446 

5.31437 

5.31436 

5.31436 

5.31436 

5.31436 

8.30888 

8.31505 

8.32112 

8.32711 

8.33302 

617 
607 
599 
591 
584  - 

1.69112 

1.68495 

1.67888 

1.67289 

1.66698 

9.99991 

9.99991 

9.99990 

9.99990 

9.99990 

50 

49 

48 

47 

46 

4500 

4560 

4620 

4680 

4740 

15 

16 

17 

18 
19 

8.33875 

8.34450 

8.35018 

8.35578 

8.36131 

5.31446 
5.31446 
5 31446 
5.31446 
5.31446 

5.31436 

5.31435 

5.31435 

5.31435 

5.31435 

8.33886 

8.34461 

8.35029 

8.35590 

8.36143 

575 

568 

561 

553 

546 

1.66114 

1.65539 

1.64971 

1.64410 

1.63857 

9.99990 

9.99989 

9.99989 

9.99989 

9.99989 

45 

44 

43 

42 

41 

4800 

4860 

4920 

4980 

5040 

20 

21 

22 

23 

24 

8.36678 

8.37217 

8.37750 

8.38276 

8.38796 

5.31446 

5.31447 
5.31447 
5.31447 
5.31447 

5.31435 

5.31434 

5.31434 

5.31434 

5.31434 

8.36689 

8.37229 

8.37762 

8.38289 

8.38809 

540 

533 

527 

520 

514 

1.63311 

1.62771 

1.62238 

1.61711 

1.61191 

9.99988 

9.99988 

9.99988 

9.99987 

9.99987 

40 

39 

38 

37 

36 

5100 

5160 

5220 

5280 

5340 

25 

26 

27 

28 
29 

8.39310 

8.39818 

8.40320 

8.40816 

8.41307 

5.31447 

5.31447 

5.31447 

5.31447 

5.31447 

5.31434 

5.31433 

5.31433 

5.31433 

5.31433 

8.39323 

8.39832 

8.40334 

8.40830 

8.41321 

509 

502 

496 

491 

486 

1.60677 

1.60168 

1.59666 

1.59170 

1.58679 

9.99987 

9.99986 

9.99986 

9.99986 

9.99985 

35 

34 

33 

32 

31 

5400 

5460 

5520 

5580 

5640 

30 

31 

32 

33 

34 

8.41792 

8.42272 

8.42746 

8.43216 

8.43680 

5.31447 

5.31448 
5.31448 
5.31448 
5.31448 

5.31433 

5.31432 

5.31432 

5.31432 

5.31432 

8.41807 

8.42287 

8.42762 

8.43232 

8.43696 

480 

475 

470 

464 

460 

1.58193 

1.57713 

1.57238 

1.56768 

1.56304 

9.99985 

9.99985 

9.99984 

9.99984 

9.99984 

30 

29 

28 

27 

26 

5700 

5760 

5820 

5880 

5940 

35 

36 

37 

38 

39 

8.44139 

8.44594 

8.45044 

8.45489 

8.45930 

5.31448 

5.31448 

5.31448 

5.31448 

5.31449 

5.31431 

5.31431 

5.31431 

5.31431 

5.31431 

8.44156 

8.44611 

8.45061 

8.45507 

8.45948 

455 

450 

446 

441 

437 

1.55844 

1.55389 

1.54939 

1.54493 

1.54052 

9.99983 

9.99983 

9.99983 

9.99982 

9.99982 

25 

24 

23  ‘ 
22 
21 

6000 

6060 

6120 

6180 

6240 

40 

41 

42 

43 

44 

8.46366 

8.46799 

8.47226 

8.47650 

8.48069 

5.31449 

5.31449 

5.31449 

5.31449 

5.31449 

5.31430 

5.31430 

5.31430 

5.31430 

5.31429 

8.46385 

8.46817 

8.47245 

8.47669 

8.48089 

432 
428 
424 
420 
• 416 
412 
408 
404 
401 
- 397 
393 
390 
386 
383 
380 

1.53615 

1.53183 

1.52755 

1.52331 

1.51911 

9.99982 

9.99981 

9.99981 

9.99981 

9.99980 

20 

19 

18 

17 

16 

6300 

6360 

6420 

6480 

6540 

45 

46 

47 

48 

49 

8.48485 

8.48896 

8.49304 

8.49708 

8.50108 

416 

411 

408 

404 

400 

5.31449 

5.31449 

5.31450 
5.31450 
5.31450 

5.31429 

5.31429 

5.31428 

5.31428 

5.31428 

8.48505 

8.48917 

8.49325 

8.49729 

8.50130 

1.51495 

1.51083 

1.50675 

1.50271 

1.49870 

9.99980 

9.99979 

9.99979 

9.99979 

9.99978 

15 

14 

13 

12 

11 

6600 

6660 

6720 

6780 

6840 

50 

51 

52 

53 

54 

8.50504 

8.50897 

8.51287 

8.51673 

8.52055 

- 396 
393 
390 
386 
382 

5.31450 

5.31450 

5.31450 

5.31450 

5.31450 

5.31428 

5.31427 

5.31427 

5.31427 

5.31427 

8.50527 
8.50920 
8.51310 
8.51696 
: 8.52079 

1.49473 

1.49080 

1.48690 

1.48304 

1.47921 

9.99978 

9.99977 

9.99977 

9.99977 

9.99976 

10 

9 

8 

7 

6 

6900 

6960 

7020 

7080 

7140 

55 

56 

57 

58 

59 

8.52434 

8.52810 

8.53183 

8.53552 

8.53919 

- 379 
376 
373 
i 369 
i 367 

5.31451 

5.31451 

5.31451 

5.31451 

5.31451 

5.31426 

5.31426 

5.31426 

5.31425 

5.31425 

8.52459 
8.52835 
8.53208 
■ 8.53578 
i 8.53945 

376 

373 

370 

367 

363 

1.47541 

1.47165 

1.46792 

1.46422 

1.46055 

9.99976 

9.99975 

9.99975 

9.99974 

9.99974 

5 

4 

3 

2' 

1 

7200 

60 

8.54282 

- 363 

5.31451 

5.31425 

> 8.54308 

1.45692 

9.99974 

0 

L.  Cos 

. d. 

L.  Cots 

% d.c.lL.  Tans 

L.  Sin. 

88° 


4»4 


mn  A T! ITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


e" 


u 

t 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

7200 

7260 

7320 

7380 

7440 

0 

1 

2 

3 

4 

8.54282 

8.54642 

8.54999 

8.55354 

8.55705 

360 

357 

355 

351 

349 

346 

343 

341 

337 

336 

332 

330 

328 

325 

323 

320 

318 

316 

313 

311 

309 

307 

305 

302 

301 

298 

296 

294 

293 

290 

288 

287 

284 

283 

281 

279 

277 

276 

274 

272 

270 

269 

267 

266 

263 

263 

260 

259 

258 

256 

254 

253 

252 

250 

249 

247 

246 

244 

243 

242 

5.31451 

5.31451 

5.31452 
5.31452 
5.31452 

5.31425 

5.31425 

5.31424 

5.31424 

5.31424 

8.54308 

8.54669 

8.55027 

8.55382 

8.55734 

361 

358 

355 

352 

349 

346 

344 

341 

338 

336 

333 

330 

328 

326 

323 

321 

319 

316 

314 

311 

310 

307 

305 

303 

301 

299 

297 

295 

292 

291 

289 

287 

285 

284 

281 

280 

278 

276 

274 

273 

271 

269 

268 

266 

264 

263 

261 

260 

258 

257 

255 

254 

252 

251 

249 

248 

246 

245 

244 

243 

1.45692 

1.45331 

1.44973 

1.44618 

1.44266 

9.99974 

9.99973 

9.99973 

9.99972 

9.99972 

60 

59 

58 

57 

56 

7500 

7560 

7620 

7680 

7740 

5 

6 

7 

8 
9 

8.56054 

8.56400 

8.56743 

8.57084 

8.57421 

5.31452 

5.31452 

5.31452 

5.31453 
5.31453 

5.31423 

5.31423 

5.31423 

5.31422 

5.31422 

8.56083 

8.56429 

8.56773 

8.57114 

8.57452 

1.43917 

1.43571 

1.43227 

1.42886 

1.42548 

9.99971 

9.99971 

9.99970 

9.99970 

9.99969 

55 

54 

53 

52 

51 

7800 

7860 

7920 

7980 

8040 

10 

11 

12 

13 

14 

8.57757 

8.58089 

8.58419 

8.58747 

8.59072 

5.31453 

5.31453 

5.31453 

5.31453 

5.31454 

5.31422 

5.31421 

5.31421 

5.31421 

5.31421 

8.57788 

8.58121 

8.58451 

8.58779 

8.59105 

1.42212 

1.41879 

1.41549 

1.41221 

1.40895 

9.99969 

9.99968 

9.99968 

9.99967 

9.99967 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

8100 

8160 

8220 

8280 

8340 

15 

16 

17 

18 
19 

8.59395 

8.59715 

8.60033 

8.60349 

8.60662 

5.31454 

5.31454 

5.31454 

5.31454 

5.31454 

5.31420 

5.31420 

5.31420 

5.31419 

5.31419 

8.59428 

8.59749 

8.60068 

8.60384 

8.60698 

1.40572 

1.40251 

1.39932 

1.39616 

1.39302 

9.99967 

9.99966 

9.99966 

9.99965 

9.99964 

8400 

8460 

8520 

8580 

8640 

20 

21 

22 

23 

24 

8.60973 

8.61282 

8.61589 

8.61894 

8.62196 

5.31455 

5.31455 

5.31455 

5.31455 

5.31455 

5.31418 

5.31418 

5.31418 

5.31417 

5.31417 

8.61009 

8.61319 

8.61626 

8.61931 

8.62234 

1.38991 

1.38681 

1.38374 

1.38069 

1.37766 

9.99964 

9.99963 

9.99963 

9.99962 

9.99962 

40 

39 

38 

37 

36 

8700 

8760 

8820 

8880 

8940 

25 

26 

27 

28 
29 

8.62497 

8.62795 

8.63091 

8.63385 

8.63678 

5.31455 

5.31456 
5.31456 
5.31456 
5.31456 

5.31417 

5.31416 

5.31416 

5.31416 

5.31415 

8.62535 

8.62834 

8.63131 

8.63426 

8.63718 

1.37465 

1.37166 

1.36869 

1.36574 

1.36282 

9.99961 

9.99961 

9.99960 

9.99960 

9.99959 

35 

34 

33 

32 

31 

9000 

9060 

9120 

9180 

9240 

30 

31 

32 

33 

34 

8.63968 

8.64256 

8.64543 

8.64827 

8.65110 

5.31456 

5.31456 

5.31457 
5.31457 
5.31457 

5.31415 

5.31415 

5.31414 

5.31414 

5.31413 

8.64009 

8.64298 

8.64585 

8.64870 

8.65154 

1.35991 

1.35702 

1.35415 

1.35130 

1.34846 

9.99959 

9.99958 

9.99958 

9.99957 

9.99956 

30 

29 

28 

27 

26 

9300 

9360 

9420 

9480 

9540 

35 

36 

37 

38 

39 

8.65391 

8.65670 

8.65947 

8.66223 

8.66497 

5.31457 

5.31457 

5.31458 
5.31458 
5.31458 

5.31413 

5.31413 

5.31412 

5.31412 

5.31412 

8.65435 

8.65715 

8.65993 

8.66269 

8.66543 

1.34565 

1.34285 

1.34007 

1.33731 

1.33457 

9.99956 

9.99955 

9.99955 

9.99954 

9.99954 

25 

24 

23 

22 

21 

9600 

9660 

9720 

9780 

9840 

40 

41 

42 

43 

44 

8.66769 

8.67039 

8.67308 

8.67575 

8.67841 

5.31458 

5.31458 

5.31459 
5.31459 
5.31459 

5.31411 

5.31411 

5.31410 

5.31410 

5.31410 

8.66816 

8.67087 

8.67356 

8.67624 

8.67890 

1.33184 

1.32913 

1.32644 

1.32376 

1.32110 

9.99953 

9.99952 

9.99952 

9.99951 

9.99951 

20 

19 

18 

17 

16 

9900 

9960 

10020 

10080 

10140 

45 

46 

47 

48 

49 

8.68104 

8.68367 

8.68627 

8.68886 

8.69144 

5.31459 

5.31459 

5.31460 
5.31460 
5.31460 

5.31409 

5.31409 

5.31408 

5.31408 

5.31408 

8.68154 

8.68417 

8.68678 

8.68938 

8.69196 

1.31846 

1.31583 

1.31322 

1.31062 

1.30804 

9.99950 

9.99949 

9.99949 

9.99948 

9.99948 

15 

14 

13 

12 

11 

10200 

10260 

10320 

10380 

10440 

50 

51 

52 

53 

54 

8.69400 

8.69654 

8.69907 

8.70159 

8.70409 

5.31460 

5.31460 

5.31461 
5.31461 
5.31461 

5.31407 

5.31407 

5.31406 

5.31406 

5.31405 

8.69453 

8.69708 

8.69962 

8.70214 

8.70465 

1.30547 

1.30292 

1.30038 

1.29786 

1.29535 

9.99947 

9.99946 

9.99946 

9.99945 

9.99944 

10 

9 

8 

7 

6 

10500 
10560  . 
10620 
10680 
10740 

55 

56 

57 

58 

59 

8.70658 

8.70905 

8.71151 

8.71395 

8.71638 

5.31461 

5.31461 

5.31462 
5.31462 
5.31462 

5.31405 

5.31405 

5.31404 

5.31404 

5.31403 

8.70714 

8.70962 

8.71208 

8.71453 

8.71697 

1.29286 

1.29038 

1.28792 

1.28547 

1.28303 

9.99944 

9.99943 

9.99942 

9.99942 

9.99941 

5 

4 

3 

2 

1 

10800 

60 

8.71880 

5.31462 

5.31403 

8.71940 

1.28060 

9.99940 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.  Tang. 

L.  Sin. 

/ 

87° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


495 


' ] 

L.  Sin.  ( 

0 1 

3.71880  0 

1 * 

3.72120  l 

2 1 

3.72359  i 

3 1 

3.72597  i 

4 

3.72834  % 

5 ! 

8.73069  0 

6 : 

8.73303  i 

7 

8.73535  i 

8 

8.73767  i 

9 

8.73997  % 

10 

8.74226 

11 

8.74454  i 

12 

8.74680  i 

13 

8.74906  f 

14 

8.75130  i 

15 

8.75353  J 

16 

8.75575  i 

17 

8.75795  i 

18 

8.76015  i 

19 

8.76234  ; 

20 

8.76451  ; 

21 

8.76667  ; 

22 

8.76883  ; 

23 

8.77097  ; 

24 

8.77310  ; 

25 

8.77522  ; 

26 

8.77733 

27 

8.77943 

28 

8.78152 

29 

8.78360 

30 

8.78568 

31 

8.78774 

32 

8.78979 

33 

8.79183 

34 

8.79386 

35 

8.79588 

36 

8.79789 

37 

8.79990 

38 

8.80189 

39 

8.80388 

40 

8.80585 

41 

8.80782 

42 

8.80978 

43 

8.81173 

44 

8.81367 

45 

' 8.81560 

46 

8.81752 

47 

8.81944 

48 

8.82134 

49 

8.82324 

50 

8.82513 

51 

8.82701 

52 

8.82888 

53 

8.83075 

54 

8.83261 

55 

8.83446 

56 

8.83630 

57 

8.83813 

58 

8.83996 

59 

8.84177 

60 

8.84358 

L.  Cos. 

229 

228 

226 

226 

224 

223 

222 

220 

220 

219 

217 

216 

216 

214 

213 

212 

211 

210 

209 

208 


L.Tang.  d. 

8.71940 
8.72181  £ 
8.72420  £ 

8.72659  % 

8.72896  £ 

8.73132  % 
8.73366  % 

8.73600  % 

8.73832  2- 

8.74063  % 

8.74292  o; 
8.74521  2 

8.74748  2 

8.74974  * 

8.75199  2 

8.75423  0 

8.75645  2 
8.75867  2 

8.76087  2 

8.76306  2 

8.76525  . 

8.76742  i 
8.76958  i 
8.77173  i 
8.77387  i 

8.77600  ' 

8.77811  ; 
8.78022  * 
' 8.78232  ; 

; 8.78441  ; 

! 8.78649  ; 

» 8.78855  ; 

| 8.79061  ; 

8.79266  ; 

5 8.79470 

' 8.79673 

\ 8.79875 

{ 8.80076 

l 8.80277 
^ 8.80476 

i 8.80674 
l 8.80872 
° 8.81068 
5 8.81264 

i 8.81459 

t 8.81653 
2 8.81846 

2 8.82038 

5 8.82230 

5>  8.82420 

7 8.82610 

» 8.82799 

4 8.82987 

7 8.83175 

8.83361 

, 8.83547 

$4  8.83732 

3 8.83916 

g 8.84100 
*1  8.84282 

31  8.84464 

d. 


L.  Cotg. 


201 

201 

199 

198 

198 

196 

196 

195 

194 

193 

192 

192 

190 

190 

189 

188 

188 

186 

186 

185 

184 

184 

182 

182 

Ic 


j.  Cotg.  ] 

L.  Cos. 

1.28060  1 

3.99940  ( 

50 

1.27819  1 

3.99940 

59 

1.27580  ! 

3.99939 

58 

1.27341  1 

3.99938 

57 

1.27104  ' 

3.99938 

56 

1.26868  1 

9.99937 

55 

1.26634 

9.99936 

54 

1.26400 

9.99936 

53 

1.26168 

9.99935 

52 

1.25937 

9.99934 

51 

1.25708 

9.99934 

50 

1.25479 

9.99933 

49 

1.25252 

9.99932 

48 

1.25026 

9.99932 

47 

1.24801 

9.99931 

46 

1.24577 

9.99930 

45 

1.24355 

9.99929 

44 

1.24133 

9.99929 

43 

1.23913 

9.99928 

42 

1.23694 

9.99927 

41 

1.23475 

9.99926 

40 

1.23258 

9.99926 

39 

1.23042 

9.99925 

38 

1.22827 

9.99924 

37 

1.22613 

9.99923 

36 

1.22400 

9.99923 

35 

1.22189 

9.99922 

34 

1.21978 

9.99921 

33 

1.21768 

9.99920 

32 

1.21559 

9.99920 

31 

1.21351 

9.99919 

30 

1.21145 

9.99918 

29 

1.20939 

9.99917 

28 

1.20734 

9.99917 

27 

1.20530 

9.99916 

26 

1.20327 

9.99915 

25 

1.20125 

9.99914 

24 

1.19924 

9.99913 

23 

1.19723 

9.99913 

22 

1.19524 

9.99912 

21 

1.19326 

9.99911 

20 

1.19128 

9.99910 

19 

1.18932 

9.99909 

18 

1.18736 

9.99909 

17 

1.18541 

9.99908 

16 

1.18347 

9.99907 

15 

1.18154 

9.99906 

14 

1.17962 

9.99905 

13 

1.17770 

9.99904 

12 

1.17580 

9.99904 

11 

1.17390 

9.99903 

10 

1.17201 

9.99902 

: 9 

1.17013 

, 9.99901 

8 

1.16825 

i 9.99900 

i 7 

1.16639 

i 9.99899 

i 6 

1.16453 

i 9.99898 

i 5 

1.1626? 

; 9.99898 

1 4 

1.16084 

[ 9.99897 

r 3 

1.1590C 

> 9.99896 

i 2 

; 1.1571? 

* 9.9989£ 

► 1 

1 1.1553* 

J 9.99894 

L 0 

5.  L.Tang 

r.  L.  Sin 

/ 

P.  P. 


238 

23.8 

27.8 

31.7 

35.7 

39.7 
79.3 

119.0 

158.7 

198.3 


234 

23.4 

27.3 

31.2 

35.1 

39.0 

78.0 

117.0 

156.0 

195.0 


229 

22.9 

26.7 
30.5 
34.4 

38.2 

76.3 
114.5 

152.7 

190.8 


225 

220 

216 

22.5 

22.0 

21.6 

26.3 

25.7 

25.2 

30.0 

29.3 

28.8 

33.8 

33.0 

32.4 

37.5 

36.7 

36.0 

75.0 

73.3 

72.0 

112.5 

110.0 

108.0 

150.0 

146.7 

144.0 

187.5 

183.3 

180.0 

212 

208 

204 

21.2 

20.8 

20.4 

24.7 

24.3 

23.8 

28.3 

27.7 

27.2 

31.8 

31.2 

30.6 

35.3 

34.7 

34.0 

70.7 

69.3 

68.0 

106.0 

104.0 

102.0 

141.3 

138.7 

136.0 

176.7 

173.3 

170.0 

201 

197 

193 

20.1 

23.5 
26.8 

30.2 

33.5 

67.0 

100.5 

134.0 

167.5 

189 

18.9 

22.1 

25.2 

28.4 

31.5 
63.0 

94.5 

126.0 
l 157.5 


19.7 
23.0 

26.3 

29.6 

32.8 

65.7 

98.5 

131.3 

164.2 

185 

18.5 

21.6 

24.7 

27.8 

30.8 
61.7 
92.5 

123.3 
154.2 


4 

3 

2 

6 

0.4 

0.3 

0.2 

7 

0.5 

0.4 

0.2 

8 

0.5 

0.4 

0.3 

9 

0.6 

0.5 

0.3 

10 

0.7 

0.5 

0.3 

20 

1.3 

1.0 

0.7 

30 

2.0 

1.5 

1.0 

40 

2.7 

2.0 

1.3 

50 

3.3 

2.5 

1.7 

19.3 

22.5 

25.7 

29.0 

32.2 

64.3 

96.5 

128.7 

160.8 

181 

18.1 

21.1 

24.1 

27.2 

30.2 

60.3 

90.5 

120.7 

150.8 


0.1 

0.1 

0.1 

0.2 

0.2 

0.3 

0.5 

0.7 

0.8 


P.  P. 


86° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


4° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

8.84358 

8.84539 

8.84718 

8.84897 

8.85075 

181 

179 

179 

178 

177 

177 

176 

175 

175 

173 

173 

173 

171 

171 

171 

169 

169 

169 

167 

168 
166 
166 
165 
164 
164 
163 
163 
162 
162 
160 
161 
159 
159 
159 
158 
157 
157 
156 
155 
155 
155 
154 
153 
153 
152 
152 
151 
151 
150 
150 
149 
149 
148 
147 
147 
147 
146 
146 
145 
145 

8.84464 

8.84646 

8.84826 

8.85006 

8.85185 

182 

180 

180 

179 

178 

177 

177 

176 

176 

174 

174 

174 

172 

172 

171 

171 

170 

169 

169 

168 

167 

167 

166 

165 

165 

165 

163 

163 

163 

161 

162 

160 

160 

160 

159 

158 

158 

157 

157 

156 

155 

155 

155 

153 

154 
153 
152 
152 
151 
151 
150 
150 
149 

148 

149 
147 
147 
147 
146 
146 

1.15536 

1.15354 

1.15174 

1.14994 

1.14815 

9.99894 

9.99893 

9.99892 

9.99891 

9.99891 

60 

59 

58 

57 

56 

181 

6 18.1 

7 21.1 

8 24.1 

9 27.2 

10  30.2 

20  60.3 

30  90.5 

40  120.7 
50  150.8 

175 

6 17.5 

7 20.4 

8 23.3 

9 26.3 

10  29.2 

20  58.3 

30  87.5 

40  116.7 
50  145.8 

168 

6 16.8 

7 19.6 

8 22.4 

9 25.2 

10  28.0 
20  56.0 

30  84.0 

40  112.0 
50  140.0 

162 

6 16.2 

7 18.9 

8 21.6 

9 24.3 

10  27.0 

20  54.0 

30  81.0 

40  108.0 
50  135.0 

155 

6 15.5 

7 18.1 

8 20.7 

9 23.3 

10  25.8 

20  51.7 

30  77.5 

40  103.3 
50  129.2 

149 

6 14.9 

7 17.4 

8 19.9 

9 22.4 

10  24.8 

20  49.7 

30  74.5 

40  99.3 

50  124.2 

179 

17.9 

20.9 

23.9 

26.9 
29.8 

59.7 

89.5 
119.3 

149.2 

173 

17.3 
20.2 

23.1 
26.0 

28.8 

57.7 

86.5 

115.3 

144.2 

166 

16.6 

19.4 

22.1 

24.9 

27.7 

55.3 

83.0 
110.7 

138.3 

159 

15.9 
18.6 
21.2 

23.9 

26.5 

53.0 

79.5 
106.0 

132.5 

153 

15.3 

17.9 

20.4 

23.0 

25.5 

51.0 

76.5 
102.0 

127.5 

147 

14.7 

17.2 

19.6 

22.1 

24.5 

49.0 

73.5 

98.0 

122.5 

177 

17.7 

20.7 

23.6 

26.6 

29.5 

59.0 

88.5 
118.0 

147.5 

171 

17.1 
20.0 

22.8 
25.7 

28.5 

57.0 

85.5 
114.0 

142.5 

164 

16.4 

19.1 

21.9 

24.6 

27.3 

54.7 
82.0 

109.3 

136.7 

157 

15.7 

18.3 

20.9 
23.6 

26.2 

52.3 

78.5 

104.7 

130.8 

151 

15.1 

17.6 

20.1 

22.7 

25.2 

50.3 
75.5 

100.7 

125.8 

1 

0.1 

0.1 

0.1 

0.2 

0.2 

0.3 

0.5 

0.7 

0.8 

5 

6 

7 

8 
9 

8.85252 

8.85429 

8.85605 

8.85780 

8.85955 

8.85363 

8.85540 

8.85717 

8.85893 

8.86069 

1.14637 

1.14460 

1.14283 

1.14107 

1.13931 

9.99890 

9.99889 

9.99888 

9.99887 

9.99886 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

8.86128 

8.86301 

8.86474 

8.86645 

8.86816 

8.86243 

8.86417 

8.86591 

8.86763 

8.86935 

1.13757 

1.13583 

1.13409 

1.13237 

1.13065 

9.99885 

9.99884 

9.99883 

9.99882 

9.99881 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

8.86987 

8.87156 

8.87325 

8.87494 

8.87661 

8.87106 

8.87277 

8.87447 

8.87616 

8.87785 

1.12894 

1.12723 

1.12553 

1.12384 

1.12215 

9.99880 
9.99879 
9 99879 
9.99878 
9.99877 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

8.87829 

8.87995 

8.88161 

8.88326 

8.88490 

8.87953 

8.88120 

8.88287 

8.88453 

8.88618 

1.12047 

1.11880 

1.11713 

1.11547 

1.11382 

9.99876 

9.99875 

9.99874 

9.99873 

9.99872 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

8.88654 

8.88817 

8.88980 

8.89142 

8.89304 

8.88783 

8.88948 

8.89111 

8.89274 

8.89437 

1.11217 

1.11052 

1.10889 

1.10726 

1.10563 

9.99871 

9.99870 

9.99869 

9.99868 

9.99867 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

8.89464 

8.89625 

8.89784 

8.89943 

8.90102 

8.89598 

8.89760 

8.89920 

8.90080 

8.90240 

1.10402 

1.10240 

1.10080 

1.09920 

1.09760 

9.99866 

9.99865 

9.99864 

9.99863 

9.99862 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

8.90260 

8.90417 

8.90574 

8.90730 

8.90885 

8.90399 

8.90557 

8.90715 

8.90872 

8.91029 

1.09601 

1.09443 

1.09285 

1.09128 

1.08971 

9.99861 

9.99860 

9.99859 

9.99858 

9.99857 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

8.91040 

8.91195 

8.91349 

8.91502 

8.91655 

8.91185 

8.91340 

8.91495 

8.91650 

8.91803 

1.08815 

1.08660 

1.08505 

1.08350 

1.08197 

9.99856 

9.99855 

9.99854 

9.99853 

9.99852 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

8.91807 

8.91959 

8.92110 

8.92261 

8.92411 

8.91957 

8.92110 

8.92262 

8.92414 

8.92565 

1.08043 

1.07890 

1.07738 

1.07586 

1.07435 

9.99851 

9.99850 

9.99848 

9.99847 

9.99846 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

8.92561 

8.92710 

8.92859 

8.93007 

8.93154 

8.92716 

8.92866 

8.93016 

8.93165 

8.93313 

1.07284 

1.07134 

1.06984 

1.06835 

1.06687 

9.99845 

9.99844 

9.99843 

9.99842 

9.99841 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

8.93301 

8.93448 

8.93594 

8.93740 

8.93885 

8.93462 

3.93609 

8.93756 

8.93903 

8.94049 

1.06538 

1.06391 

1.06244 

1.06097 

1.05951 

9.99840 

9.99839 

9.99838 

9.99837 

9.99836 

5 

4 

3 

2 

1 

60 

8.94030 

8.94195 

1.05805 

9.99834 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

/ 

P.  P. 

85° 


497 


Logarithms  of  trigonometric  functions. 

5°  . 


) 

L.  Sin. 

d.  I 

j.Tang. 

d.  c.  1 

Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

8794030  “ 

8.94174 

8.94317 

8.94461 

8.94603 

144 

143 

144 
142 

8.94195 

8.94340 

8.94485 

8.94630 

8.94773 

145 

145 

145 

143 

I'M 

1.05805 

1.05660 

1.05515 

1.05370 

1.05227 

9.99834 

9.99833 

9.99832 

9.99831 

9.99830 

60 

59 

58 

57 

56 

6 

7 

8 
9 

145 

14.5 

16.9 

19.3 

21.8 

143 

14.3 

16.7 

19.1 

21.5 

141 

14.1 

16.5 
18.8 

21.2 

23.5 

47.0 

70.5 

94.0 
117.5 

5 

6 

7 

8 
9 

8.94746 

8.94887 

8.95029 

8.95170 

8.95310 

143 

141 

142 
141 
140 
140 
139 
139 
139 
138 
138 
137 
137 
136 
136 
136 
135 
135 
134 
134 
133 
133 
133 
132 
132 
131 
131 
131 
130 
130 
129 
129 
129 
128 
128 
128 
127 
127 
126 
126 

8.94917 

8.95060 

8.95202 

8.95344 

8.95486 

143 

142 

142 

142 

i/ii 

1.05083 

1.04940 

1.04798 

1.04656 

1.04514 

9.99829 

9.99828 

9.99827 

9.99825 

9.99824 

55 

54 

53 

52 

51 

10 

20 

30 

40 

50 

24.2 

48.3- 

72.5 

96.7 

120.8 

23.8 

47.7 

71.5 

95.3 

119.2 

10 

11 

12 

13 

14 

8.95450 

8.95589 

8.95728 

8.95867 

8.96005 

8.95627 

8.95767 

8.95908 

8.96047 

8.96187 

140 

141 

139 

140 

138 

139 
138 

137 

138 

1.04373 

1.04233 

1.04092 

1.03953 

1.03813 

9.99823 

9.99822 

9.99821 

9.99820 

9.99819 

50 

49 

48 

47 

46 

6 

7 

8 
9 

139 

13.9 
16.2 
18.5 

20.9 

138 

13.8 

16.1 

18.4 

20.7 

136 

13.6 

15.9 

18.1 

20.4 

15 

16 

17 

18 
19 

8.96143 

8.96280 

8.96417 

8.96553 

8.96689 

8.96325 

8.96464 

8.96602 

8.96739 

8.96877 

1.03675 

1.03536 

1.03398 

1.03261 

1.03123 

9.99817 

9.99816 

9.99815 

9.99814 

9.99813 

45 

44 

43 

42 

41 

10 

20 

30 

40 

50 

23.2 

46.3 
69.5 
92.7 

115.8 

23.0 

46.0 

69.0 

92.0 
115.0 

22.7 
45.3 
68.0 

90.7 
113.3 

20 

21 

22 

23 

24 

8.96825 

8.96960 

8.97095 

8.97229 

8.97363 

8.97013 

8.97150 

8.97285 

8.97421 

8.97556 

137 

135 

136 
135 

1.02987 

1.02850 

1.02715 

1.02579 

1.02444 

9.99812 

9.99810 

9.99809 

9.99808 

9.99807 

40 

39 

38 

37 

36 

6 

7 

8 
9 

135 

13.5 

15.8 

18.0 

20.3 

133 

13.3 

15.5 

17.7 

20.0 

131 

13.1 

15.3 

17.5 

19.7 

25 

26 

27 

28 
29 

8.97496 

8.97629 

8.97762 

8.97894 

8.98026 

8.97691 

8.97825 

8.97959 

8.98092 

8.98225 

134 

134 

133 

133 

133 

1.02309 

1.02175 

1.02041 

1.01908 

1.01775 

9.99806 

9.99804 

9.99803 

9.99802 

9.99801 

35 

34 

33 

32 

31 

10 

20 

30 

40 

50 

22.5 

45.0 

67.5 

90.0 
112.5 

22.2 

44.3 

66.5 

88.7 

110.8 

21.8 

43.7 

65.5 

87.3 

109.2 

30 

31 

32 

33 

34 

8.98157 

8.98288 

8.98419 

8.98549 

8.98679 

8.98358 

8.98490 

8.98622 

8.98753 

8.98884 

132 

132 

131 

131 

131 

130 

130 

130 

129 

198 

1.01642 

1.01510 

1.01378 

1.01247 

1.01116 

9.99800 

9.99798 

9.99797 

9.99796 

9.99795 

30 

29 

28 

27 

26 

6 

7 

8 
9 

129 

12.9 

15.1 

17.2 
19.4 

128 

12.8 

14.9 

17.1 

19.2 

126 

12.6 

14.7 

16.8 
18.9 

35 

36 

37 

38 

39 

8.98808 

8.98937 

8.99066 

8.99194 

8.99322 

8.99015 

8.99145 

8.99275 

8.99405 

8.99534 

1.00985 

1.00855 

1.00725 

1.00595 

1.00466 

9.99793 

9.99792 

9.99791 

9.99790 

9.99788 

25 

24 

23 

22 

21 

10 

20 

30 

40 

50 

21.5 
43;0 

64.5 
86.0 

107,5 

21.3 
42.7 
64.0 

85.3 
106.7 

21.0 

42.0 

63.0 

84.0 
105.0 

40 

41 

42 

43 

44 

8.99450 

8.99577 

8.99704 

8.99830 

8.99956 

8.99662 

8.99791 

8.99919 

9.00046 

9.00174 

129 

128 

127 

128 
127 
126 
126 
126 
126 
196 

1.00338 

1.00209 

1.00081 

0.99954 

0.99826 

9.99787 

9.99786 

9.99785 

9.99783 

9.99782 

20 

19 

18 

17 

16 

6 

7 

8 
q 

125 

12.5 

14.6 

16.7 

1ft  8 

123 

12.3 

14.4 

16.4 

18.5 

20.5 

41.0 

61.5 

82.0 
102.5 

122 

12.2 

14.2 

16.3 

18.3 

45 

46 

47 

48 

49 

9.00082 

9.00207 

9.00332 

9.00456 

9.00581 

126 

125 

125 

124 

125 

9.00301 

9.00427 

9.00553 

9.00679 

9.00805 

0.99699 

0.99573 

0.99447 

0.99321 

0.99195 

9.99781 

9.99780 

9.99778 

9.99777 

9.99776 

15 

14 

13 

12 

11 

10 

20 

30 

40 

50 

20.8 

41.7 

62.5 

83.3 

104.2 

20.3 
40.7 
61.0 

81.3 
101.7 

50 

51 

52 

53 

54 

9.00704 

9.00828 

9.00951 

9.01074 

9.01196 

- 123 
124 
123 
123 
| 122 

9.00930 

9.01055 

9.01179 

9.01303 

9.01427 

125 
124 
124 
124 
1 92 

0.99070 

0.98945 

0.98821 

0.98697 

0.98573 

9.99775 

9.99773 

9.99772 

9.99771 

9.99769 

to 

9 
8 
- 7 
6 

6 

7 

8 

121 

12.1 

14.1 

16.1 
18.2 
20.2 
40.3 
60.5 
80.7 

100.8 

120 

12.0 

14.0 

16.0 
18  0 

1 

0.1 

0.1 

0.1 

0.2 

55 

56 

57 

58 

59 

9.01318 

9.01440 

9.01561 

9.01682 

9.01802 

- 122 

1 m 
► 121 
; 121 

9.01550 

9.01673 

9.01796 

9.01918 

9.0204C 

' 123 

; 123 
122 
122 
122 

0.98450 

0.98327 

0.98204 

0.98082 

0.97960 

9.99768 
9.99767 
9.99765 
9.99764 
i 9.99763 

5 

4 

3 

2 

1 

V 

10 

20 

30 

40 

50 

iO.v 

20.0 

40.0 

60.0 
80.0 

100.0 

0.2 

0.3 

0.5 

0.7 

0.8 

60 

9.01922 

- 120 

9.0216S 

0.97838 

1 9.99761 

0 

L.  Cos 

. d. 

L.  Cots 

r.  d.  c 

*.  L.Tang 

; L.  Sin. 

/ 

P.  P. 

84° 


498 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


6° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

9.01923 

9.02043 

9.02163 

9.02283 

9.02402 

120 

120 

120 

119 

118 

119 

118 

117 

118 
117 
117 
116 
116 
116 
116 
115 
115 

114 

115 

113 

114 
114 
113 
112 
113 
112 
112 
112 
111 
111 
111 
110 
110 
110 
110 
109 
109 
109 
108 
109 
108 

107 

108 
107 
107 
106 
107 
106 

105 

106 
105 
105 
105 
105 
104 
104 
104 
103 
103 
103 

9.02162 

9.02283 

9.02404 

9.02525 

9.02645 

121 

121 

121 

120 

121 

119 

120 
119 
118 
119 
118 
118 

117 

118 
116 
117 
116 
116 
116 
115 
115 
115 
115 
114 
114 

113 

114 
113 
112 
113 
112 
112 
112 
111 
111 
111 
110 
111 
110 

109 

110 
109 
109 
108 
109 
108 
108 

107 

108 
107 
106 
107 
106 
106 
106 
106 
105 
105 
105 
104 

0.97838 

0.97717 

0.97596 

0.97475 

0.97355 

9.99761 

9.99760 

9.99759 

9.99757 

9.99756 

60 

59 

58 

57 

56 

12! 

6 12.1 

7 14.1 

8 16.1 
9 ' 18.2 

10  20.2 
20  40.3 

3C  60.5 
40  80.7 

50  100.8 

120 

12.0 

14.0 

16.0 
18.0 
20.0 

40.0 

60.0 
80.0 

100.0 

117 

11.7 

13.7 

15.6 

17.6 

19.5 

39.0 

58.5 

78.0 

97.5 

114 

11.4 

13.3 

15.2 

17.1 

19.0 

38.0 

57.0 

76.0 

95.0 

II! 

11.1 

13.0 

14.8 

16.7 

18.5 

37.0 

55.5 

74.0 

92.5 

108 

10.8 

12.6 

14.4 

16.2 

18.0 

36.0 

54.0 

72.0 

90.0 

105 

10.5 
12.3 

14.0 
15.8 

17.5 

35.0 

52.5 

70.0 

87.5 

119 

11.9 

13.9 

15.9 

17.9 
19.8 
39.7 
59.5 
79.3 
99.2 

116 

11.6 

13.5 

15.5 

17.4 

19.3 

38.7 

58.0 

77.3 

96.7 

113 

11.3 

13.2 

15.1 

17.0 

18.8 

37.7 

56.5 

75.3 

94.2 

110 

11.0 

12.8 

14.7 

16.5 

18.3 

36.7 

55.0 

73.3 

91.7 

107 

10.7 

12.5 

14.3 

16.1 

17.8 
35.7 

53.5 

71.3 

89.2 

IQ4 

10.4 
12.1 

13.9 

15.6 

17.3 

34.7 
52.0 

69.3 

86.7 

5 

6 

7 

8 
9 

9.02520 

9.02639 

9.02757 

9.02874 

9.02992 

9.02766 

9.02885 

9.03005 

9.03124 

9.03242 

0.97234 

0.97115 

0.96995 

0.96876 

0.96758 

9.99755 

9.99753 

9.99752 

9.99751 

9.99749 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.03109 

9.03226 

9.03342 

9.03458 

9.03574 

9.03361 

9.03479 

9.03597 

9.03714 

9.03832 

0.96639 

0.96521 

0.96403 

0.96286 

0.96168 

9.99748 

9.99747 

9.99745 

9.99744 

9.99742 

60 

49 

48 

47 

46 

6 

7 

8 
9 

10 
20 
30 
40 
1 50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

Ii8 

11.8 

13.8 

15.7 

17.7 

19.7 

39.3 

59.0 

78.7 

98.3 

115 

11.5 

13.4 

15.3 

17.3 

19.2 

38.3 

57.5 

76.7 

95.8 

112 

11.2 

13.1 

14.9 
16.8 

18.7 

37.3 

56.0 

74.7 

93.3 

<09 

10.9 

12.7 

14.5 

16.4 

18.2 

36.3 

54.5 

72.7 

90.8 

106 

10.6 

12.4 

14.1 

15.9 

17.7 

35.3 
53.0 

70.7 

88.3 

15 

16 

17 

18 
19 

9.03690 

9.03805 

9.03920 

9.04034 

9.04149 

9.03948 

9.04065 

9.04181 

9.04297 

9.04413 

0.96052 

0.95935 

0.95819 

0.95703 

0.95587 

9.99741 

9.99740 

9.99738 

9.99737 

9.99736 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.04262 

9.04376 

9.04490 

9.04603 

9.04715 

9.04528 

9.04643 

9.04758 

9.04873 

9.04987 

0.95472 

0.95357 

0.95242 

0.95127 

0.95013 

9.99734 

9.99733 

9.99731 

9.99730 

9.99728 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.04828 

9.04940 

9.05052 

9.05164 

9.05275 

9.05101 

9.05214 

9.05328 

9.05441 

9.05553 

0.94899 

0.94786 

0.94672 

0.94559 

0.94447 

9.99727 

9.99726 

9.99724 

9.99723 

9.99721 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.05386 

9.05497 

9.05607 

9.05717 

9.05827 

9.05666 

9.05778 

9.05890 

9.06002 

9.06113 

0.94334 

0.94222 

0.94110 

0.93998 

0.93887 

9.99720 

9.99718 

9.99717 

9.99716 

9.99714 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.05937 

9.06046 

9.06155 

9.06264 

9.06372 

9.06224 

9.06335 

9.06445 

9.06556 

9.06666 

0.93776 

0.93665 

0.93555 

0.93444 

0.93334 

9.99713 

9.99711 

9.99710 

9.99708 

9.99707 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.06481 

9.06589 

9.06696 

9.06804 

9.06911 

9.06775 

9.06885 

9.06994 

9.07103 

9.07211 

0.93225 

0.93115 

0.93006 

0.92897 

0.92789 

9.99705 

9.99704 

9.99702 

9.99701 

9.99699 

20 

15 
18 
17 

16 

45 

46 

47 

48 

49 

9.07018 

9.07124 

9.07231 

9.07337 

9.07442 

9.07320 

9.07428 

9.07536 

9.07643 

9.07751 

0.92680 

0.92572 

0.92464 

0,92357 

0.92249 

9.99698 

9.99696 

9.99695 

9.99693 

9.99692 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.07548 

9.07653 

9.07758 

9.07863 

9.07968 

9.07858 

9.07964 

9.08071 

9.08177 

9.08283 

0.92142 

0.92036 

0.91929 

0.91823 

0.91717 

9.99690 

9.99689 

9.99687 

9.99686 

9.99684 

to 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.08072 

9.08176 

9.08280 

9.08383 

9.08486 

9.08389 

9.08495 

9.08600 

9.08705 

9.08810 

0.91611 

0.91505 

0.91400 

0.91295 

0.91190 

9.99683 

9.99681 

9.99680 

9.99678 

9.99677 

5 

4 

3 

2 

1 

60 

9.08589 

9.08914 

0.91086 

9.99675 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

/ 

P.  P. 

83° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS . 

7° 


499 


' ] 

L Sin.  c 

0 * 

>.08589 

1 * 

>.08692  { 

2 * 

>.08795  | 

3 t 

>.08897  ]) 

4 < 

>.08999  l 

5 ! 

>.09101 

6 ! 

>.09202  }) 

7 1 

>.09304  1 

8 ! 

>.09405  j 

9 1 

9.09506  * 

10  1 

9.09606  , 

11  1 

9.09707  } 

12 

9.09807  } 

13 

9.09907  1 

14 

9.10006 

15 

9.10106 

16 

9.10205 

17 

9.10304 

18 

9.10402 

19 

9.10501 

20 

9.10599 

21 

9.10697 

22 

9.10795 

23 

9.10893 

24 

9.10990 

25 

9.11087 

26 

9.11184 

27 

9.11281 

28 

9.11377 

29 

9.11474 

30 

9.11570 

31 

9.11666 

32 

9.11761 

33 

9.11857 

34 

9.11952 

35 

9.12047 

36 

9.12142 

37 

9.12236 

38 

9.12331 

39 

9.12425 

40 

9.12519 

41 

9.12612 

42 

9.12706 

43 

9.12799 

44 

9.12892 

45 

9.12985 

46 

9.13078 

47 

9.13171 

48 

9.13263 

49 

9.13355 

50 

9.13447 

51 

9.13539 

52 

9.13630 

53 

9.13722 

54 

9.13813 

55 

9.13904 

56 

9.13994 

57 

9.14085 

58 

9.14175 

59 

9.14266 

60 

9.14356 

L.  Cos. 

d.  L.Tang. 
9.08914 
9.09019 
9.09123 
9.09227 
9.09330 


9.09434 

9.09537 

9.09640 

9.09742 

9.09845 


99 
00 
99 
99 

98 

99 
98 
98 
98 
98 
97 
97 
97 
97 

96 

97 
96 
96 

95 

96 
95 
95 
95 

94 

95 
94 
94 

93 

94 
93 
93 
93 
93 
93 
92 
92 
92 
92 

91 

92 
91 
91 

90 

91 

90 

91 
90 


9.09947 

9.10049 

9.10150 

9.10252 

9.10353 


9.10454 

9.10555 

9.10656 

9.10756 

9.10856 


9.10956 

9.11056 

9.11155 

9.11254 

9.11353 


9.11452 

9.11551 

9.11649 

9.11747 

9.11845 


9.11943 

9.12040 

9.12138 

9.12235 

9.12332 


105 

104 

104 

103 

104 
103 
103 
102 
103 
102 
102 
101 
102 
101 
101 
101 
101 
100 
100 
100 
100 

99 

99 


9.12428 

9.12525 

9.12621 

9.12717 

9.12813 


9.12909 

9.13004 

9.13099 

9.13194 

9.13289 


9.13384 

9.13478 

9.13573 

9.13667 

9.13761 

9.13854 

9.13948 

9.14041 

9.14134 

9.14227 


9.14320 

9.14412 

9.14504 

9.14597 

9.14688 


99 

99 

99 

98 

98 

98 

98 

97 

98 
97 
97 

96 

97 
96 
96 
96 
96 
95 
95 
95 
95 
95 

94 

95 
94 
94 


9.14780 


d.  L.  Cotg 


L.  Cotg. 

L.  Cos. 

0.91086 

9.99675  f 

>0 

0.90981 

9.99674  J 

59 

0.90877 

9.99672  J 

58 

0.90773 

9.99670  ; 

57 

0.90670 

9.99669 

56 

0.90566 

9.99667 

55 

0.90463 

9.99666 

54 

0.90360 

9.99664 

53 

0.90258 

9.99663 

52 

0.90155 

9.99661 

51 

0.90053 

9.99659  ! 

50 

0.89951 

9.99658 

49 

0.89850 

9.99656 

48 

0.89748 

9.99655 

47 

0.89647 

9.99653 

46 

0.89546 

9.99651 

45 

0.89445 

9.99650 

44 

0.89344 

9.99648 

43 

0.89244 

9.99647 

42 

0.89144 

9.99645 

41 

0.89044 

9.99643 

40 

0.88944 

9.99642 

39 

0.88845 

9.99640 

38 

0.88746 

9.99638 

37 

0.88647 

9.99637 

36 

0.88548 

9.99635 

35 

0.88449 

9.99633 

34 

0.88351 

9.99632 

33 

0.88253 

9.99630 

32 

0.88155 

9.99629 

31 

0.88057 

9.99627 

30 

0.87960 

9.99625 

29 

0.87862 

9.99624 

28 

0.87765 

9.99622 

27 

0.87668 

9.99620 

26 

0.87572 

9.99618 

25 

0.87475 

9.99617 

24 

0.87379 

9.99615 

23 

0.87283 

9.99613 

22 

0.87187 

9.99612 

21 

0.87091 

9.99610 

20 

0.86996 

9.99608 

19 

0.86901 

9.99607 

18 

0.86806 

9.99605 

17 

0.86711 

9.99603 

16 

0.86616 

9.99601 

15 

0.86522 

9.99600 

14 

0.86427 

9.99598 

13 

0.86333 

, 9.99596 

12 

j 0.86239 

i 9.99595 

11 

’ 0.86146 

1 9.99593 

10 

: 0.86052 

5 9.99591 

9 

I 0.85952 

) 9.99589 

8 

» 0.8586( 

} 9.99588 

7 

5 0.8577; 

5 9.99586 

6 

' 0.8568( 

) 9.99584 

5 

\ 0.85585 

3 9.99582 

1 4 

2 0.85491 

5 9.99581 

3 

} 0.8540: 

3 9.99572 

) 2 

\ 0.8531! 

2 9.99577 

* 1 

2 0.8522 

C 9.9957c 

) 0 

c.  L.Tanj 

g.  L.  Sin 

! 

P.  P. 


105 

10.5 
12.3 

14.0 
15.8 

17.5 

35.0 

52.5 

70.0 

87.5 


102 

6 ! 10.2 
11.9 
13.6 
15.3 

17.0 

34.0 

51.0 

68.0 

85.0 


104 

10.4 
12.1 
13.9 

15.6 

17.3 

34.7 

52.0 

69.3 

86.7 

101 

10.1 

11.8 

13.5 

15.2 
16.8 
33.7 

50.5 

67.3 
84.2 


103 

10.3 

12.0 

13.7 

15.5 

17.2 

34.3 

51.5 

68.7 

85.8 

100 

10.0 

11.7 

13.3 
-15.0 

16.7 

33.3 
50.0 

66.7 

83.3 


99 

9.9 

11.6 

13.2 

14.9 

16.5 

33.0 

49.5 

66.0 

82.5 


98 

9.8 

11.4 

13.1 

14.7 

16.3 

32.7 
49.0 

65.3 

81.7 


97 

9.7 

11.3 
12.9 

14.6 
16.2 

32.3 

48.5 

64.7 

80.8 

94 

9.4 

11.0 

12.5 
14.1 

15.7 

31.3 
47.0 

62.7 

78.3 


96 

9.6 

11.2 

12.8 

14.4 
16.0 

32.0 

48.0 

64.0 

80.0 

93 

9.3 

10.9 

12.4 

14.0 

15.5 

31.0 

46.5 

62.0 

77.5 


91 

9.1 

10.6 

12.1 

13.7 

15.2 

30.3 
45.5 

60.7 

75.8 


90  I 

9.0  1 

10.5 

12.0 

13.5 

15.0 

30.0 

45.0 

60.0 
75.0 


95 

9.5 

11.1 

12.7 

14.3 

15.8 

31.7 

47.5 

63.3 

79.2 

92 

9.2 

10.7 

12.3 

13.8 

15.3 

30.7 
46.0 

61.3 

76.7 

I 2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.7 

1.0 

1.3 
1.7 


P.  P. 


82° 


500 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 


8° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P. 

p. 

0 

9.14356 

9.14780 

0.85220 

9.99575 

60 

1 

9.14445 

89 

9.14872 

92 

0.85128 

9.99574 

59 

! SI 

90 

2 

9.14535 

90 

9.14963 

91 

0.85037 

9.99572 

58 

6 

9.2 

| 9.1 

9.0 

B 

9.14624 

89 

9.15054 

91 

0.84946 

9.99570 

57 

7 

10.7 

10.6 

10.5 

4 

9.14714 

90 

89 

9.15145 

91 

91 

0.84855 

9.99568 

56 

8 

9 

12.3 

J3.8 

1 12.1 
13.7 

12.0 

13.5 

5 

9.14803 

9.15236 

0.84764 

9.99566 

55 

10 

15^3 

15^2 

15.0 

6 

9.14891 

88 

9.15327 

91 

0.84673 

9.99565 

54 

20 

30.7 

30.3 

30.0 

7 

9.14980 

sy 

9.15417 

90 

0.84583 

9.99563 

53 

30 

46.0 

! 45.5 

45.0 

8 

9.15069 

»y 

9.15508 

9L 

0.84492 

9.99561 

52 

40 

61.3 

1 60.7 

60.0 

9 

9.15157 

8o 

88 

9.15598 

90 

90 

0.84402 

9.99559 

51 

50 

76.7 

i 75.8 

75.0 

10 

9.15245 

9.15688 

0.84312 

9.99557 

50 

11 

9.15333 

88 

9.15777 

89 

0.84223 

9.99556 

49 

89 

88 

12 

9.15421 

88 

9.15867 

90 

0.84133 

9.99554 

48 

6 

1 8.9 

8.8 

13 

9.15508 

87 

9.15956 

89 

0.84044 

9.99552 

47 

7 

i 10.4 

10.3 

14 

9.15596 

88 

87 

9.16046 

90 

89 

0.83954 

9.99550 

46 

8 

A 

i 11.9 

! 1 Q A 

11.7 

IQ  O 

15 

9.15683 

9.16135 

0.83865 

9.99548 

45 

V 

10 

lo.4 

14.8 

lo.  Z 

14.7 

16 

9.15770 

o7 

9.16224 

89 

0.83776 

9.99546 

44 

20 

1 20.7 

90 

17 

9.15857 

8/ 

9.16312 

88 

0.83688 

9.99545 

43 

30 

44.5 

L.  J.O 

44.0 

18 

9.15944 

g7 

9.16401 

89 

0.83599 

9.99543 

42 

40 

1 593 

58.7 

19 

9.16030 

ob 

86 

9.16489 

88 

88 

0.83511 

9.99541 

41 

50 

! 74.2 

73^3 

20 

9.16116 

9.16577 

0.83423 

9.99539 

40 

21 

9.16203 

8/ 

9.16665 

88 

0.83335 

9.99537 

39 

87 

86 

22 

9.16289 

86 

9.16753 

88 

0.83247 

9.99535 

38 

6 

8.7 

8.6 

23 

9.16374 

85 

9.16841 

88 

0.83159 

9.99533 

37 

7 

10.2 

10.0 

24 

9.16460 

86 

85 

9.16928 

87 

qq 

0.83072 

9.99532 

36 

8 

11.6 

11.5 

25 

9.16545 

9.17016 

0.82984 

9.99530 

35 

y 

1 A 

13.1 

12.9 

26 

9.16631 

86 

9.17103 

87 

0.82897 

9.99528 

34 

10 

14.5 

14.3 

27 

9.16716 

85 

9.17190 

87 

0.82810 

9.99526 

33 

20 

on 

29.0 

AO  K 

28.7 

28 

9.16801 

85 

9.17277 

87 

0.82723 

9.99524 

32 

30 

A A 

CQ  A 

43.0 

cr?  o 

29 

9.16886 

85 

84 

or; 

9.17363 

86 

87 

0.82637 

9.99522 

31 

40 

RO 

Oo.U 
79  * 

5/.o 
71  7 

30 

9.16970 

9.17450 

0.82550 

9.99520 

30 

31 

9.17055 

85 

O/l 

9.17536 

86 

0.82464 

9.99518 

29 

85 

84 

32 

9.17139 

84 

9.17622 

86 

0.82378 

9.99517 

28 

6 

8.5 

8.4 

33 

9.17223 

84 

0/4 

9.17708 

86 

0.82292 

9.99515 

27 

7 

9.9 

9.8 

34 

9.17307 

84 

84 

9.17794 

86 

86 

0.82206 

9.99513 

26 

8 

11.3 

11.2 

35 

9.17391 

9.17880 

0.82120 

9.99511 

25 

9 

12.8 

12.6 

36 

9.17474 

83 

9.17965 

85 

0.82035 

9.99509 

24 

10 

14.2 

14.0 

37 

9.17558 

84 

9.18051 

86 

0.81949 

9.99507 

23 

20 

28.3 

28.0 

38 

9.17641 

83 

9.18136 

85 

0.81864 

9.99505 

22 

30 

42.5 

42.0 

39 

9.17724 

83 

83 

QO 

9.18221 

85 

85 

0.81779 

9.99503 

21 

40 

! £;a 

56.7 

'7A  Q 

56.0 

>7  n n 

40 

9.17807 

9.18306 

0.81694 

9.99501 

20 

• V / ;j 

41 

9.17890 

oS 

QO 

9.18391 

85 

0.81609 

9.99409 

19 

83 

82 

42 

9.17973 

GO 

QO 

9.18475 

84 

0.81525 

9.99497 

18 

6 

8.3 

8.2 

43 

9.18055 

oZ 

QO 

9.18560 

85 

O A 

0.81440 

9.99495 

17 

7 

9.7 

9.6 

44 

9.18137 

oZ 

83 

9.18644 

g4 

84 

0.81356 

9.99494 

16 

8 

11.1 

10.9 

45 

9.18220 

9.18728“ 

0.81272 

9.99492 

15 

9 

12.5 

12.3 

46 

9.18302 

82 

Q1 

9.18812 

84 

0.81188 

9.99490 

14 

JO 

13.8 

13.7 

47 

9.18383 

ol 

QO 

9.18896 

84 

0.81104 

9.99488 

13 

20 

27.7 

27.3  ! 

48 

9.18465 

oZ 

9.18979 

83 

0.81021 

9.99486 

12 

30 

41.5 

41.0 

49 

9.18547 

82 

81 

9.19063 

84 

83 

0.80937 

9.99484 

11 

40 

55.3 

£Q  O 

54.7 

£Q  O 

50 

9.18628 

Q t 

9.19146 

0.80854 

9.99482 

10 

OU 

oy . z 

DO.O  | 

51 

9.18709 

ol 

Q1 

9.19229 

83 

0.80771 

9.99480 

9 

81 

80 

9 

52 

9.18790 

ol 

9.19312 

83 

0.80688 

9.99478 

8 

6 

8.1 

8.0 

0.2 

53 

9.18871 

G1 

Q1 

9.19395 

83 

QO 

0.80605 

9.99476 

fT 

! 

7 

9.5 

9.3 

0 2 

54 

9.18952 

G± 

81 

9.19478 

GO 

83 

0.80522 

9.99474 

6 

8 

10.8 

10.7 

0.3 

55 

9.19033 

qh 

9.19561 

0.80439 

9.99472 

5 

9 

12.2 

12.0 

0.3 

56 

9.19113 

oU 

QO 

9.19643 

82 

0.80357 

9.99470 

4 

10 

13.5 

13.3 

0.3 

57 

9.19193 

oU 

QO 

9.19725 

82 

0.80275 

9.99468 

3 

20 

27.0 

26.7 

0.7 

58 

9.19273 

GU 
QO  * 

9.19807 

82 

0.80193 

9.99466 

2 

30 

40.5 

40.0 

1.0 

59 

9.19353 

oU 

80 

9.19889 

82 

82 

0.80111 

9.99464 

1 

40 

54.0  ; 

53.3 

1.3 

60 

9.19433 

9.19971 

0.80029 

9.99462 

0 

50 

67.5  i 

66.7 

1.7 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

t 

p. 

P. 

81° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  501 


t 

L.  Sin.  < 

0 

9.19433  , 

1 

9.19513  ; 

2 

9.19592 

3 

9.19672  ; 

4 

9.19751 

5 

9.19830 

6 

9.19909 

7 

9.19988 

8 

9.20067 

9 

9.20145 

10 

9.20223 

11 

9.20302 

12 

9.20380 

13 

9.20458 

14 

9.20535 

15 

9.20613 

16 

9.20691 

17 

9.20768 

18 

9.20845 

19 

9.20922 

20 

0.20999 

21 

9.21076 

22 

9.21153 

23 

9.21229 

24 

9.21306 

25 

9.21382 

26 

9.21458 

27 

9.21534 

28 

9.21610 

29 

9.21685 

30 

9.21761 

31 

9.21836 

32 

9.21912 

33 

9.21987 

34 

9.22062 

35 

9.22137 

36 

9.22211 

37 

9.22286 

38 

9.22361 

39 

9.22435 

40 

9.22509 

41 

9.22583 

42 

9.22657 

43 

9.22731 

44 

9.22805 

45 

9.22878 

46 

9.22952 

47 

9.23025 

48 

9.23098 

49 

9.23171 

50 

' 9.23244 

51 

9.23317 

52 

9.23390 

53 

9.23462 

54 

9.23535 

55 

9.23607 

56 

9.23679 

57 

9.23752 

58 

9.23823 

59 

9.23895 

60 

9.23967 

L.  Cos. 

L.  Cotg. 

L.  Cos. 

0.80029 

9.99462  l 

BO 

0.79947 

9.99460 

59 

0.79866 

9.99458 

58 

0.79784 

9.99456 

57 

0.79703 

9.99454 

56 

0.79622 

9.99452 

55  ] 

0.79541 

9.99450 

54  $ 

0.79460 

9.99448 

53  £ 

0.79379 

9.99446 

52  t 

0.79299 

9 99444 

51  l 

0.79218 

9.99442 

50 

0.79138 

9.99440 

49 

0.79058 

9.99438 

48 

0.78978 

9.99436 

47 

0.78898 

9.99434 

46 

0.78818 

9.99432 

45 

0.78739 

9.99429 

44 

0.78659 

9.99427 

43 

0.78580 

9.99425 

42 

0.78501 

9.99423 

41 

0.78422 

9.99421 

40 

0.78343 

9.99419 

39 

0.78264 

9.99417 

38 

0.78186 

9.99415 

37 

0.78107 

9.99413 

36 

0.78029 

9.99411 

35 

0.77951 

9.99409 

34 

0.77873 

9.99407 

33 

0.77795 

9.99404 

32 

0.77717 

9.99402 

31 

0.77639 

9.99400 

30 

0.77562 

9.99398 

29 

0.77484 

9.99396 

28 

0.77407 

9.99394 

27 

0.77330 

9.99392 

26 

0.77253 

9.99390 

25 

0.77176 

9.99388 

24 

0.77099 

9.99385 

23 

0.77023 

9.99383 

22 

0.76946 

9.99381 

21 

0.76870 

9.99379 

20 

0.76794 

9.99377 

19 

0.76717 

9.99375 

18 

0.76641 

9.99372 

17 

0.76565 

9.99370 

16 

0.76490 

9.99368 

15 

0.76414 

9.99366 

14 

0.76339 

9.99364 

13 

0.76263 

9.99362 

12 

0.76188 

9.99359 

' 11 

0.76113 

" 9.99357 

10 

0.76038 

9.99355 

9 

0.75963 

9.99353 

8 

0.75888 

9.99351 

7 

0.75814 

9.99348 

6 

0.75739 

' 9.99346 

5 

0.75665 

. 9.99344 

4 

1 0.75590 

i 9.99342 

; 3 

0.75516 

i 9.99340 

i 2 

■ 0.75442 

\ 9.99337 

’ 1 

0.7536* 

5 9.9933E 

» 0 

c.  L.Tang 

f.  L.  Sin. 

f 

d. 


79 

80 
79 
79 
79 
79 
79 
78 

78 

79 
78 
78 

77 

78 
78 
77 
77 
77 
77 
77 
77 

76 

77 
76 
76 
76 
76 

75 

76 

75 

76 
75 
75 
75 

74 

75 
75 
74 
74 
74 
74 
74 
74 

73 

74 
73 
73 
73 
73 
73 
73 

72 

73 
72 

72 

73 

71 

72 
72 


d. 


Tang. 


.19971 

.20053 

.20134 

.20216 

.20297 


20378 

20459 

.20540 

.20621 

.20701 


20782 

9.20862 

9.20942 

9.21022 

9.21102 


d.  c. 


9.21182 

9.21261 

9.21341 

9.21420 

9.21499 


9.21578 

9.21657 

9.21736 

9.21814 

9.21893 


9.21971 

9.22049 

9.22127 

9.22205 

9.22283 


9.22361 

9.22438 

9.22516 

9.22593 

9.22670 


9.22747 

9.22824 

9.22901 

9.22977 

9.23054 


9.23130 

9.23206 

9.23283 

9.23359 

9.23435 


9.23510 

9.23586 

9.23661 

9.23737 

9.23812 


9.23887 

9.23962 

9.24037 

9.24112 

9.24186 


9.24261 

9.24335 

9.24410 

9.24484 

9.24558 


82 

81 

82 

81 

81 

81 

81 

81 

80 

81 

80 

80 

80 

80 

80 

79 

80 
79 
79 
79 
79 
79 

78 

79 
78 
78 
78 
78 
78 
78 

77 

78 
77 
77 
77 
77 
77 

76 

77 
76 

76 

77 
76 
76 

75 

76 

75 

76 
75 
75 
75 
75 
75 
74 


9.24632 


L.  Cotg. 


P.  P. 


82 

81 

80 

8.2 

8.1 

8.0 

9.6 

9.5 

9.3 

10.9 

10.8 

10.7 

12.3 

12.2 

12.0 

13.7 

13.5 

13.3 

27.3 

27.0 

26.7 

41.0 

40.5 

40.0 

54.7 

54.0 

53.3 

68.3 

67.5 

66.7 

6 i 

?! 

9 

10 

20 

30 

40 

50 


6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 
20 
30 
40 
50 


79 

7.9 

9.2 

10.5 
11.9 

13.2 

26.3 

39.5 

52.7 

65.8 

77 

7.7 

9.0 

10.3 

11.6 

12.8 
25.7 

38.5 

51.3 

64.2 

75 

7.5 

8.8 

10.0 

11.3 

12.5 

25.0 

37.5 

50.0 

62.5 

73 

7.3 

8.5 
9.7 

11.0 
12.2 

24.3 

36.5 

48.7 

60.8 

71 


78 

7.8 
9.1 

10.4 

11.7 

13.0 

26.0 

39.0 

52.0 

65.0 

76 

7.6 

8.9 
10.1' 

11.4 

12.7 

25.3 

38.0 

50.7 

63.3 

74 

7.4 

8.6 

9.9 

11.1 

12.3 

24.7 

37.0 

49.3 

61.7 

72 

7.2 

8.4 
9.6 

10.8 

12.0 

24.0 

36.0 

48.0 

60.0 

3 


80 


7.1 

0.3 

0.2 

8.3 

0.4 

0.2 

9.5 

0.4 

0.3 

10.7 

0.5 

0.3 

11.8 

0.5 

0.3 

23.7 

1.0 

0.7 

35.5 

1.5 

1.0 

47.3 

2.0 

1.3 

59.2 

2.5 

1.7 

P. 

P. 

502 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


10° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

9.23967 

9.24039 

9.24110 

9.24181 

9.24253 

72 

71 

71 

72 
71 
71 
71 

70 

71 

70 

71 
70 
70 
70 
70 
70 
70 

69 

70 
69 
69 
69 
69 
69 
69 
69 
68 
69 
68 
68 
68 
68 
68 
68 
68 

67 

68 
67 
67 
67 
67 
67 
67 
67 
66 
67 
66 
67 
66 
66 
66 
66 

65 

66 
66 
65 

65 

66 
65 
65 

9.24632 

9.24706 

9.24779 

9.24853 

9.24926 

74 

73 

74 

73 

74 
73 
73 
73 
73 
73 

72 

73 

72 

73 
72 
72 
72 
72 
72 

71 

72 

71 

72 
71 
71 
71 
71 

70 

71 
71 
70 

70 

71 
70 
70 
70 
70 

69 

70 

69 

70 
69 
69 
69 
69 
69 
69 
69 
68 
69 
68 
69 
68 
68 
68 
68 

67 

68 
68 
67 

0.75368 

0.75294 

0.75221 

0.75147 

0.75074 

9.99335 

9.99333 

9.99331 

9.99328 

9.99326 

60 

59 

58 

57 

56 

6 

7 

8 

9 
10 
20 
30 
40 
50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 
20 
30 
40 
50 

6 

7 

1 8 
9 
10 
20 
30 
40 
50 

6 

7 

8 

9 
10 
20 
30 
40 
50 

6 

7 

8 

9 

10 
10 
30 
40 
50 

74 

7.4 
8.6 

9.9 
11.1 

12.3 

24.7 

37.0 

49.3 

61.7 

72 

7.2 

8.4 

9.6 

10.8 

12.0 

24.0 

36.0 

48.0 

60.0 

70 

7.0 

8.2 
9.3 

10.5 

11.7 

23.3 

35.0 

46.7 

58.3 

68 

6.8 

7.9 

9.1 
10.2 

11.3 

22.7 

34.0 

45.3 

56.7 

66 

6.6 

7.7 

8.8 

9.9 

11.0 
22.0 

33.0 

44.0 

55.0 

3 

0.3 

0.4 

0.4 

0.5 

0.5 

1.0 

1.5 
2.0 

2.5 

73 

7.3 

8.5 

9.7 
11.0 
12.2 

24.3 

36.5 

48.7 
60.8. 

71 

7.1 

8.3 

9.5 

10.7 

11.8 

23.7 

35.5 

47.3 

59.2 

69 

6.9 

8.1 
9.2 

10.4 

11.5 

23.0 

34.5 

46.0 

57.5 

67 

6.7 

7.8 

8.9 

10.1 

11.2 

22.3 

33.5 

44.7 

55.8 

65 

6.5  , 

7.6 

8.7 

9.8 

10.8 

21.7 

32.5 

43.3 
54.2 

2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.7  ! 

1.0 

1.3 

1.7 

5 

6 

7 

8 
9 

9.24324 

9.24395 

9.24466 

9.24536 

9.24607 

9.25000 

9.25073 

9.25146 

9.25219 

9.25292 

0.75000 

0.74927 

0.74854 

0.74781 

0.74708 

9.99324 

9.99322 

9.99319 

9.99317 

9.99315 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.24677 

9.24748 

9.24818 

9.24888 

9.24958 

9,25365 

9.25437 

9.25510 

9.25582 

9.25655 

0.74635 

0.74563 

0.74490 

0.74418 

0.74345 

9.99313 

9.99310 

9.99308 

9.99306 

9.99304 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.25028 

9.25098 

9.25168 

9.25237 

9.25307 

9.25727 

9.25799 

9.25871 

9.25943 

9.26015 

0.74273 

0.74201 

0.74129 

0.74057 

0.73985 

9.99301 

9.99299 

9.99297 

9.99294 

9.99292 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.25376 

9.25445 

9.25514 

9.25583 

9.25652 

9.26086 

9.26158 

9.26229 

9.26301 

9.26372 

0.73914 

0.73842 

0.73771 

0.73699 

0.73628 

9.99290 

9.99288 

9.99285 

9.99283 

9.99281 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.25721 

9.25790 

9.25858 

9.25927 

9.25995 

9.26443 

9.26514 

9.26585 

9.26655 

9.26726 

0,73557 

0.73486 

0.73415 

0.73345 

0.73274 

9.99278 

9.99276 

9.99274 

9.99271 

9.99269 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.26063 

9.26131 

9.26199 

9.26267 

9.26335 

9.26797 

9.26867 

9.26937 

9.27008 

9.27078 

0.73203 

0.73133 

0.73063 

0.72992 

0.72922 

9.99267 

9.99264 

9.99262 

9.99260 

9.99257 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.26403 

9.26470 

9.26538 

9.26605 

9.26672 

9.27148 

9.27218 

9.27288 

9.27357 

9.27427 

0.72852 

0.72782 

0.72712 

0.72643 

0.72573 

9.99255 

9.99252 

9.99250 

9.99248 

9.99245 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.26739 

9.26806 

9.26873 

9.26940 

9.27007 

9.27496 

9.27566 

9.27635 

9.27704 

9.27773 

0.72504 

0.72434 

0.72365 

0.72296 

0.72227 

9.99243 

9.99241 

9.99238 

9.99236 

9.99233 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.27073 

9.27140 

9.27206 

9.27273 

9.27339 

9.27842 

9.27911 

9.27980 

9.28049 

9.28117 

0.72158 

0.72089 

0.72020 

0.71951 

0.71883 

9.99231 

9.99229 

9.99226 

9.99224 

9.99221 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.27405 

9.27471 

9.27537 

9.27602 

9.27668 

9.28186 

9.28254 

9.28323 

9.28391 

9.28459 

0.71814 

0.71746 

0.71677 

0.71609 

0.71541 

9.99219 

9.99217 

9.99214 

9.99212 

9.99209 

10 

9 

8 

7 

6 

t>5 

56 

57 

58 

59 

9.27734 

9.27799 

9.27864 

9.27930 

9.27995 

9.28527 

9.28595 

9.28662 

9.28730 

9.28798 

0.71473 

0.71405 

0.71338 

0.71270 

0.71202 

9.99207 

9.99204 

9.99202 

9.99200 

9.99197 

5 

4 

3 

2 

1 

60 

9.28060 

9.28865 

0.71135 

9.99195 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

f 

P.  P. 

79° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

11° 


503 


/ 

L.  Sin. 

d.  I 

j.  Tang. 

d.  c.  L.  Cotg. 

L.  Cos. 

P. 

P. 

o 

9.28060 

9.28865 

0.71135 

9.99195 

60 

fif 

t 

6 

1 

9.28125 

65 

9.28933 

68 

0.71007 

9.99192 

59 

6 

6.8 

6 

2 

9.28190 

65 

9 29000 

67 

0.71000 

9.99190 

58 

7 

7.9 

7 

3 

9.28254 

64 

9.29067 

67 

0.70933 

9.99187 

57 

8 

9.1 

8 

4 

9.28319 

65 

9.29134 

67 

0.70866 

9.99185 

56 

9 

10.2 

10 

9.28384 

65 

9.29201 

0.70799 

9.99182 

55 

10 

11.3 

11 

6 

9.28448 

64 

9.29268 

67 

0.70732 

9.99180 

54 

20 

22.7 

22 

7 

9.28512 

64 

9.29335 

67 

0.70665 

9 99177 

53 

30 

34.0 

33 

8 

9.28577 

65 

9.29402 

67 

0.70598 

9.99175 

52 

40 

45  3 

44 

9 

9.28641 

64 

9.29468 

& , 

0.70532 

9.99172 

51 

50 

56.7 

55 

10 

9.28705 

64 

9.29535 

0.70465 

9.99170 

50 

cc 

11 

9.28769 

64 

9.29601 

66 

0.70399 

9.99167 

49 

A 

uu 

A A 

12 

9.28833 

64 

9.29668 

67 

0.70332 

9.99165 

48 

O 

7 

0.0 
7 7 

13 

9.28896 

63 

9.29734 

66 

0.70266 

9.99162 

47 

i 

Q 

ft  ft 

14 

9.28960 

64 

9.29800 

66 

66  - 

0.70200 

9.99160 

46 

O 

9 

0.0 

9.9 

15 

9.29024 

64 

9.29866 

0.70134 

9.99157 

45 

10 

li.o  : 

16 

9.29087 

63 

9.29932 

66 

0.70068 

9.99155 

44 

20 

22.0  : 

17 

9.29150 

63 

9.29998 

66 

0.70002 

9.99152 

43 

30 

33.0  ! 

18 

9.29214 

64 

9.30064 

66 

0.69936 

9.99150 

42 

40 

44.0  - 

19 

9.29277 

63 

9.30130 

66 

65 

0.69870 

9.99147 

41 

50 

55.0  1 

20 

9.29340 

bo 

9.30195 

0.69805 

9.99145 

40 

21 

9.29403 

63 

9.30261 

66 

0.69739 

9.99142 

39 

64 

22 

9.29466 

63 

9.30326 

65 

0.69674 

9.99140 

38 

6 

0 .3.  : 

M C 

23 

9.29529 

63 

9.30391 

65 

0.69609 

9.99137 

37 

7.5 

24 

9.29591 

62 

9.30457 

66 

65 

0.69543 

9.99135 

36 

9 

8.5  j 

Q fi 

25 

9.29654 

60 

9.30522 

0.69478 

9.99132 

35 

10 

10.7  j 

26 

9.29716 

62 

9.30587 

65 

0.69413 

9.99130 

34 

20 

21.3 

27 

9.29779 

63 

9.30652 

65 

0.69348 

9.99127 

33 

30 

32.0 

28 

9.29841 

62 

9.30717 

65 

0.69283 

9.99124 

32 

40 

42.7 

29 

9.29903 

62 

no 

9.30782 

65 

64 

0.69218 

9.99122 

31 

50 

53.3 

30 

9.29966 

DO 

9.30846 

vr± 

0.69154 

9.99119 

30 

31 

9.30028 

62 

9.30911 

65 

0.69089 

9.99117 

29 

62 

32 

9.30090 

62 

9.30975 

64 

0.69025 

9.99114 

28 

6 

6.2 

33 

9.30151 

61 

9.31040 

65 

0.68960 

9.99112 

27 

7 

7.2 

34 

9.30213 

62 

9.31104 

64 

64 

0.68896 

9.99109 

26 

8 

8.3 

35 

9.30275 

62 

9.31168 

Cr± 

/»r 

0.68832 

9.99106 

25 

y 

10 

y.o 
10  8 

36 

9.30336 

61 

9.31233 

65 

0.68767 

9.99104 

24 

J.U 

90 

1U.O 

90  7 

37 

9.30398 

62 

9.31297 

64 

0.68703 

9.99101 

23 

ZU 

Qfk 

ZU.  1 

31.0 

38 

9.30459 

61 

9.31361 

64 

0.68639 

9.99099 

22 

OU 

40 

41.3 

39 

9.30521 

62 

61 

9.31425 

64 

64 

0.68575 

9.99096 

21 

1U 

50 

51.7 

40 

9.30582 

9.31489 

0.68511 

9.99093 

20 

41 

9.30643 

61 

9.31552 

63 

0.68448 

9.99091 

19 

60 

42 

9.30704 

61 

9.31616 

64 

0.68384 

9.99088 

18 

6 

6.0 

43 

9.30765 

61 

9.31679 

63 

0.68321 

9.99086 

17 

7 

7.0 

44 

9.30826 

61 

9.31743 

64 

63 

0.68257 

9.99083 

16 

8 

8.0 

45 

9.30887 

61 

9.31806 

0.68194 

9.99080 

15 

9 

9.0 

46 

9.30947 

60 

9.31870 

64 

0.68130 

9.99078 

14 

1U 

1U.U 

47 

9.31008 

61 

9.31933 

63 

0.68067 

9.99075 

13 

20 

20.0 

48 

9.31068 

60 

9.31996 

63 

0.68004 

9.99072 

12 

30 

30.0 

49 

9.31129 

61 

V»A 

9.32059 

63 

63 

0.67941 

9.99070 

11 

40 

*0 

40.0 

fiO  0 

50 

9.31189 

oU 

9.32122 

0.67878 

9.99067 

10 

51 

9.31250 

61 

9.32185 

63 

0.67815 

9.99064 

9 

3 

52 

9.31310 

60 

9.32248 

63 

0.67752 

9.99062 

8 

< 

5 

0.3 

53 

9.31370 

60 

9.32311 

63 

0.67689 

9.99059 

7 

1 

7 

0.4 

54 

9.31430 

60 

AH 

9.32373 

62 

63 

0.67627 

9.99056 

6 

8 

0.4 

55 

9.31490 

bU 

9.32436 

0.67564 

9.99054 

5 

. ( 

3 

0.5 

56 

9.31549 

59 

9.32498 

62 

0.67502 

: 9.99051 

4 

10 

0.5 

57 

9.31609 

60 

9.32561 

63 

0.67439 

9.99048 

3 

20 

1.0 

58 

9.31669 

60 

9.32623 

62 

0.67377 

9.99046 

i 2 

30 

1.5 

1 59 

9.31728 

59 

' AH 

9.32685 

62 

62 

0.67315 

i 9.99043 

1 

40 

2.0 

9 

60 

9.31788 

r 60 

9.32747 

0.67253 

; 9.99040 

i 0 

OU 

Z.D 

I 

L.  Cos 

d. 

L.  Cotg 

d.  c. 

L.Tang 

L.  Sin. 

t 

P 

. P 

65 

6.5 

7.6 

8.7 

9.8 


63 

6.3 

7.4 

8.4 

9.5 

10.5 

21.0 

31.5 
42.0 

52.5 

6i 

6.1 

7.1 

8.1 

9.2 

10.2 

20.3 

30.5 

40.7 

50.8 

59 

5.9 

6.9 

7.9 

8.9 
9.8 

19.7 

29.5 

39.3 

49.2 

2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.7 

1.0 

1.3 

1.7 


78° 


504 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


12° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

9.31788 

9.32747 

0.67253 

9.99040 

60 

1 

9.31847 

59 

9.32810 

63 

0.67190 

9.99038 

59 

DO 

62 

2 

9.31907 

60 

9.32872 

62 

0.67128 

9.99035 

58 

6 

6.3 

ff  A 

6.2 

3 

9.31966 

59 

9.32933 

61 

0.67067 

9.99032 

57 

7 

7.4 

7.2  j 

4 

9.32025 

59 

59 

9.32995 

62 

62 

0.67005 

9.99030 

56 

8 

9 

8.4 

9.5 

8.3 

9.3  ' 

5 

9.32084 

9.33057 

0.66943 

9.99027 

55 

10 

10*5 

io!3 

6 

9.32143 

59 

9.33119 

62 

0.66881 

9.99024 

54 

20 

21.0 

20.7 

7 

9.32202 

59 

9.33180 

61 

0.66820 

9.99022 

53 

30 

31.5 

31.0 

8 

9.32261 

59 

9.33242 

62 

0.66758 

9.99019 

52 

40 

42.0 

41.3 

9 

9.32319 

58 

9.33303 

61 

62 

0.66697 

9.99016 

51 

50 

52.5 

51.7 

10 

9.32378 

9.33365 

0.66635 

9.99013 

50 

11 

9.32437 

59 

9.33426 

61 

0.66574 

9.99011 

49 

61 

60 

12 

9.32495 

58 

9.33487 

61 

0.66513 

9.99008 

48 

6 

6.1 

6.0 

13 

9.32553 

58 

9.33548 

61 

0.66452 

9.99005 

47 

7 

7.1 

7.0 

14 

9.32612 

59 

58 

9.33609 

61 

61 

0.66391 

9.99002 

46 

8 

Q 

8.1 
Q O 

8.0 
. Q A 

15 

9.32670 

9.33670 

0.66330 

9.99000 

45 

y 

10 

y.z 

10.2 

y.u 

10.0 

16 

9.32728 

58 

9.33731 

61 

0.66269 

9.98997 

44 

20 

on  q 

20.0 

17 

9.32786 

58 

9.33792 

61 

0.66208 

9.98994 

43 

30 

so  5 

30.0 

18 

9.32844 

58 

9.33853 

61 

0.66147 

9.98991 

42 

40 

407 

4o!o 

19 

9.32902 

58 

9.33913 

60 

61 

0.66087 

9.98989 

41 

50 

50^8 

5o!o 

20 

9.32960 

9.33974 

0.66026 

9.98986 

40 

21 

9.33018 

58 

9.34034 

60 

0.65966 

9.98983 

39 

59 

22 

9.33075 

57 

9.34095 

61 

0.65905 

9.98980 

38 

6 

5.9 

23 

9.33133 

58 

9.34155 

60 

0.65845 

9.98978 

37 

7 

6.9 

24 

9.33190 

57 

9.34215 

60 

61 

0.65785 

9.98975 

36 

8 

7.9 

25 

9.33248 

Oo 

9.34276 

0.65724 

9.98972 

35 

9 

1 A 

8.9 

Q Q 

26 

9.33305 

57 

9.34336 

60 

0.65664 

9.98969 

34 

10 

OA 

y.s 

in  7 

27 

9.33362 

57 

9.34396 

60 

0.65604 

9.98967 

33 

20 

QA 

iy.7 

on 

28 

9.33420 

58 

9.34456 

60 

0.65544 

9.98964 

32 

30 

zy.o 

on  o 

29 

9.33477 

57 

9.34516 

60 

60 

0.65484 

9.98961 

31 

40 

Aft 

i oy .6 
1 4Q  9 

30 

9.33534 

O/ 

9.34576 

0.65424 

9.98958 

30 

31 

9.33591 

57 

9.34635 

59 

0.65365 

9.98955 

29 

58 

57 

32 

9.33647 

56 

9.34695 

60 

0.65305 

9.98953 

28 

6 

5.8 

5.7 

33 

9.33704 

57 

9.34755 

60 

0.65245 

9.98950 

27 

7 

6.8 

6.7 

34 

9.33761 

57 

57 

9.34814 

59 

60 

0.65186 

9.98947 

26 

8 

7.7 

7.6 

35 

9.33818 

9.34874 

0.65126 

9.98944 

25 

9 

8.7 

8.6 

36 

9.33874 

56 

9.34933 

59 

0.65067 

9.98941 

24 

10 

9.7 

9.5 

37 

9.33931 

57 

9.34992 

59 

0.65008 

9.98938 

23 

20 

19.3 

19.0 

38 

9.33987 

56 

9.35051 

59 

0.64949 

9.98936 

22 

30 

29.0 

28.5 

39 

9.34043 

56 

9.35111 

60 

fSQ 

0.64889 

9.98933 

21 

40 

50 

38.7 

AQ  Q 

38.0 

47.5 

40 

9.34100 

0/ 

9.35170 

V** 

0.64830 

9.98930 

20 

41 

9.34156 

56 

9.35229 

59 

0.64771 

9.98927 

19 

56 

55 

42 

9.34212 

56 

9.35288 

59 

0.64712 

9.98924 

18 

6 

5.6 

5.5 

43 

9.34268 

56 

9.35347 

59 

0.64653 

9.98921 

17 

7 

6.5 

6.4 

44 

9.34324 

56 

56 

9.35405 

58 

59 

0.64595 

9.98919 

16 

8 

7.5 

7.3 

45 

9.34380 

9.35464 

0.64536 

9.98916 

15 

9 

8.4 

8.3 

46 

9.34436 

56 

9.35523 

59 

0.64477 

9.98913 

14 

10 

9.3 

9.2 

47 

9.34491 

55 

9.35581 

58 

0.64419 

9.98910 

13 

20 

18.7 

.18.3 

48 

9.34547 

56 

9.35640 

59 

0.64360 

9.98907 

12 

30 

28.0 

27.5 

49 

9.34602 

55 

9.35698 

58 

0.64302 

9.98904 

11 

40 

37.3 

36.7 

59 

50 

45.8 

50 

9.34658 

oo 

9.35757 

0.64243 

9.98901 

10 

4:0.  t 

51 

9.34713 

55 

9.35815 

58 

0.64185 

9.98898 

9 

3 

2 

52 

9.34769 

56 

9.35873 

58 

0.64127 

9.98896 

8 

a 

0.3 

0.2 

53 

9.34824 

55 

9.35931 

58 

0.64069 

9.98893 

7 

7 

0.4 

0.2 

54 

9.34879 

55 

55 

9.35989 

58 

58 

0.64011 

9.98890 

6 

8 

0.4 

0.3 

55 

9.34934 

9.36047 

0.63953 

9.98887 

5 

9 

0.5 

0.3 

56 

9.34989 

55 

9.36105 

58 

0.63895 

9.98884 

4 

10 

0.5 

0.3 

57 

9.35044 

55 

9.36163 

58 

0.63837 

9.98881 

3 

20 

1.0 

0.7 

58 

9.35099 

55 

9.36221 

58  ■ 

0.63779 

9.98878 

2 

30 

1.5 

1.0 

59 

9.35154 

55 

9.36279 

58 

0.63721 

9.98875 

1 

40 

2.0 

1.3 

55 

57 

1.7 

60 

9.35209 

9.36336 

0.63664 

9.98872 

0 

i ou 

A.  0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

t 

P.  P. 

77° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

13° 


505 


r 

L.  Sin. 

0 

9.35209 

1 

9.35263 

2 

9.35318 

3 

9.35373 

4 

9.35427 

5 

9.35481 

6 

9.35536 

7 

9.35590 

8 

9.35644 

9 

9.35698 

10 

9.35752 

11 

9.35806 

12 

9.35860 

13 

9.35914 

14 

9.35968 

15 

9.36022 

16 

9.36075 

17 

9.36129 

18 

9.36182 

19 

9.36236 

20 

9.36289 

21 

9.36342 

22 

9.36395 

23 

9.36449 

24 

9.36502 

25 

9.36555 

26 

9.36608 

27 

9.36660 

28 

9.36713 

29 

9.36766 

30 

9.36819 

31 

9.36871 

32 

9.36924 

33 

9.36976 

34 

9.37028 

35 

9.37081 

36 

9.37133 

37 

9.37185 

38 

9.37237 

39 

9.37289 

40 

9.37341 

41 

9.37393 

42 

9.37445 

43 

9.37497 

44 

9.37549 

45 

9.37600 

46 

9.37652 

47 

9.37703 

48 

9.37755 

49 

9.37806 

50 

9.37858 

51 

9.37909 

52 

9.37960 

53 

9.38011 

54 

9.38062 

55 

9.38113 

56 

9.38164 

57 

9.38215 

58 

9.38266 

59 

9.38317 

60 

9.38368 

L.  Cos. 

d. 


54 

55 
55 
54 

54 

55 
54 
54 
54 
54 
54 
54 
54 
54 
54 

53 

54 

53 

54 
53 
53 

53 

54 
53 
53 
53 

52 

53 
53 
53 

52 

53 
52 

52 

53 
52 
52 
52 
52 
52 
52 
52 
52 
52 

51 

52 

51 

52 

51 

52 
51 
51 
51 
51 
51 
51 
51 
51 
51 


d. 


L.Tang.  6 

9.36336 

9.36394 

9.36452 

9.36509 

9.36566 

9.36624 

9.36681 

9.36738 

9.36795 

9.36852 

9.36909 

9.36966 

9.37023 

9.37080 

9.37137 

9.37193 

9.37250 

9.37306 

9.37363 

9.37419 

9.37476 

9.37532 

9.37588 

9.37644 

9.37700 

9.37756 

9.37812 

9.37868 

9.37924 

9.37980 

9.38035 

9.38091 

9.38147 

9.38202 

9.38257 

9.38313 

9.38368 

9.38423 

9.38479 

9.38534 

9.38589 

9.38644 

9.38699 

9.38754 

9.38808 

9.38863 

9.38918 

9.38972 

9.39027 

9.39082 

9.39136 

9.39190 

9.39245 

9.39299 

9.3935a 

9.39407 

9.39461 

9.39515 

9.39569 

9.39623 

9.39677 

L.  Cotg. 

d.c. 

58 

58 

57 

57 

58 
57 
57 
57 
57 
57 
57 
57 
57 
57 

56 

57 

56 

57 

56 

57 
56 
56 
56 
56 
56 
56 
56 
56 
56 

55 

56 
56 
55 

55 

56 
55 

55 

56 
55 
55 
55 
55 
55 

54 

55 
55 

54 

55 
55 
54 

54 

55 
54 
54 
54 
54 
54 
54 
54 


L.  Cotg. 

L.  Cos. 

0.63004 

9.98872 

60 

0.63606 

9.98869 

59 

0.63548 

9.98867 

58 

0.63491 

9.98864 

57 

0.63434 

9.98861 

56 

0.63376 

9.98858 

55 

0.63319 

9.98855 

54 

0.63262 

9.98852 

53 

0.63205 

9.98849 

52 

0.63148 

9.98846 

51 

0.63091 

9.98843 

50 

0.63034 

9.98840 

49 

0.62977 

9.98837 

48 

0.62920 

9.98834 

47 

0.62863 

9.98831 

46 

0.62807 

9.98828 

45 

0.62750 

9.98825 

44 

0.62694 

9.98822 

43 

0.62637 

9.98819 

42 

0.62581 

9.98816 

41 

0.62524 

9.98813 

40 

0.62468 

9.98810 

39 

0.62412 

9.98807 

38 

0.62356 

9.98804 

37 

0.62300 

9.98801 

36 

0.62244 

9.98798 

35 

0.62188 

9.98795 

34 

0.62132 

9.98792 

33 

0.62076 

9.98789 

32 

0.62020 

9.98786 

31 

0.61965 

9.98783 

30 

0.61909 

9.98780 

29 

0.61853 

9.98777 

28 

0.61798 

9.98774 

27 

0.61743 

9.98771 

26 

0.61687 

9.98768 

25 

0.61632 

9.98765 

24 

0.61577 

9.98762 

23 

0.61521 

9.98759 

22 

0.61466 

9.98756 

21 

0.61411 

9.98753 

20 

0.61356 

9.98750 

19 

0.61301 

9.98746 

18 

0.61246 

9.98743 

17 

0.61192 

9.98740 

16 

0.61137 

9.98737 

15 

0.61082 

9.98734 

14 

0.61028 

9.98731 

13 

0.60973 

9.98728 

12 

0.60918 

9.98725 

11 

0.60864 

9.98722 

10 

0.60810 

9.98719 

9 

0.60755 

i 9.98715 

8 

0.60701 

9.98712 

7 

0.60647 

’ 9.98709 

6 

0.60593 

1 9.98706 

5 

0.6053S 

1 9.98703 

: 4 

0.60485 

1 9.98700 

i 3 

0.60431 

L 9.98697 

' 2 

0.60377 

t 9.98694 

l 1 

0.6032; 

1 9.9869C 

) 0 

3.  L.Tang 

r.  L.  Sin, 

/ 

P.  P. 


58 

5.8 

6.8 

7.7 

8.7 

9.7 

19.3 

29.0 

38.7 

48.3 

56 

5.6 

6.5 

7.5 
8.4 
9.3 

18.7 

28.0 

37.3 

46.7 


57 

5.7 

6.7 

7.6 

8.6 

9.5 

19.0 

28.5 

38.0 

47.5 

55 

5.5 
6.4 

7.3 

8.3 
9.2 

18.3 

27.5 

36.7 

45.8 


6 

7 

8 
9 

10 

20 

30 

40 

50 


54 

5.4 

6.3 

7.2 

8.1 

9.0 

18.0 

27.0 

36.0 

45.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


53 

5.3 

6.2 

7.1 
8.0 
8.8 

17.7 

26.5 
35.3 
44.2 

51 

5.1 
6.0 
6.8 
7.7 

8.5 

17.0 

25.5 

34.0 

42.5 

3 

0.3 

0.4 

0.4 

0.5 

0.5 

1.0 

1.5 

2.0 

2.5 


52 

5.2 

6.1 

6.9 

7.8 

8.7 

17.3 
26.0 
34.7 

43.3 

4 

0.4 

0.5 

0.5 

0.6 

0.7 

1.3 

2.0 

2.7 

3.3 

2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.7 

1.0 

1.3 

1.7 


P.  P. 


76 


506  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


14° 


t 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P 

0 

9.38368 

9.39677 

0.60323 

9.98690 

60 

1 

9.38418 

50 

9.39731 

54 

0.60269 

9.98687 

3 

59 

2 

9.38469 

51 

9.39785 

54 

0.60215 

9.98684 

3 

58 

3 

9.38519 

50 

9.39838 

53 

0.60162 

9.98681 

3 

57 

54 

53 

4 

9.38570 

51 

50 

9.39892 

54 

53 

0.60108 

9.98678 

3 

q 

56 

6 

7 

5.4 

6.3 

5.3 

fi  9 

5 

9.38620 

9.39945 

0.60055 

9.98675 

6 

55 

8 

in 

7.1 

6 

9.38670 

50 

9.39999 

54 

0.60001 

9.98671 

4 

54 

9 

8.1 

8*0 

7 

9.38721 

51 

9.40052 

53 

0.59948 

9.98668 

3 

53 

10 

9.0 

8.8 

8 

9.38771 

50 

9.40106 

54 

0.59894 

9.98665 

3 

52 

20 

18.0 

ii.7 

9 

9.38821 

50 

50 

9.40159 

53 

53 

0.59841 

9.98662 

3 

q 

51 

30 

27.0 

26.5 

10 

9.38871 

9.40212 

0.59788 

9.98659 

o 

50 

40 

36.0 

35.3 

11 

9.38921 

50 

9.40266 

54 

0.59734 

9.98656 

3 

49 

50 

45.0 

44.2 

12 

9.38971 

50 

9.40319 

53 

0.59681 

9.98652 

4 

48 

13 

9.39021 

50 

9.40372 

53 

0.59628 

9.98649 

3 

47 

14 

9.39071 

50 

50 

9.40425 

53 

53 

0.59575 

9.98646 

3 

q 

46 

52 

51 

15 

9.39121 

9.40478 

0.59522 

9.98643 

6 

45 

6 

5.2 

5.1 

16 

9.39170 

49 

9.40531 

53 

0.59469 

9.98640 

3 

44 

7 

6.1 

6.0 

17 

9.39220 

50 

9.40584 

53 

0.59416 

9.98636 

4 

43 

8 

6.9 

6.8 

18 

9.39270 

50 

9.40636 

52 

0.59364 

9.98633 

3 

42 

9 

7.8 

7.7 

19 

9.39319 

49 

50 

9.40689 

53 

53 

0.59311 

9.98630 

3 

q 

41 

10 

8.7 

8.5 

20 

9.39369 

9.40742 

0.59258 

9.98627 

o 

40 

20 

17.3 

17.0 

21 

9.39418 

49 

9.40795 

53 

0.59205 

9.98623 

4 

39 

30 

26.0 

25.5 

22 

9.39467 

49 

9.40847 

52 

0.59153 

9.98620 

3 

38 

40 

34.7 

34.0 

23 

9.39517 

50 

9.40900 

53 

0.59100 

9.98617 

3 

37 

50 

43.3 

42.5 

24 

9.39566 

49 

9.40952 

52 

0.59048 

9.98614 

3 

36 

49 

53 

A 

25 

9.39615 

9.41005 

0.58995 

9.98610 

35 

26 

9.39664 

49 

9.41057 

52 

0.58943 

9.98607 

3 

34 

50 

49 

27 

9.39713 

49 

9.41109 

52 

0.58891 

9.98604 

3 

33 

6 

5.0 

4.9 

28 

9.39762 

49 

9.41161 

52 

0.58839 

9.98601 

3 

32 

7 

5.8 

5.7 

29 

9.39811 

49 

49 

9.41214 

53 

52 

0.58786 

9.98597 

4 

q 

31 

8 

6.7 

6.5 

30 

9.39860 

9.41266 

0.58734 

9.98594 

o 

30 

9 

7 .5 

7.4 

31 

9.39909 

49 

9.41318 

52 

0.58682 

9.98591 

3 

29 

10 

8.3 

8.2 

32 

9.39958 

49 

9.41370 

52 

0.58630 

9.98588 

3 

28 

20 

16.7 

16.3 

33 

9.40006 

48 

9.41422 

52 

0.58578 

9.98584 

4 

27 

30 

25.0 

24.5 

34 

9.40055 

49 

48 

9.41474 

52 

52 

0.58526 

9.98581 

3 

q 

26 

40 

50 

66.6 

41.7 

32.7 

40.8 

35 

9.40103 

9.41526 

0.58474 

9.98578 

o 

25 

36 

9.40152 

49 

9.41578 

52 

0.58422 

9.98574 

4 

24 

37 

9.40200 

48 

9.41629 

51 

0.58371 

9.98571 

3 

23 

38 

9.40249 

49 

9.41681 

52 

0.58319 

9.98568 

3 

22 

48 

47 

39 

9.40297 

48 

9.41733 

52 

0.58267 

9.98565 

3 

21 

6 

4.8 

4.7 

49 

51 

A 

I *7 

E K 

40 

9.40346 

9.41784 

0.58216 

9.98561 

20 

/ 

Q 

0.0 
ft  d 

0.0 

41 

9.40394 

48 

9.41836 

52 

0.58164 

9.98558 

3 

19 

O 

Q 

u.i 
7 9 

0.0 
7 i 

42 

9.40442 

48 

9.41887 

51 

0.58113 

9.98555 

3 

18 

10 

/ .z 
q ft 

/.i 
7 S 

43 

9.40490 

48 

9.41939 

52 

0.58061 

9.98551 

4 

17 

iU 

90 

o.U 
1ft  ft 

/ .o 
i f;  7 

44 

9.40538 

48 

48 

9.41990 

51 

51 

0.58010 

9.98548 

3 

q 

16 

ZA) 

30 

10.0 

24.0 

19.  / 

23.5 

45 

9.40586 

9.42041 

0.57959 

9.98545 

6 

15 

40 

32.0 

31.3 

46 

9.40634 

48 

9.42093 

52 

0.57907 

9.98541 

4 

14 

50 

40.0 

39.2 

47 

9.40682 

48 

9.42144 

51 

0.57856 

9.98538 

3 

13 

48 

9.40730 

48 

9.42195 

51 

0.57805 

9.98535 

3 

12 

49 

9.40778 

48 

47 

9.42246 

51 

51 

0.57754 

9.98531 

4 

q 

11 

A 

9 

50 

9.40825 

9.42297 

0.57703 

9.98528 

o 

10 

6 

0.4 

V 

0.3 

51 

9.40873 

48 

9.42348 

51 

0.57652 

9.98525 

3 

9 

7 

0.5 

0.4 

52 

9.40921 

48 

9.42399 

51 

0.5760L 

9.98521 

4 

8 

8 

0.5 

0.4 

53 

9.40968 

47 

9.42450 

51 

0.57550 

9.98518 

3 

7 

9 

0.6 

0.5 

54 

9.41016 

48 

47 

9.42501 

51 

51 

0.57499 

9.98515 

3 

A 

6 

10 

0.7 

0.5 

55 

9.41063 

9.42552 

0.57448 

9.98511 

' 5 

20 

1.3 

1.0 

56 

9.41111 

48 

9.42603 

51 

0.57397 

9.98508 

3 

4 

30 

2.0 

1.5 

57 

9.41158 

47 

9.42653 

50 

0.57347 

9.98505 

3 

3 

40 

2.7 

2.0 

58 

9.41205 

47 

9.42704 

51 

0.57296 

9.98501 

4 

2 

50 

3.3 

2.5 

59 

9.41252 

47 

48 

9.42755 

51 

50 

0.57245 

9.98498 

3 

A 

1 

60 

9.41300 

9.42805 

0.57195 

9.98494 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

t 

P.  P. 

75° 


logarithms  of  trigonometric  functions. 


507 


' ] 

Li.  Sin.  6 

o (. 

141300  . 

1 < 

141347  \ 

2 1 

141394  4 

3 1 

141441  4 

4 ' 

141488  4 

5 1 

141535  . 

1 6 1 

141582  4 

1 7 1 

9.41628  ; 

8 1 

9.41675 

9 

9.41722  ; 

10 

9.41768 

11 

9.41815 

12 

9.41861 

13 

9.41908  ; 

14 

9.41954  ; 

15 

9.42001 

16 

9.42047 

17 

9.42093 

18 

9.42140 

19 

9.42186 

20 

9.42232 

21 

9.42278 

22 

9.42324 

23 

9.42370 

24 

9.42416 

25 

9.42461 

26 

9.42507 

27 

9.42553 

28 

9.42599 

29 

9.42644 

30 

9.42690 

31 

9.42735 

32 

9.42781 

33 

9.42826 

34 

9.42872 

35 

9.42917 

36 

9.42962 

37 

9.43008 

38 

9.43053 

39 

9.43098 

40 

0.43143 

41 

9.43188 

42 

9.43233 

43 

9.43278 

44 

9.43323 

45 

' 9.43367 

46 

9.43412 

47 

9.43457 

48 

9.43502 

49 

9.43546 

50 

“ 9.43591 

51 

9.43635 

52 

9.43680 

53 

9.43724 

54 

9.43769 

55 

~ 9.43813 

56 

9.43857 

57 

9.43901 

58 

9.43946 

59 

i 9.43990 

60 

i 9.44034 

| 

L.  Cos. 

L.Tang. 


9.42805 

9.42856 

9.42906 

9.42957 

9.43007 


9.43057 

9.43108 

9.43158 

9.43208 

9.43258 


9.43308 

9.43358 

9.43408 

9.43458 

9.43508 


46 

46 

46 

46 

46 

45 

46 
46 
46 

45 

46 

45 

46 

45 

46 
45 

45 

46 
45 
45 
45 
45 
45 
45 
45 

44 

45 
45 
45 

44 

45 

44 

45 

44 

45 
44 
44 

44 

45 
44 
44 


9.43558 

9.43607 

9.43657 

9.43707 

9.43756 

9.43806 

9.43855 

9.43905 

9.43954 

9.44004 


d.  c. 


9.44053 

9.44102 

9.44151 

9.44201 

9.44250 


9.44299 

9.44348 

9.44397 

9.44446 

9.44495 


9.44544 

9.44592 

9.44641 

9.44690 

9.44738 


9.44787 

9.44836 

9.44884 

9.44933 

9.44981 


9.45029 

9.45078 

9.45126 

9.45174 

9.45222 


9.45271 

9.45319 

9.45367 

9.45415 

9.45463 


51 

50 

51 
50 

50 

51 
50 
50 
50 
50 
50 
50 
50 
50 
50 

49 

50 
50 

49 

50 

49 

50 

49 

50 
49 
49 

49 

50 
49 
49 
49 
49 
49 
49 
49 

48 

49 
49 

48 

49 
49 

48 

49 
48 

48 

49 


9.45511 

9.45559 

9.45606 

9.45654 

9.45702 


9.45750 


d.  L.  Cotg 


L.  Cotg.  1 

Li.  Cos.  d 

1157195 

9.98494  Q 

0.57144 

9.98491  * 

0.57094 

9.98488  6. 

0.57043 

9.98484  % 

0.56993 

9.98481  « 

0.56943 

9.98477  Q 

0.56892 

9.98474  % 

0.56842 

9.98471  « 

0.56792 

9.98467  4 

0.56742 

9.98464  ‘ 

0.56692 

9.98460  f 

0.56642 

9.98457  * 

0.56592 

9.98453  ; 

0.56542 

9.98450  i 

0.56492 

9.98447  ; 

0.56442 

9.98443  , 

0.56393 

9.98440  1 

0.56343 

9.98436  : 

0.56293 

9.98433  1 

0.56244 

9.98429  ; 

0.56194 

9.98426 

0.56145 

9.98422 

0.56095 

9.98419 

0.56046 

9.98415 

0.55996 

9.98412 

0.55947 

9.98409 

0.55898 

9.98405 

0.55849 

9.98402 

0.55799 

9.98398 

0.55750 

9.98395 

0.55701 

9.98391 

0.55652 

9.98388 

0.55603 

9.98384 

0.55554 

9.98381 

0.55505 

9.98377 

0.55456 

9.98373 

0.55408 

9.98370 

0.55359 

9.98366 

0.55310 

9.98363 

0.55262 

9.98359 

0.55213 

9.98356 

0.55164 

9.98352 

0.55116 

9.98349 

0.55067 

9.98345 

0.55019 

9.98342 

0.54971 

9.98338 

1 0.54922 

9.98334 

’ 0.54874 

9.98331 

’ 0.54826 

9.98327 

1 0.54778 

9.98324 

1 0.54729 

9.98320 

1 0.54681 

9.98317 

* 0.54633 

9.98313 

* 0.54585 

, 9.98309 

\ 0.54537 

9.98306 

5 0.54488 

> 9.98302 

3 0.54441 

. 9.98299 

7 0.5439-1 

t 9.98295 

l 0.5434( 

> 9.98291 

5 0.5429* 

5 9.98288 

8 0.5425( 

) 9.98284 

c.  L.Tang 

r.  L.  Sin. 

60 

59 

58 

57 

56_ 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

_31 

30 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 
11 

10 

9 


d. 


P.  P. 


51 

50 

6 

5.1 

5.0 

7 

6.0 

5.8 

8 

6.8 

6.7 

9 

7.7 

7.5 

10 

8.5 

8.3 

20 

17.0 

16.7 

30 

25.5 

25.0 

40 

34.0 

33.3 

50 

42.5 

41.7 

49 

48 

6 

4.9 

4.8 

7 

5.7 

5.6 

8 

6.5 

6.4 

9 

7.4 

7.2 

10 

8.2 

8.0 

20 

16.3 

16.0 

30 

24.5 

24.0 

40 

32.7 

32.0 

50 

40.8 

40.0 

47 

46 

6 

4.7 

4.a 

7 

5.5 

5.4 

8 

6.3 

6.1 

9 

7.1 

6.9 

10 

7.8 

7.7 

20 

15.7 

15.3 

30 

23.5 

23.0 

40 

31.3 

30.7 

50 

39.2 

38.3 

45 

4.5 
5.3 
6.0 
6.8 

7.5 
15.0 
22.5 


44 

4.4 

5.1 

5.9 

6.6 

7.8 

14.7 

22.0 


30.0  29.3 
37.5  36.7 


4 

0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


3 

0.3 

0.4 

0.4 

0.5 

0.5 

1.0 

1.5 

2.0 

2.5 


P.  P. 


74 


508 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


16° 


f 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P 

0 

9.44034 

9.45750 

0.54250 

9.98284 

60 

1 

9.44078 

44 

9.45797 

47 

0.54203 

9.98281 

3 

59 

2 

9.44122 

44 

9.45845 

48 

0.54155 

9.98277 

4 

58 

48 

A O 

3 

9.44166 

44 

9.45892 

47 

0.54108 

9.98273 

4 

57 

47 

A *7 

4 

9.44210 

44 

43 

9.45940 

48 

47 

0.54060 

9.98270 

3 

A 

56 

6 

7 

4.8 

5.6 

4.7 

5.5 

5 

9.44253 

9.45987 

0.54013 

9.98266 

4 

55 

8 

6!4 

6^3 

6 

9.44297 

44 

9.46035 

48 

0.53965 

9.98262 

4 

54 

9 

7.2 

7.1 

7 

9.44341 

44 

9.46082 

47 

0.53918 

9.98259 

3 

53 

10 

8.0 

7.8 

8 

9.44385 

44 

9.46130 

48 

0.53870 

9.98255 

4 

52 

20 

16.0 

15.7 

9 

9.44428 

43 

44 

9.46177 

47 

0.53823 

9.98251 

4 

q 

51 

30 

24.0 

23.5 

10 

9.44472 

9.46224 

4/ 

0.53776 

9.98248 

o 

50 

40 

32.0 

31.3 

11 

9.44516 

44 

9.46271 

47 

0.53729 

9.98244 

4 

49 

50 

40.0 

39.2 

12 

9.44559 

43 

9.46319 

48 

0.53681 

9.98240 

4 

48 

13 

9.44602 

43 

9.46366 

47 

0.53634 

9.98237 

3 

47 

14 

9.44646 

44 

AO 

9.46413 

47 

0.53587 

9.98233 

4 

A 

46 

46 

45 

15 

9.44689 

9.46460 

4/ 

0.53540 

9.98229 

4 

45 

6 

4.6 

4.5 

16 

9.44733 

44 

9.46507 

47 

0.53493 

9.98226 

3 

44 

7 

5.4 

5.3 

17 

9.44776 

43 

9.46554 

47 

0.53446 

9.98222 

4 

43 

8 

6.1 

6.0 

18 

9.44819 

43 

9.46601 

47 

0.53399 

9.98218 

4 

42 

9 

6.9 

6.8 

19 

9.44862 

43 

43 

9.46648 

47 

0.53352 

9.98215 

3 

A 

41 

10 

7.7 

7.5 

20 

9.44905 

9.46694 

40 

0.53306 

9.98211 

4 

40 

20 

15.3 

15.0 

21 

9.44948 

43 

9.46741 

47 

0.53259 

9.98207 

4 

39 

30 

23.0 

22.5 

22 

9.44992 

44 

9.46788 

47 

0.53212 

9.98204 

3 

38 

40 

30.7 

30.0 

23 

9.45035 

43 

9.46835 

47 

0.53165 

9.98200 

4 

37 

50 

38.3 

37.5 

24 

9.45077 

42 

A Q 

9.46881 

46 

0.53119 

9.98196 

4 

A 

36 

25 

9.45120 

9.46928 

4/ 

0.53072 

9.98192 

4 

35 

26 

9.45163 

43 

9.46975 

47 

0.53025 

9.98189 

3 

34 

44 

43 

27 

9.45206 

43 

9.47021 

46 

0.52979 

9.98185 

4 

33 

6 

4.4 

4.3 

28 

9.45249 

43 

9.47068 

47 

0.52932 

9.98181 

4 

32 

7 

5.1 

5.0 

29 

9.45292 

43 

AO 

9.47114 

46 

An 

0.52886 

9.98177 

4 

q 

31 

8 

5.9 

5.7 

30 

9.45334 

9.47160 

4o 

0.52840 

9.98174 

o 

30 

9 

6.6 
*1  O 

6.5 

31 

9.45377 

43 

9.47207 

47 

0.52793 

9.98170 

4 

29 

10 

OA 

7.0 

-f  A hr 

7.2 

1/IO 

32 

9.45419 

42 

9.47253 

46 

0.52747 

9.98166 

4 

28 

20 

14.7 

14.3 

33 

9.45462 

43 

9.47299 

46 

0.52701 

9.98162 

4 

27 

30 

22.0 

21.5 

no  17 

34 

9.45504 

42 

9.47346 

47 

0.52654 

9.98159 

3 

A 

26 

40 

50 

29.3 

36.7 

28.7 

35.8 

35 

9.45547 

40 

9.47392 

40 

0.52608 

9.98155 

4 

25 

36 

9.45589 

42 

9.47438 

46 

0.52562 

9.98151 

4 

24 

37 

9.45632 

43 

9.47484 

46 

0.52516 

9.98147 

4 

23 

38 

9.45674 

42 

9.47530 

46 

0.52470 

9.98144 

3 

22 

42 

41 

39 

9.45716 

42 

AO 

9.47576 

46 

A(K 

0.52424 

9.98140 

4 

A 

21 

6 

7 

4.2 

A Q 

4.1 

A 8 

40 

9.45758 

4Z 

9.47622 

40 

0.52378 

9.98136 

4 

20 

g 

4.y 

5.6 

4.0 

5.5 

41 

9.45801 

43 

9.47668 

46 

0.52332 

9.98132 

4 

19 

9 

6.3 

6^2 

42 

9.45843 

42 

9.47714 

46 

0.52286 

9.98129 

3 

18 

10 

7.0 

6.8 

43 

9.45885 

42 

9.47760 

46 

0.52240 

9.98125 

4 

17 

20 

140 

13.7 

44 

9.45927 

42 

AO 

9.47806 

46 

Ad 

0.52194 

9.98121 

4 

A 

16 

30 

2L0 

20i5 

45 

9.45969 

4Z 

9.47852 

40 

0.52148 

9.98117 

15 

40 

28.0 

27.3 

46 

9.46011 

42 

9.47897 

45 

0.52103 

9.98113 

4 

14 

50 

35.0 

34.2 

47 

9.46053 

42 

9.47943 

46 

0.52057 

9.98110 

3 

13 

48 

9.46095 

42 

9.47989 

46 

0.52011 

9.98106 

4 

12 

49 

9.46136 

41 

AO 

9.48035 

46 

AK 

0.51965 

9.98102 

4 

A 

11 

4 

3 

50 

9.46178 

4Z 

9.48080 

40 

0.51920 

9.98098 

‘x 

10 

6 

0.4 

0.3 

51 

9.46220 

42 

9.48126 

46 

0.51874 

9.98094 

4 

9 

7 

0.5 

0.4 

52 

9.46262 

42 

9.48171 

45 

0,51829 

9.98090 

4 

8 

8 

0.5 

0.4 

53 

9.46303 

41 

9.48217 

46 

0.51783 

9.98087 

3 

7 

9 

0.6 

0.5 

54 

9.46345 

42 

41 

9.48262 

45 

45 

0.51738 

9.98083 

4 

4 

6 

10 

0.7 

0.5 

55 

9.46386 

9.48307 

0.51693 

9.98079 

5 

20 

1.3 

1.0 

56 

9.46428 

42 

8.48353 

46 

0.51647 

9.98075 

4 

4 

30 

2.0 

1.5 

57 

9.46469 

41 

9.48398 

45 

0.51602 

9.98071 

4 

3 

40 

2.7 

2.0 

58 

9.46511 

42 

9.48443 

45 

0.51557 

9.98067 

4 

2 

50 

| 3.3 

2.5 

59 

9.46552 

41 

42 

9.48489 

46 

A*\ 

0.51511 

9.98063 

4 

q 

1 

60 

9.46594 

9.48534 

40 

0.51466 

9.98060 

o 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

f 

P.  P. 

73° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

17° 


509 


' 

[j.  Sin. 

d.  I 

,.Tang.  c 

0 

1 

).46594 
). 46635 

41 

{148534 

9.48579 

2 

D.46676 

41 

9.48624 

3 

3.46717 

41 

9.48669 

4 

3.46758 

41 

42 

9.48714 

5 

6 

3.46800 

3.46841 

41 

9.48759 

9.48804 

7 

9.46882 

41 

9.48849 

8 

9.46923 

41 

9.48894 

9 

9.46964 

41 

41 

9.48939 

10 

11 

9.47005 

9.47045 

'll 

40 

9.48984 

9.49029 

12 

9.47086 

41 

9.49073 

13 

9.47127 

41 

9.49118 

14 

9.47168 

41 

41 

9.49163 

15 

16 

9.47209 

9.47249 

‘i-L 

40 

9.49207 

9.49252 

17 

9.47290 

41 

9.49296 

18 

9.47330 

40 

9.49341 

19 

9.47371 

41 

40 

9.49385 

20 

21 

9.47411 

9.47452 

41 

9.49430 

9.49474 

22 

9.47492 

40 

9.49519 

23 

9.47533 

41 

9.49563 

24 

9.47573 

40 

40 

41 

9.49607 

25 

26 

9.47613 

9.47654 

9.49652 

9.49696 

27 

9.47694 

40 

9.49740 

28 

9.47734 

40 

9.49784 

29 

9.47774 

‘ 40 
40 
40 

9.49828 

30 

31 

9.47814 

9.47854 

9.49872 

9.49916 

32 

9.47894 

40 

9.49960 

33 

34 

9.47934 

9.47974 

40 

40 

40 

40 

9.50004 

9.50048 

35 

36 

9.48014 

9.48054 

9.50092 

9.50136 

37 

9.48094 

40 

9.50180 

38 

9.48133 

39 

9.50223 

39 

9.48173 

40 

40 

39 

9.50267 

40 

41 

9.48213 

9.48252 

9.50311 

9.50355 

42 

9.48292 

40 

9.50398 

43 

9.48332 

40 

9.50442 

44 

9.48371 

39 

40 
39 

9.50485 

45 

46 

9.48411 

9.48450 

9.50529 

9.50572 

47 

9.48490 

40 

9.50616 

48 

9.48529 

39 

9.50659 

49 

9.48568 

39 

39 

40 

9.50703 

50 

51 

' 9.48607 
9.48647 

9.50746 

9.50789 

52 

9.48686 

39 

9.50833 

53 

9.48725 

39 

9.50876 

54 

9.48764 

39 

39 

9.50919 

55 

56 

9.48803 

9.48842 

QQ 

l OU 

1 OA 

9.50962” 

9.51005 

57 

9.48881 

39 

9.51048 

58 

9.4892C 

1 

9.51092 

59 

9.4895c 

’ 39 

9.51135 

60 

9.4899* 

» 

9.51178 

L.  Cos 

. 1 d. 

L.  Cotg 

d.c. 


L.  Cotg. 


45 

45 

45 

45 

45 

45 

45 

45 

45 

45 

45 

44 

45 
45 

44 

45 

44 

45 

44 

45 

44 

45 
44 

44 

45 
44 
44 
44 
44 
44 

44 

44 

44 

44 

44 

44 

44 

43 

44 
44 
44 

43 

44 

43 

44 

43 

44 

43 

44 
43 

43 

44 
43 
43 
43 
43 

43 

44 
43 
43 


0.51466 

0.51421 

0.51376 

0.51331 

0.51286 


0.51241 

0.51196 

0.51151 

0.51106 

0.51061 


0.51016 

0.50971 

0.50927 

0.50882 

0.50837 


0.50793 

0.50748 

0.50704 

0.50659 

0.50615 


0.50570 

0.50526 

0.50481 

0.50437 

0.50393 


0.50348 

0.50304 

0.50260 

0.50216 

0.50172 


0.50128 

0.50084 

0.50040 

0.49996 

0.49952 


0.49908 

0.49864 

0.49820 

0.49777 

0.49733 


0.49689 

0.49645 

0.49602 

0.49558 

0.49515 


0.49471 

0.49428 

0.49384 

0.49341 

0.49297 


0.49254 

0.49211 

0.49167 

0.49124 

0.49081 


0.49038 

0.48995 

0.48952 

0.48908 

0.48865 


0.48822 


d.  c.  IL.Tang 


Cos.  d. 


.98060 

.98056 

98052 

98048 

.98044 


98040 

98036 

.98032 

.98029 

98025 


.98021 

98017 

9.98013 

9.98009 

9.98005 


9.98001 

9.97997 

9.97993 

9.97989 

9.97986 


9.97982 

9.97978 

9.97974 

9.97970 

9.97966 


9.97962 

9.97958 

9.97954 

9.97950 

9.97946 


9.97942 

9.97938 

9.97934 

9.97930 

9.97926 


9.97922 

9.97918 

9.97914 

9.97910 

9.97906 


9.97902 

9.97898 

9.97894 

9.97890 

9.97886 


9.97882 

9.97878 

9.97874 

9.97870 

9.97866 


9.97861 

9.97857 

9.97853 

9.97849 

9.97845 


9.97841 

9.97837 

9.97833 

9.97829 

9.97825 


9.97821 


. L.  Sin.  d 


4 

4 

3 

4 
4 
4 
4 
4 
4 
4 
4 
4 
4 

3 

4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 

4 

5 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 


60 

59 

58 

57 

56^ 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 


P.  P. 


45 

4.5 
5.3 
6.0 
6.8 

7.5 

15.0 

22.5 

30.0 

37.5 


44 

4.4 

5.1 

5.9 

6.6 

7.3 

14.7 
22.0 
29.3 

36.7 


43 

4.3 

5.0 

5.7 

6.5 

7.2 

14.3 

21.5 

28.7 

35.8 


42 

4.2 
4.9 
5.6 

6.3 
7.0 

14.0 

21.0 
28.0 
35.0 


40 

4.0 

4.7 
5.3 

6.0 

6.7 

13.3 
20.0 
26.7 

33.3 


41 

4.1 

4.8 

5.5 

6.2 

6.8 

13.7 

20.5 
27.3 
34.2 


39 

3.9 
4.6 
5.2 

5.9 
6.5 

13.0 

19.5 

26.0 

32.5 


11 

5 

4 

3 

JO 

6 

0.5 

0.4 

0.3 

9 

7 

0.6 

0.5 

0.4 

8 

8 

0.7 

0.5 

0.4 

7 

9 

0.8 

0.6 

0.5 

6 

10 

0.8 

0.7 

0.5 

5 

' 20 

1.7 

1.3 

1.0 

4 

30 

2.5 

2.0 

1.5 

40 

3.3 

2.7 

2.0 

0 
2 

1 

50 

4.2 

3.3 

2.5 

0 

t 

P.  P. 

72° 


510  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

18° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

0 

9.48998 

9.51178 

0.48822 

9.97821 

60 

1 

9.49037 

39 

9.51221 

43 

0.48779 

9.97817 

4 

59 

2 

9.49076 

39 

9.51264 

43 

0.48736 

9.97812 

5 

58 

3 

9.49115 

39 

9.51306 

42 

0.48694 

9.97808 

4 

57 

4 

9.49153 

38 

39 

9.51349 

43 

43 

0.48651 

9.97804 

4 

A 

56 

5 

9.49192 

9.51392 

0.48608 

9.97800 

4 

55 

6 

9.49231 

39 

9.51435 

43 

0.48565 

9.97796 

4 

54 

7 

9.49269 

38 

9.51478 

43 

0.48522 

9.97792 

4 

53 

8 

9.49308 

39 

9.515:4) 

42 

0.48480 

9.97788 

4 

52 

9 

9.49347 

39 

38 

9.51563 

43 

43 

0.48437 

9.97784 

4 

51 

10 

9.49385 

9.51606 

0.48394 

9.97779 

0 

50 

11 

9.49424 

39 

9.51648 

42 

0.48352 

9.977“5 

4 

49 

12 

9.49462 

38 

9.51691 

43 

0.48309 

9.97771 

4 

48 

13 

9.49500 

38 

9.51734 

43 

0.48266 

9.97767 

4 

47 

14 

9.49539 

39 

38 

9.51776 

42 

43 

0.48224 

9.97763 

4 

A 

46 

15 

9.49577 

9.51819 

0.48181 

9.97759 

*± 

45 

16 

9.49615 

38 

9.51861 

42 

0.48139 

9.97754 

5 

44 

17 

9.49654 

39 

9.51903 

42 

0.48097 

9.97750 

4 

43 

18 

9.49692 

38 

9.51946 

43 

0.48054 

9.97746 

4 

42 

19 

9.49730 

38 

9.51988 

42 

0.48012 

9.97742 

4 

41 

38 

A 

20 

9.49768 

9.52031 

*±0 

0.47969 

9.97738 

'i 

40 

21 

9.49806 

oS 

9.52073 

42 

0.47927 

9.97734 

4 

39 

22 

9.49844 

38 

9.52115 

42 

0.47885 

9.97729 

5 

38 

23 

9.49882 

38 

9.52157 

42 

0.47843 

9.97725 

4 

37 

24 

9.49920 

38 

38 

9.52200 

43 

42 

0.47800 

9.97721 

4 

A 

36 

25 

9.49958 

9.52242 

0.47758 

9.97717 

Tt 

35 

26 

9.49996 

38 

9.52284 

42 

0.47716 

9.97713 

4 

34 

27 

9.50034 

38 

9.52326 

42 

0.47674 

9.97708 

5 

33 

28 

9.50072 

38 

9.52368 

42 

0.47632 

9.97704 

4 

32 

29 

9.50110 

38 

38 

9.52410 

42 

42 

0 47590 

9.97700 

4 

A 

31 

30 

9.50148 

9.52452 

0.47548 

9.97696 

rk 

30 

31 

9.50185 

37 

oo 

9.52494 

42 

0.47506 

9.97691 

5 

29 

32 

9.50223 

38 

oo 

9.52536 

42 

0.47464 

9.97687 

4 

28 

33 

9.50261 

38 

0*7 

9.52578 

42 

0.47422 

9.97683 

4 

27 

34 

9.50298 

37 

38 

oo 

9.52620 

42 

41 

0.47380 

9.97679 

4 

5 

26 

35 

9.50336 

9.52661 

0.47339 

9.97674 

25 

36 

9.50374 

38 

9.52703 

42 

0.47297 

9.97670 

4 

24 

37 

9.50411 

37 

oo 

9.52745 

42 

0.47255 

9.97666 

4 

23 

38 

9.50449 

38 

0*7 

9.52787 

42 

0.47213 

9.97662 

4 

22 

39 

9.50486 

37 

37 

OQ 

9.52829 

42 

0.47171 

9.97657 

5 

A 

21 

40 

9.50523 

9.52870 

“±1 

0.47130 

9.97653 

20 

41 

9.50561 

38 

0*7 

9.52912 

42 

0.47088 

9.97649 

4 

19 

42 

9-50598 

37 

9.52953 

41 

0.47047 

9.97645 

4 

18 

43 

9.50635 

37 

oo 

9.52995 

42 

0.47005 

9.97640 

5 

17 

44 

9.50673 

38 

37 

9.53037 

42 

41 

0.46963 

9 97636 

4 

4 

16 

45 

9.50710 

0*7 

9.53078 

0.46922 

9.97632 

15 

46 

9.50747 

3/ 

0*7 

9.53120 

42 

0.46880 

9.97628 

4 

14 

47 

9.50784 

37 

9.53161 

41 

0.46839 

9.97623 

5 

13 

48 

9.50821 

37 

0*7 

9.53202 

41 

0.46798 

9.97619 

4 

12 

49 

9.50858 

37 

38 

9.53244 

42 

41 

0.46756 

9.97615 

4 

11 

50 

9.50896 

0*7 

9.53285 

0.46715 

9.97610 

u 

A 

10 

51 

9.50933 

37 

0*7 

9.53327 

42 

0.46673 

9.97606 

4 

9 

52 

9.50970 

37 

9.53368 

41 

0.46632 

9.97602 

4 

8 

53 

9.51007 

37 

oo 

9.53409 

41 

0.46591 

9.97597 

5 

7 

54 

9.51043 

3b 

37 

9.53450 

41 

42 

0.46550 

9.97593 

4 

4 

6 

55 

9.51080 

9.53492 

0.46508 

9.97589 

5 

56 

9.51117 

37 

9.53533 

41 

0.46467 

9.97584 

5 

4 

57 

9.51154 

37 

9.53574 

41 

0.46426 

9.97580 

4 

3 

58 

9.51191 

37 

9.53615 

41 

0.46385 

9.97576 

4 

2 

59 

9.51227 

36 

37 

9.53656 

41 

0.46344 

9.97571 

5 

A 

1 

60 

9.51264 

9.53697 

0.46303 

9.97567 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 


43 

4.3 

5.0 

5.7 

6.5 

7.2 

14.3 

21.5 

28.7 

35.8 


42 

4.2 
4.9 
5.6 

6.3 
7.0 

14.0 

21.0 
28.0 
35.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


41 

4.1 

4.8 
5.5 

6.2 

6.8 
13.7 
20.5 
27.3 
34.2 


6 

7 

8 
9 

10 

20 

30 

40  I 
50  ! 


6 

7 

8 
9 

10 

20 

30 

40 

50 


39 

3.9 
4.6 
5.2 

5.9 
6.5 

13.0 

19.5 

26.0 

32.5 


37 

3.7 

4.3 

4.9 

5.6 

6.2 

12.3 

18.5 

24.7 

30.8 


5 

0.5 

0.6 

0.7 

0.8 

0.8 

1.7 

2.5 

3.3 

4.2 


P.  P. 


38 

3.8 

4.4 

5.1 

5.7 

6.3 

12.7 
19.0 
25.3 

31.7 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


4 

0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


71° 


/ 1 ] 

L.  Sin.  i 

0 < 

1 h 

2 1 

3 ! 

4 1 

2.51264  , 

2.51301  : 

2.51338  ; 

2.51374  ; 

2.51411 

5 ' 

2.51447 

6 1 

9.51484 

7 

9.51520 

8 

9.51557 

9 

9.51593 

10 

9.51629 

11 

9.51666 

12 

9.51702 

13 

9.51738 

14  L 

9.51774 

15 

9.51811 

16 

9.51847 

17 

9.51883 

18 

9.51919 

19 

9.51955 

20 

9.51991 

21 

9.52027 

22 

9.52063 

23 

9.52099 

24 

9.52135 

25 

9.52171 

26 

9.52207 

27 

9.52242 

28 

9.52278 

29 

9.52314 

30 

| 9.52350 

31 

9.52385 

32 

9.52421 

33 

9.52456 

34  1 

9.52492 

35 

9.52527 

36 

9.52563 

37 

9.52598 

38 

9.52634 

39 

9.52669 

40 

9.52705 

41 

9.52740 

42 

9.52775 

43 

9.52811 

44 

9.52846 

45 

9.52881 

46 

9.52916 

47 

9.52951 

48 

9.52986 

49 

9.53021 

50 

9.53056 

51 

9.53092 

52 

9.53126 

53 

9.53161 

54 

9.53196 

55 

9.53231 

56 

9.53266 

57 

9.53301 

58 

9.53336 

59 

i 9.53370 

JO 

9.53405 
1 L.  Cos. 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

19°  


511 


d.  L.Tang. 
9.53697 
9.53738 
9.53779 
9.53820 
9.53861 


37 

36 

37 
36 

36 

37 
36 
36 

36 

37 
36 
36 
36 
36 
36 
36 
36 
36 
36 


9.53902 

9.53943 

9.53984 

9.54025 

9.54065 


9.54106 

9.54147 

9.54187 

9.54228 

9.54269 


36 

35 

36 
36 
36 

35 

36 

35 

36 

35 

36 

35 

36 

35 

36 
35 

35 

36 
35 
35 
35 
35 
35 
35 

35 

36 

34 

35 
35 
35 
35 
35 
35 

34 

35 


d.  c. 


9.54309 

9.54350 

9.54390 

9.54431 

9.54471 

9.54512 

9.54552 

9.54593 

9.54633 

9.54673 

9.54714 

9.54754 

9.54794 

9.54835 

9.54875 


9.54915 

9.54955 

9.54995 

9.55035 

9.55075 


9.55115 
9.55155 
9.55195 
9 55235 
9.55275 


9.55315 

9.55355 

9.55395 

9.55434 

9.55474 


9.55514 

9.55554 

9.55593 

9.55633 

9.55673 


9.55712 

9.55752 

9.55791 

9.55831 

9.55870 

9.55910 

9.55949 

9.55989 

9.56028 

9.56067 


9.56107 


41 
41 
41 
41 
41 
41 
41 
41 

40 

41 
41 

40 

41 
41 

40 

41 

40 

41 

40 

41 

40 

41 
40 

40 

41 

40 

40 

41 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 

39 

40 
40 
40 

39 

40 
40 

39 

40 

39 

40 

39 

40 

39 

40 
39 

39 

40 


d.  L.  Cotg.l  d.  c. 


j.  Cotg.  : 

L.  Cos. 

d. 

I 

0.46303 

9.97567 

50 

0.46262 

9.97563 

4 

E 

59 

0.46221 

9.97558 

5 

58 

0.46180 

9.97554 

4 

57 

5 

0.46139 

9.97550 

4 

5 

56 

7 

0.46098 

9.97545 

A 

55 

8 

0.46057 

9.97541 

4 

54 

9 

0.46016 

9.97536 

5 

A 

53 

10 

0.45975 

9.97532 

4 

52 

20 

•1 

0.45935 

9.97528 

4 

5 

51 

30 

( 

0.45894 

9.97523 

50 

40 

0.45853 

9.97519 

4 

49 

50 

0.45813 

9.97515 

4 

E 

48 

0.45772 

9 97510 

0 

A 

47 

0.45731 

9.97506 

4 

5 - 

46 

0.45691 

9.97501 

V 

A 

'45 

( 

0.45650 

9.97497 

4 

44 

0.45610 

9.97492 

5 

43 

i 

0.45569 

9.97488 

4 

42 

< 

0.45529 

9.97484 

4 

41 

li 

"0.45488 

9.97479 

o 

A 

40 

2< 

0.45448 

9.97475 

4 

39 

o' 

At 

0.45407 

9.97470 

5 

38 

41 

E, 

0.45367 

9.97466 

4 

E 

37 

O1 

0.45327 

9.97461 

0 

4 

36 

0.45286 

9.97457 

35 

0.45246 

9.97453 

4 

34 

0.45206 

9.97448 

5 

33 

6 

0.45165 

9.97444 

4 

E 

32 

7 

0.45125 

9.97439 

0 

4 

31 

8 

Q 

1 

0.45085 

9.97435 

E 

30 

10 

0.45045 

9.97430 

O 

A 

29 

20 

0.45005 

9.97426 

4 

E 

28 

30 

0.44965 

9.97421 

0 

A 

27 

40 

0.44925 

9.97417 

4 

5 

26 

50 

044885 

9.97412 

A 

25 

0.44845 

9.97408 

4 

E 

24 

0.44805 

9.97403 

0 

A 

23 

0.44765 

9.97399 

4 

c 

22 

a 

0.44725 

9.97394 

O 

4 

21 

u 

7 

0.44685 

9.97390 

20 

8 

0.44645 

9.97385 

0 

A 

19 

9 

0.44605 

9.97381 

4 

E 

18 

10 

0.44566 

9.97376 

o 

A 

17 

20 

0.44526 

9.97372 

4 

5 

16 

30 

0.44486 

9.97367" 

A 

15" 

40 

0.44446 

9.97363 

4 

E 

14 

50 

0.44407 

9.97358 

0 

E 

13 

0.44367 

9.97353 

0 

12 

0.44327 

9.97349 

4 

5 

11 

0.44288 

9.97344 

'0 

6 

0.44248 

9.97340 

; i 

9 

*3 

0.44209 

i 9.97335 

• l 

8 

* 

0.44169 

i 9.97331 

4 

7 

c 

0.44130 

l 9.97326 

L t 

6 

1C 

0.4409C 

1 9.97322 

5 

2( 

0.44051 

. 9.9731*3 

r 0 

4 

OK 

At 

0.44011 

l 9.97312 

> 5 

3 

41 

0.43971 

> 9.9730* 

S \ 

2 

Ol 

0.4393* 

5 9.9730* 

\ l 

1 

0.4389* 

5 9.97295 

0 

i.  L.Tani 

I L.  Sin 

. d. 

/ 

P.  P. 


41 

4.1 

4.8 
5.5 

6.2 

6.8 


40 

4.0 

4.7 
5.3 

6.0 

6.7 

13.3 
20.0 
26.7 

33.3 


39 

3.9 
4.6 
5.2 

5.9 
6.5 

13.0 

19.5 

26.0 

32.5 


37 

3.7 
4.3 
4.9 
5.6 
6.2 

12.3 

18.5 

24.7 

30.8 


35 

3.5 
4.1 

4.7 
5.3 

5.8 
11.7 

17.5 
23.3 
29.2 


0.6 

0.7 

0.8 

0.8 

1.7 

2.5 

3.3 

4.2 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


34 

3.4 

4.0 

4.5 

5.1 
5.7 

11.3 
17.0 
22.7 

28.3 


4 

0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


P.  P. 


70° 


512  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

20° 


/ 

L.  Sin. 

0 

9.53405 

1 

9.53440 

2 

9.53475 

3 

9.53509 

4 

9.53544 

5 

9.53578 

6 

9.53613 

7 

9.53647 

8 

9.53682 

9 

9.53716 

10 

9.53751 

11 

9.53785 

12 

9.53819 

13 

9.53854 

14 

9.53888 

15 

9.53922 

16 

9.53957 

17 

9.53991 

18 

9.54025 

19 

9.54059 

20 

9.54093 

21 

9 54127 

22 

9.54161 

23 

9.54195 

24 

9.54229 

25 

9.54263 

26 

9.54297 

27 

9.54331 

28 

9.54365 

29 

9.54399 

30 

9.54433 

31 

9.54466 

32 

9.54500 

33 

9.54534 

34 

9.54567 

35 

9.54601 

36 

9.54635 

37 

9.54668 

38 

9.54702 

39 

9.54735 

40 

9.54769 

41 

9.54802 

42 

9.54836 

43 

9.54869 

44 

9.54903 

45 

9.54936 

46 

9.54969 

47 

9.55003 

48 

9.55036 

49 

9.55069 

50 

9.55102 

51 

9.55136 

52 

9.55169 

53 

9.55202 

54 

9.55235 

55 

9.55268 

56 

9.55301 

57 

9.55334 

58 

9.55367 

59 

9.55400 

60 

9.55433 

L.  Cos. 

d. 


35 

35 

34 

35 

34 

35 

34 

35 

34 

35 
34 

34 

35 
34 

34 

35 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 

33 

34 
34 

33 

34 
34 

33 

34 

33 

34 

33 

34 

33 

34 
33 

33 

34 
33 
33 

33 

34 
33 
33 
33 
33 
33 
33 
33 
33 
33 


L.Tang. 


9.56107 

9.56146 

9.56185 

9.56224 

9.56264 


9.56303 

9.56342 

9.56381 

9.56420 

9.56459 

9.56498 

9.56537 

9.56576 

9.56615 

9.56654 


9.56693 

9.56732 

9.56771 

9.56810 

9.56849 


9.56887 

9.56926 

9.56965 

9.57004 

9.57042 


9.57081 

9.57120 

9.57158 

9.57197 

9.57235 

9.57274 

9.57312 

9.57351 

9.57389 

9.57428 


9.57466 

9.57504 

9.57543 

9.57581 

9.57619 


9.57658 

9.57696 

9.57734 

9.57772 

9.57810 


9.57849 

9.57887 

9.57925 

9.57963 

9.58001 


9.58039 

9.58077 

9.58115 

9.58153 

9.58191 


9.58229 

9.58267 

9.58304 

9.58342 

9.58380 


9.58418 


d.  L.  Cotg, 


d.  c. 


39 

39 

39 

40 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 

38 

39 
39 
39 

38 

39 
39 

38 

39 

38 

39 

38 

39 

38 

39 
38 

38 

39 
38 

38 

39 
38 
38 
38 

38 

39 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 

37 

38 
38 
38 


L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0.43893 

9.97299 

60 

0.43854 

9.97294 

5 

59 

0.43815 

9.97289 

5 

58 

0.43776 

9.97285 

4 

57 

4U 

39 

0.43736 

9.97280 

5 

A 

56 

6 

7 

4.0 

4.7 

3.9 

4.6 

0.43697 

9.97276 

‘i. 

55 

8 

5.3 

5.2, 

0.43658 

9.97271 

5 

54 

9 

6.0 

5.9 

0.43619 

9.97266 

5 

53 

10 

6.7 

6.5 

0.43580 

9.97262 

4 

52 

20 

13.3 

13.0 

0.43541 

9.97257 

5 

51 

30  ! 

20.0 

19.5 

0.43502 

9.97252 

0 

50 

40 

26.7 

26.0 

0.43463 

9.97248 

4 

49 

50  1 

33.3 

32.5 

0.43424 

9.97243 

5 

48 

0.43385 

9.97238 

5 

47 

0.43346 

9.97234 

4 

46 

38 

37 

0.43307 

9.97229 

o 

45 

6 

3.8 

3.7 

0.43268 

9.97224 

5 

44 

7 

4.4 

4.3 

0.43229 

9.97220 

4 

43 

8 

5.1 

4.9 

0.43190 

9.97215 

c 

42 

9 

5.7 

5.6 

0.43151 

9.97210 

5 

A 

41 

10 

6.3 

6.2 

0.43113 

9.97206 

‘i 

40 

20 

12.7 

12.3 

0.43074 

9.97201 

5 

39 

30 

19.0 

18.5 

0.43035 

9.97196 

5 

38 

40 

25.3 

24.7 

0.42996 

9.97192 

4 

37 

50 

31.7 

30.8 

0.42958 

9.97187 

5 

36 

0.42919 

9.97182 

O 

35 

0.42880 

9.97178 

4 

34 

35 

0.42842 

9.97173 

5 

33 

6 

3.5 

0.42803 

9.97168 

5 

32 

7 

4.1 

0.42765 

9.97163 

5 

A 

31 

8 

4.7 

0.42726 

9.97159 

30 

y 

in 

5.3 

p;  Q 

0.42688 

9.97154 

5 

29 

on 

O.o 

ii  7 

0.42649 

9.97149 

5 

28 

ZU 

on 

11.  / 
ir  c 

0.42611 

9.97145 

4 

27 

30 

An 

1/.0 
OQ  Q 

0.42572 

9.97140 

5 

F» 

26 

Z6.6 
9Q  9 

0.42534 

9.97135 

o 

25 

0.42496 

9.97130 

5 

24 

0.42457 

9.97126 

4 

23 

0.42419 

9.9712] 

5 

22 

34 

33 

0.42381 

9.97116 

5 

r 

21 

6 

7 

3.4 
4 0 

3.3 
q Q 

0.42342 

9.97111 

o 

20 

i 

8 

4.5 

4.4 

0.42304 

9.97107 

4 

19 

9 

5.1 

5.0 

0.42266 

9.97102 

5 

18 

10 

5.7 

5.5 

0.42228 

9.97097 

5 

17 

20 

11.3 

11.0 

0.42190 

9.97092 

5 

K 

16 

30 

17.0 

16.5 

0.42151 

9.97087 

0 

15 

40 

22.7 

22.0 

0.42113 

9.97083 

4 

14 

50 

28.3 

27.5 

0.42075 

9.97078 

5 

13 

0.42037 

9.97073 

5 

12 

0.41999 

9.97068 

5 

k 

11 

5 

4 

0.41961 

9.97063 

o 

A 

10 

6 

0.5 

0.4 

0.41923 

9.97059 

4 

9 

7 

0.6 

0.5 

0.41885 

9.97054 

5 

8 

8 

0.7 

0.5 

0.41847 

9.97049 

5 

7 

9 

0.8 

0.6 

0.41809 

9.97044 

5 

f; 

6 

10 

0.8 

0.7 

0.41771 

9.97039 

o 

5 

20 

1.7 

1.3 

0.41733 

9.97035 

4 

4 

30 

2.5 

2.0 

0.41696 

9.97030 

5 

3 

40 

3.3 

2.7 

0.41658 

9.97025 

5 

2 

50 

4.2 

3.3 

0.41620 

9.97020 

5 

1 

0.41582 

9.97015 

o 

0 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

21° 


513 


/ 

L.  Sin. 

0 1 

3.55433 

1 1 

3.55466 

2 ! 

9.55499 

3 ( 

9.55532 

4 ! 

9.55564 

5 1 

9.55597 

6 

9.55630 

7 

9.55663 

8 

9.55695 

9 

9.55728 

10 

9.55761 

11 

9.55793 

12 

9.55826 

13 

9.55858 

14 

9.55891 

15 

9.55923 

16 

9.55956 

17 

9.55988 

18 

9.56021 

19 

9.56053 

20 

9.56085 

21 

9.56118 

22 

9.56150 

23 

9.56182 

24 

9.56215 

25 

9.56247 

26 

9.56279 

27 

9.56311 

28 

9.56343 

29 

9.56375 

30 

9.56408 

31 

9.56440 

32 

9.56472 

33 

9.56504 

34 

9.56536 

35 

9.56568 

36 

9.56599 

37 

9.56631 

38 

9.56663 

39 

9.56695 

40 

9.56727 

41 

9.56759 

42 

9.56790 

43 

9.56822 

44 

9.56854 

45 

9.56886 

46 

9.56917 

47 

9.56949 

48 

9.56980 

49 

9.57012 

50 

9.57044 

51 

9.57075 

52 

9.57107 

53 

9.57138 

54 

9.57169 

55 

‘ 9.57201 

56 

9.57232 

57 

9.57264 

58 

9.57295 

59 

9.57326 

60 

9.57358 

L.  Cos. 

33 

33 

33 

32 

33 
33 
33 

32 

33 
33 

32 

33 

32 

33 

32 

33 

32 

33 
32 

32 

33 
32 

32 

33 
32 
32 
32 
32 

32 

33 
32 
32 
32 
32 
32 

31 

32 
32 
32 
32 
32 

31 

32 
32 
32 

31 

32 

31 

32 
32 

31 

32 
31 

31 

32 

31 

32 
31 

31 

32 

If. 


.Tang. 

d.c.  I 

j.  Cotg. 

L.  Cos. 

d. 

158418 

158455 

>.58493 

158531 

>.58569 

37 

38 
38 
38 

Q7 

0.41582 

0.41545 

0.41507 

0.41469 

0.41431 

9.97015 

9.97010 

9.97005 

9.97001 

9.96996 

5 

5 

4 

5 
5 

60 

59 

58 

57 

56 

>.58606 

61 

0.41394 

9.96991 

55 

>.58644 

38 

0.41356 

9.96986 

5 

54 

>.58681 

37 

0.41319 

9.96981 

5 

53 

>.58719 

38 

0.41281 

9.96976 

5 

52 

>.58757 

38 

Q7 

0.41243 

9.96971 

5 

5 

51 

>.58794 

61 

0.41206 

9.96966 

A 1 

50 

>.58832 

38 

0.41168 

9.96962 

4 

49 

9.58869 

37 

0.41131 

9.96957 

5 

E 

48 

9.58907 

38 

0.41093 

9.96952 

0 

r 

47 

3.58944 

37 

07 

0.41056 

9.96947 

5 

5 

46 

9.58981 

6/ 

0.41019 

9.96942 

e 

45 

9.59019 

38 

0.40981 

9.96937 

0 

e 

44 

9.59056 

37 

0.40944 

9.96932 

0 

E 

43 

9.59094 

38 

0.40906 

9.96927 

O 

e 

42 

9.59131 

37 

Q7 

0.40869 

9.96922  . 

5 
1 5 

41 

9.59168 

61 

0.40832 

9.96917 

e 

40 

9.59205 

37 

0.40795 

9.96912 

0 

e 

39 

9.59243 

38 

0.40757 

9.96907 

0 

A 

38 

9.59280 

37 

0.40720 

9.96903 

4 

E 

37 

9.59317 

37 

07 

0.40683 

9.96898 

5 

5 

36 

9.59354 

Oi 

0.40646 

9.96893 

e 

35 

9.59391 

37 

0.40609 

9.96888 

O 

E 

34 

9.59429 

38 

0.40571 

9.96883 

5 

e 

33 

9.59466 

37 

0.40534 

9.96878 

O 

E 

32 

9.59503 

37 

07 

0.40497 

9.96873 

0 

5 

31 

9.59540 

61 

0.40460 

9.96868 

c 

30 

9.59577 

37 

0.40423 

9.96863 

0 

E 

29 

9.59614 

37 

0.40386 

9.96858 

0 

E 

28 

9.59651 

37 

0.40349 

9.96853 

D 

E 

27 

9.59688 

37 

Q7 

0.40312 

9.96848 

0 

5 

26 

9.59725 

04. 

0.40275 

9.96843 

E 

25 

9.59762 

37 

0.40238 

9.96838 

0 

E 

24 

9.59799 

37 

0.40201 

9.96833 

0 

E 

23 

9.59835 

36 

0.40165 

9.96828 

0 

E 

22 

9.59872 

37 

Q7 

0.40128 

9.96823 

0 

5 

21 

9.59909 

04 

0.40091 

9.96818 

E 

20 

9.59946 

37 

0.40054 

9.96813 

0 

E 

19 

9.59983 

37 

0.40017 

9.96808 

0 

E 

18 

9.60019 

36 

0.39981 

9.96803 

0 

E 

17 

9.60056 

37 

37 

0.39944 

9.96798 

0 

5 

16 

9.60093 

0.39907 

9.96793 

E 

15 

9.60130 

37 

0.39870 

9.96788 

0 

E 

14 

9.60166 

36 

0.39834 

9.96783 

0 

E 

13 

9.60203 

37 

0.39797 

9.96778 

0 

a 

12 

9.60240 

37 

oa 

0.39760 

9.96772 

D 

- 5 

11 

9.60276 

DO 

0.39724 

9.96767 

E 

10 

9.60313 

37 

0.39687 

9.96762 

0 

E 

9 

9.60349 

36 

0.39651 

9.96757 

0 

E 

8 

9.60386 

37 

0.39614 

9.96752 

D 

E 

7 

9.60422 

36 

*37 

0.39578 

9.96747 

0 

5 

6 

9.60459 

oi 

0.39541 

9.96742 

5 

9.60495 

gg 

0.39505 

9.96737 

5 

4 

9.60532 

i 37 

0.39468 

; 9.96732 

> 5 

3 

9.60568 

l jj® 

0.39432 

: 9.96727 

’ 5 

2 

9.60605 

' 36 

0.39395 

> 9.96722 

! ^ 
r & 

1 

9.60641 

0.3935? 

> 9.96717 

0 

L.  Cotg 

d.  c. 

, L.Tang 

;.  L.  Sin, 

. d. 

/ 

P.  P. 


38 

3.8 

4.4 

5.1 

5.7 

6.3 

12.7 
19.0 
25.3 

31.7 


38 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


37 

3.7 
4.3 
4.9 
5.6 
6.2 

12.3 

18.5 

24.7 

30.8 


33 

3.3 
3.9 

4.4 
5.0 

5.5 
11.0 

16.5 

22.0 

27.5 


6 

7 

8 
9 

10 

20 

30 

40 

50 


32 

3.2 

3.7 

4.3 

4.8 

5.3 

10.7 
16.0 
21.3 

26.7 


6 

7 

8 
9 

10 

20 

30 

40 

50 


31 

3.1 

3.6 

4.1 

4.7 

5.2 
10.3 
15.5 

20.7 

25.8 


6 

7 

8 
9 

10 

20 

30 

40 

50 


5 

0.5 

0.6 

0.7 

0.8 

0.8 

1.7 

2.5 

3.3 

4.2 


6 

0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


4 

0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


P.  P. 


lO 


514 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


22° 


r 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

. P. 

0 

9.57358 

9.60641 

0.39359 

9.96717 

60 

1 

9.57389 

31 

9.60677 

36 

0.39323 

9.96711 

6 

59 

2 

9.57420 

31 

9.60714 

37 

0.39286 

9.96706 

5 

58 

3 

9.57451 

31 

9.60750 

36 

0.39250 

9.96701 

5 

57 

ct 

a/ 

O *7 

36 

4 

9.57482 

31 

QO 

9.60786 

36 

37 

0.39214 

9.96696 

5 

56 

D 

7 

3.7 

4.3 

3.6 

4.2 

5 

9.57514 

9.60823 

0.39177 

9.96691 

o 

'55 

8 

4!9 

4^8 

6 

9.57545 

31 

9.60859 

36 

0.39141 

9.96686 

5 

54 

9 

5.6 

5.4 

7 

9.57576 

31 

9.60895 

36 

0.39105 

9.96681 

5 

53 

10 

6.2 

6.0 

. 8 

9.57607 

31 

9.60931 

36 

0.39069 

9.96676 

5 

52 

20 

12.3 

12.0 

9 

9.57638 

31 

9.60967 

36 

37 

0.39033 

9.96670 

6 

51 

30 

18.5 

18.0 

10 

9.57669 

9.61004 

0.38996 

9.96665 

O 

50 

40 

24.7 

24.0 

11 

9.57700 

31 

9.61040 

36 

0.38960 

9.96660 

5 

49 

50 

30.8 

30.0 

12 

9.57731 

31 

9.61076 

36 

0.38924 

9.96655 

5 

48 

13 

9.57762 

31 

9.61112 

36 

0.38888 

9.96650 

5 

47 

14 

9.57793 

31 

q-i 

9.61148 

36 

36 

0.38852 

9.96645 

5 

46 

35 

15 

9.57824 

9.61184 

0.38816 

9.96640 

0 

45 

6 

3.5 

16 

9.57855 

31 

9.61220 

36 

0.38780 

9.96634 

6 

44 

7 

4.1 

17 

9.57885 

30 

9.61256 

36 

0.38744 

9.96629 

5 

43 

8 

4.7 

18 

9.57916 

31 

9.61292 

36 

0.38708 

9.96624 

5 

42 

9 

5.3 

19 

9.57947 

31 

9.61328 

36 

36 

0.38672 

9.96619 

5 

41 

10 

5.8 

20 

9.57978 

o± 

9.61364 

0.38636 

9.96614 

0 

40 

20 

11.7 

21 

9.58008 

30 

9.61400 

36 

0.38600 

9.96608 

6 

39 

30 

17 .5 

22 

9.58039 

31 

9.61436 

36 

0.38564 

9.96603 

5 

38 

40 

23.3 

23 

9.58070 

31 

9.61472 

36 

0.38528 

9.96598 

5 

37 

50 

29.2 

24 

9.58101 

31 

9.61508 

36 

36 

0.38492 

9.96593 

5 

36 

25 

9.58131 

9.61544 

0.38456 

9.96588 

0 

35 

26 

9.58162 

31 

9.61579 

35 

0.38421 

9.96582 

6 

34 

32 

31 

27 

9.58192 

30 

9.61615 

36 

0.38385 

9.96577 

5 

33 

6 

3.2 

3.1 

28 

9.58223 

31 

9.61651 

36 

0.38349 

9.96572 

5 

32 

7 

3.7 

3.6 

29 

9.58253 

30 

31 

9.61687 

36 

35 

0.38313 

9.96567 

5 

31 

8 

4.3 

4.1 

30 

9.58284 

9.61722 

0.38278 

9.96562 

o 

30 

9 

1 A 

4.8 

K Q 

4.7 

K O 

31 

9.58314 

30 

9.61758 

36 

0.38242 

9.96556 

6 

29 

1U 

on 

O.o 
in  *7 

O.Z 
in  q 

32 

9.58345 

31 

9.61794 

36 

0.38206 

9.96551 

5 

28 

ZU 

on 

1U.  / 
i c*  n 

1 KJ.O 

ICC 

33 

9.58375 

30 

9.61830 

36 

0.38170 

9.96546 

5 

27 

oU 

An 

Lo.U 

Ol  Q 

10. 0 
on  h 

34 

9.58406 

31 

30 

9.61865 

35 

36 

0.38135 

9.96541 

5 

a 

26 

50 

Zl.o 

9fi.7 

Zkj.  / 

25.8 

35 

9.58436 

9.61901 

0.38099 

9.96535 

0 

25 

36 

9.58467 

31 

9.61936 

. 35 

0.38064 

9.96530 

5 

24 

37 

9.58497 

30 

9.61972 

36 

0.38028 

9.96525 

5 

23 

38 

9.58527 

30 

9.62008 

36 

0.37992 

9.96520 

5 

22 

ou 

29 

39 

9.58557 

30 

31 

9.62043 

35 

36 

0.37957 

9.96514 

6 

21 

6 

7 

3.0 

q f; 

2.9 

Q 1 

40 

9.58588 

9.62079 

0.37921 

9.96509 

o 

20 

i 

3 

0.0 

4.0 

O.i 

3.9 

41 

9.58618 

30 

9.62114 

35 

0.37886 

9.96504 

5 

19 

9 

4/5 

4/4 

42 

9.58648 

30 

9.62150 

36 

0.37850 

9.96498 

6 

18 

10 

5^0 

4*8 

43 

9.58678 

30 

9.62185 

35 

0.37815 

9.96493 

5 

17 

20 

io!o 

9^7 

44 

9.58709 

31 

30 

9.62221 

36 

35 

0.37779 

9.96488 

5 

K 

16 

30 

15!o 

14.5 

45 

9.58739 

9.62256 

0.37744 

9.96483 

o 

15 

40 

20.0 

19.3 

46 

9.58769 

30 

9.62292 

36 

0.37708 

9.96477 

6 

14 

50 

25.0 

24.2 

47 

9.58799 

30 

9.62327 

35 

0.37673 

9.96472 

5 

13 

48 

9.58829 

30 

9.62362 

35 

0.37638 

9.96467 

5 

12 

49 

9.58859 

30 

30 

9.62398 

36 

35 

0.37602 

9.96461 

6 

11 

fi 

5 

50 

9.58889 

9.62433 

0.37567 

9.96456 

o 

10 

6 

0.6 

0.5 

51 

9.58919 

30 

9.62468 

35 

0.37532 

9.96451 

5 

9 

7 

0.7 

0.6 

52 

9.58949 

30 

9.62504 

3 6l 

0.37496 

9.96445 

6 

8 

8 

0.8 

0.7 

53 

9.58979 

30 

9.62539 

35 

0.37461 

9.96440 

5 

7 

9 

0.9 

0.8 

54 

9.59009 

30 

30 

9.62574 

35 

35 

0.37426 

9.96435 

5 

6 

6 

10 

1.0 

0.8 

55 

9.59039 

9.62609 

0.37391 

9.96429 

5 

20 

2.0 

1.7 

56 

9.59069 

30 

9.62645 

36 

0.37355 

9.96424 

5 

4 

30 

3.0 

2.5 

57 

9.59098 

29 

9.62680 

35 

0.37320 

9.96419 

5 

3 

40 

4.0 

3.3 

58 

9.59128 

30 

9.62715 

35 

0.37285 

9.96413 

6 

2 

50 

5.0 

4.2 

59 

9.59158 

30 

30 

9.62750 

35 

35 

0.37250 

9.96408 

5 

* 

1 

60 

9.59188 

9.62785 

0.37215 

9.96403 

O 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

t 

P.  P. 

67° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

23° 


515 


t 

L.  Sin.^ 

0 

9.59188 

1 

9.59218 

2 

9.59247 

3 

9.59277 

4 

9.59307 

5 

9.59336 

6 

9.59366 

7 

9.59396 

8 

9.59425 

9 

9.59455 

10 

9.59484 

11 

9.59514 

12 

9.59543 

13 

9.59573 

14 

9.59602 

15 

9.59632 

16 

9.59661 

17 

9.59690 

18 

9.59720 

19 

9.59749 

20 

9.59778 

21 

9.59808 

22 

9.59837 

23 

9.59866 

24 

9.59895 

25 

9.59924 

26 

9.59954 

27 

9.59983 

28 

9.60012 

29 

9.60041 

30 

9.60070 

31 

9.60099 

32 

9.60128 

33 

9.60157 

34 

9.60186 

35 

9.60215 

36 

9.60244 

37 

9.60273 

38 

9.60302 

39 

9.60331 

40 

9.60359 

41 

9.60388 

42 

9.60417 

43 

9.60446 

44 

9.60474 

45 

*9.60503 

46 

9.60532 

47 

9.60561 

48 

9.60589 

49 

9.60618 

50 

9.60646 

51 

9.60675 

52 

9.60704 

53 

9.60732 

54 

9.60761 

55 

9.60789 

56 

9.60818 

57 

9.60846 

58 

9.60875 

59 

9.60903 

60 

9.60931 

L.  Cos. 

L.  Cotg. 

L.  Cos. 

d. 

0.37215 

9.96403 

60 

0.37180 

9.96397 

6 

59 

0.37145 

9.96392 

5 

58 

0.37110 

9.96387 

5 

57 

0.37074 

9.96381 

6 

f; 

56 

0.37039 

9.96376 

u 

55 

0.37004 

9.96370 

6 

54 

0.36969 

9.96365 

5 

53 

0.36934 

9.96360 

5 

52 

0.36899 

9.96354 

6 

5 

51 

0.36865 

9.96349 

50 

0.36830 

9.96343 

6 

49 

0.36795 

9.96338 

5 

48 

0.36760 

9.96333 

5 

47 

0.36725 

9.96327 

6 

46 

0.36690 

9.96322 

o 

6 

45 

0.36655 

9.96316 

44 

0.36621 

9.96311 

5 

43 

0.36586 

9.96305 

6 

42 

0.36551 

9.96300 

5 

6 

41 

0.36516 

9.96294 

40 

0.36481 

9.96289 

5 

39 

0.36447 

9.96284 

5 

38 

0.36412 

9.96278 

6 

37 

0.36377 

9.96273 

5 

6 

36 

0.36343 

9.96267 

35 

0.36308 

9.96262 

5 

34 

0.36274 

9.96256 

6 

33 

0.36239 

9.96251 

5 

32 

0.36204 

9.96245 

6 

5 

31 

0.36170 

9.9624C 

30 

0.36135 

9.96234 

6 

29 

0.36101 

9.96229 

5 

28 

0.36066 

9.96223 

6 

27 

0.36032 

9.96218 

5 

6 

26 

0.35997 

9.96212 

25 

0.35963 

9.96207 

5 

24 

0.35928 

9.96201 

6 

23 

0.35894 

9.96196 

5 

22 

0.35860 

9.96190 

6 

5 

21 

0.35825 

9.96185 

20 

0.35791 

9.96179 

6 

19 

0.35757 

9.96174 

5 

18 

0.35722 

9.96168 

6 

17 

0.35688 

9.96162 

6 

5 

16 

0.35654 

9.96157 

15 

0.35619 

9.96151 

6 

14 

0.35585 

9.96146 

5 

6 

13 

0.35551 

9.96140 

12 

0.35517 

9.96135 

5 

6 

11 

0.35483 

9.96129 

10 

0.35448 

9.96123 

6 

9 

0.35414 

9.96118 

5 

8 

0.35380 

9.96112 

6 

7 

0.35346 

9.96107 

5 

6 

6 

0.35312 

9.96101 

5 

0.35278 

9.96095 

6 

4 

0.35244 

9.96090 

5 

3 

0.35210 

9.96084 

6 

2 

0.35176 

9.96079 

5 

6 

1 

0.35142 

9.96073 

0 

L.Tang. 

L.  Sin. 

d. 

t 

d.  L.Tang. 


30 

29 

30 
30 

29 

30 
30 

29 

30 

29 

30 

29 

30 

29 

30 
29 

29 

30 
29 

29 

30 
29 
29 
29 

29 

30 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
28 
29 
29 
29 
28 
29 
29 
29 
28 
29 
28 
29 
29 
28 
29 
28 
29 
28 
29 
28 
28 


9.62785 

9.62820 

9.62855 

9.62890 

9.62926 


9.62961 

9.62996 

9.63031 

9.63066 

9.63101 


9.63135 

9.63170 

9.63205 

9.63240 

9.63275 


9.63310 

9.63345 

9.63379 

9.63414 

9.63449 


9.63484 

9.63519 

9.63553 

9.63588 

9.63623 


9.63657 

9.63692 

9.63726 

9.63761 

9.63796 


9.63830 

9.63865 

9.63899 

9.63934 

9.63968 


d.  c. 


9.64003 

9.64037 

9.64072 

9.64106 

9.64140 


9.64175 

9.64209 

9.64243 

9.64278 

9.64312 


9.64346 

9.64381 

9.64415 

9.64449 

9.64483 


9.64517 

9.64552 

9.64586 

9.64620 

9.64654 

1164688 

9.64722 

9.64756 

9.64790 

9.64824 

9164858 


d.  L.  Cotg 


35 

35 

35 

36 
35 
35 
35 
35 
35 

34 

35 
35 
35 
35 
35 
35 

34 

35 
35 
35 

35 

34 

35 
35 

34 

35 

34 

35 
35 

34 

35 

34 

35 

34 

35 

34 

35 
34 

34 

35 
34 

34 

35 
34 

34 

35 
34 
34 
34 

34 

35 
34 
34 
34 
34 
34 
34 
34 
34 
34 


d.  c. 


P.  P. 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


35 

3.5 

4.1 

4.7 

5.3 

5.8- 

11.7* 

17.5 

23.3 

29.2 


6 

7 

8 
9 

10 

20 

30 

40 

50 


34 

3.4 

4.0 

4.5 

5.1 
5.7 

11.3 
17.0 
22.7 

28.3 


30 

3.0 

3.5 

4.0 

4.5 

5.0 
10.0 

15.0 

20.0 

25.0 


29 

2.9 
3.4 

3.9 
•4.4 
4.8 
9.7 

14.5 

19.3 

24.2 


6 

7 

8 
9 

10 

20 

30 

40 

50 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


6 

7 

8 
9 

10 

.20 

30 

40 

50 


6 

0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


5 

0.5 

0.6 

0.7 

0.8 

0.8 

1.7 

2.5 

3.3 

4.2 


P.  P. 


66 


516  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

24° 


f 

L.  Sin. 

d. 

L.Tang. 

d.  c.  ] 

L.  Cotg. 

L.  Cos. 

0 

1 

9.60931 

9.60960 

29 

9.64858 

9.64892 

34 

0.35142 

0.35108 

9.96073 

9.96067 

2 

9.60988 

28 

9.64926 

34 

0.35074 

9.96062 

3 

9.61016 

28 

9.64960 

34 

0.35040 

9.96056 

4 

9.61045 

29 

28 

28 

9.64994 

34 

34  - 
34 

0.35006 

9.96050 

5 

6 

9.61073 

9.61101 

9.65028 

9.65062 

0.34972 

0.34938 

9.96045 

9.96039 

7 

9.61129 

28 

9.65096 

34 

0.34904 

9.96034 

8 

9.61158 

29 

9.65130 

34 

0.34870 

9.96028 

9 

9.61186 

28 

28 

28 

9.65164 

34 

33 

34 

0.34836 

9.96022 

10 

11 

9.61214 

9.61242 

9.65197 

9.65231 

0.34803 

0.34769 

9.96017 

9.96011 

12 

9.61270 

28 

9.65265 

34 

0.34735 

9.96005 

13 

9.61298 

28 

9.65299 

34 

0.34701 

9.96000 

14 

9.61326 

28 

28 

28 

9.65333 

34 

qq 

0.34667 

9.95994 

15 

16 

9.61354 

9.61382 

9.65366 

9.65400 

OO 

34 

0.34634 

0.34600 

9.95988 

9.95982 

17 

9.61411 

29 

9.65434 

34 

0.34566 

9.95977 

18 

9.61438 

27 

9.65467 

33 

0.34533 

9.95971 

19 

9.61466 

28 

28 

28 

9.65501 

34 

04. 

0.34499 

9.95965 

20 

21 

9.61494 

9.61522 

9.65535 

9.65568 

cyi 

33 

0.34465 

0.34432 

9.95960 

9.95954 

22 

9.61550 

28 

9.65602 

34 

0.34398 

9.95948 

23 

9.61578 

28. 

9.65636 

34 

0.34364 

9.95942 

24 

9.61606 

28 

28 

28 

9.65669 

33 

°A 

0.34331 

9.95937 

25 

26 

9.61634 

9.61662 

9.65703 

9.65736 

irt 

33 

0.34297 

0.34264 

9.95931 

9.95925 

27 

9.61689 

27 

9.65770 

34 

0.34230 

9.95920 

28 

9.61717 

28 

9.65803 

33 

0.34197 

9.95914 

29, 

9.61745 

28 

28 

27 

9.65837 

34 

QQ 

0.34163 

9.95908 

30 

31 

9.61773 

9.61800 

9.65870 

9.65904 

Ot) 

34 

0.34130 

0.34096 

9.95902 

9.95897 

32 

9.61828 

28 

9.65937 

33 

0.34063 

9.95891 

33 

9.61856 

28 

9.65971 

34 

0.34029 

9.95885 

34 

9.61883 

27 

28 
28 

9.66004 

33 

0.33996 

9.95879 

35 

36 

9.61911 

9.61939 

9.66038 

9.66071 

33 

0.33962 

0.33929 

9.95873 

9.95868 

37 

9.61966 

27 

9.66104 

33 

0.33896 

9.95862 

38 

9.61994 

28 

9.66138 

34 

0.33862 

9.95856 

39 

9.62021 

27 

28 
27 

9.66171 

33 

0.33829 

9.95850 

40 

41 

1162049 

9.62076 

9.66204 

9.66238 

OO 

34 

0.33796 

0.33762 

9.95844 

9.95839 

42 

9.62104 

28 

9.66271 

33 

0.33729 

9.95833 

43 

9.62131 

27 

9.66304 

33 

0.33696 

9.95827 

44 

9.62159 

28 

27 

28 

9.66337 

33 

34 
33 

0.33663 

9.95821 

45 

46 

9.62186 

9.62214 

9.66371 

9.66404 

0.33629 

0.33596 

9.95815 

9.95810 

47 

9.62241 

27 

9.66437 

33 

0.33563 

9.95804 

48 

9.62268 

27 

9.66470 

33 

0.33530 

9.95798 

49 

9.62296 

28 

27 

27 

9.66503 

33 

34 
33 

0.33497 

9.95792 

50 

51 

9.62323 

9.62350 

9.66537 

9.66570 

0.33463 

0.33430 

9.95786 

9.95780 

52 

9.62377 

27 

9.66603 

33 

0.33397 

9.95775 

53 

9.62405 

28 

9.66636 

33 

0.33364 

9.95769 

54 

9.62432 

27 

27 

9.66669 

33 

33 

0.33331 

9.95763 

55 

9.62459 

9.66702 

0.33298 

9.95757 

56 

9.62486 

27 

9.66735 

33 

0.33265 

9.95751 

57 

9.62513 

27 

9.66768 

33 

0.33232 

9.95745 

58 

9.62541 

28 

9.66801 

33 

0.33199 

9.95739 

59 

9.62568 

27 

07 

9.66834 

33 

QQ 

0.33166 

9.95733 

60 

' 9.62595 

9.66867 

OO 

0.33133 

9.95728 

L.  Cos. 

d. 

L.  Cotg 

. d.  c. 

L.Tang 

. L.  Sin. 

d. 


6 

5 

6 
6 

5 

6 

5 

6 
6 

5 

6 
6 

5 

6 
6 
6 

5 

6 
6 

5 

6 
6 
6 

5 

6 
6 

5 

6 
6 
6 

5 

6 
6 
6 
6 

5 

6 
6 
6 
6 

5 

6 
6 
6 
6 

5 

6 
6 
6 
6 
6 

5 

6 
6 
6 
6 
6 
6 
6 
5 

~dT 


45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

to 

9 

8 

7 

_6 

5 

4 

3 

2 

1 


P.  P. 


34 

3.4 

4.0 

4.5 

5.1 
5.7 

11.3 
17.0 
22.7 

28.3 


33 

3.3 
3.9 

4.4 
5.0 

5.5 
11.0 

16.5 
22.0 

27.5 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


29 

2.9 

3.4 

3.9 

4.4 
4.8 
9.7 

14.5 

19.3 

24.2 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


7 

8 
9 

10 

20 

30 

40 

50 


6 

0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


5 

0.5 

0.6 

0.7 

0.8 

0.8 

1.7 

2.5 

3.3 

4-2 


P.  P. 


65° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS . 

25° 


517 


/ 

L.  Sin. 

0 

9.62595 

1 

9.62622 

2 

9.62649 

3 

9.62676 

4 

9.62703 

5 

9.62730 

6 

9.62757 

7 

9.62784 

8 

9.62811 

9 

9.62838 

10 

'9.62865 

11 

9.62892 

12 

9.62918 

13 

9.62945 

14 

9.62972 

15 

9.62999 

16 

9.63026 

17 

9.63052 

18 

9.63079 

19 

9.63106 

20 

9.63133 

21 

9.63159 

22 

9.63186 

23 

9.63213 

24 

9.63239 

25 

9.63266 

26 

9.63292 

27 

9.63319 

28 

9.63345 

29 

9.63372 

30 

9.63398 

31 

9.63425 

32 

9.63451 

33 

9.63478 

34 

9.63504 

35 

9.63531 

36 

9.63557 

37 

9.63583 

38 

9.63610 

39 

9.63636 

40 

9.63662 

41 

9.63689 

42 

9.63715 

43 

9.63741 

44 

9.63767 

45 

9.63794 

46 

9.63820 

47 

9.63846 

48 

9.63872 

49 

9.63898 

50 

9.63924 

51 

9.63950 

52 

9.63976 

53 

9.64002 

54 

9.64028 

55 

9.64054 

56 

9.64080 

57 

9.64106 

58 

9.64132 

59 

9.64158 

60 

9.64184 

L.  Cos. 

d. 

27 
27  . 
27 
27 
27 
27 
27 
27 
27 
27 
27 
26 
27 
27 
27 
27 
26 
27 
27 
27 
26 
27 
27 
26 
27 
26 
27 
26 
27 
26 
27 
26 
27 
26 
27 
26 
26 
27 
26 
26 
27 
26 
26 
26 
27 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 


L.Tang.  d.  c.  |L.  Cotg. 


9.66867 

9.66900 

9.66933 

9.66966 

9.66999 


9.67032 

9.67065 

9.67098 

9.67131 

9.67163 


9.67196 

9.67229 

9.67262 

9.67295 

9.67327 


9.67360 

9.67393 

9.67426 

9.67458 

9.67491 


9.67524 

9.67556 

9.67589 

9.67622 

9.67654 


d. 


9.67687 

9.67719 

9.67752 

9.67785 

9.67817 


9.67850 

9.67882 

9.67915 

9.67947 

9.67980 


9.68012 

9.68044 

9.68077 

9.68109 

9.68142 


9.68174 

9.68206 

9.68239 

9.68271 

9.68303 


9.68336 

9.68368 

9.68400 

9.68432 

9.68465 


9.68497 

9.68529 

9.68561 

9.68593 

9.68626 


9.68658 

9.68690 

9.68722 

9.68754 

9.68786 


9.68818 


L.  Cotg. 


33 

33 

33 

33 

33 

33 

33 

33 

32 

33 
33 
33 
33 

32 

33 
33 
33 

32 

33 
33 

32 

33 
33 

32 

33 

32 

33 
33 

32 

33 

32 

33 

32 

33 
32 

32 

33 

32 

33 
32 

32 

33 
32 

32 

33 
32 
32 

32 

33 
32 
32 
32 

32 

33 
32 
32 
32 
32 
32 
32 


0.33133 

0.33100 

0.33067 

0.33034 

0.33001 


0.32968 

0.32935 

0.32902 

0.32869 

0.32837 


0.32804 

0.32771 

0.32738 

0.32705 

0.32673 


0.32640 

0.32607 

0.32574 

0.32542 

0.32509 


d.  c. 


0.32476 

0.32444 

0.32411 

0.32378 

0.32346 


0.32313 

0.32281 

0.32248 

0.32215 

0.32183 


L.  Cos^ 
9.95728 
9.95722 
9.95716 
9.95710 
9.95704 


9.95698 

9.95692 

9.95686 

9.95680 

9.95674 


9.95668 

9.95663 

9.95657 

9.95651 

9.95645 


9.95639 

9.95633 

9.95627 

9.95621 

9.95615 


9.95609 

9.95603 

9.95597 

9.95591 

9.95585 


0.32150 

0.32118 

0.32085 

0.32053 

0.32020 


0.31988 

0.31956 

0.31923 

0.31891 

0.31858 


0.31826 

0.31794 

0.31761 

0.31729 

0.31697 


0.31664 

0.31632 

0.31600 

0.31568 

0.31535 


0.31503 

0.31471 

0.31439 

0.31407 

0.31374 


0.31342 

0.31310 

0.31278 

0.34246 

0.31214 


0.31182 


9.95579 

9.95573 

9.95567 

9.95561 

9.95555 


9.95549 

9.95543 

9.95537 

9.95531 

9.95525 


9.95519 

9.95513 

9.95507 

9.95500 

9.95494 


9.95488 

9.95482 

9.95476 

9.95470 

9.95464 


9.95458 

9.95452 

9.95446 

9.95440 

9.95434 


9.95427 

9.95421 

9.95415 

9.95409 

9.95403 


9.95397 

9.95391 

9.95384 

9.95378 

9.95372 


9.95366 


_d._ 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

5 

6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
7 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 
7 
6 
6 
6 
6 
6 
6 
7 
6 
6 
6 


L.Tang.  L.  Sin. 

64° 


d. 


55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

_36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 


P.  P. 


33 

3.3 
3.9 

4.4 
5.0 

5.5 
11.0 

16.5 

22.0 

27.5 


32 

3.2 

3.7 

4.3 

4.8 

5.3 

10.7 
16.0 
21.3 

26.7 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


6 

7 

8 
9 

10 

20 

30 

40 

50 


7 

0.7 

0.8 

0.9 

1.1 

1.2 

2.3 

3.5 

4.7 

5.8 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


5 

0.5 

0.6 

0.7 

0.8 

0.8 

1.7 

2.5 

3.3 

4.2 


P.  P. 


518  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS . 

' 26° 


/ 

L.  Sin. 

0 

9.64  L84 

1 

9.64210 

2 

9.64236 

3 

9.64262 

4 

9.64288 

5 

9.64313 

6 

9.64339 

7 

9.64365 

8 

9.64391 

9 

9.64417 

10 

9.64442 

11 

9.64468 

12 

9.64494 

13 

9.64519 

14 

9.64545 

15 

9.64571 

16 

9.64596 

17 

9.64622 

18 

9.64647 

19 

9.64673 

20 

9 64698 

21 

9.34724 

22 

9.64749 

23 

9.64775 

24 

9.64800 

25 

9.64826 

26 

9.64851 

27 

9.64877 

28 

9.64902 

29 

9.64927 

30 

9.64953 

31 

9.64978 

32 

9.65003 

33 

9.65029 

34 

9.65054 

35 

9.65079 

36 

9.65104 

37 

9.65130 

38 

9.65155 

39 

9.65180 

40 

9.65205 

41 

9.65230 

42 

9.65255 

43 

9.65281 

44 

9.65306 

45 

9.65331 

46 

9.65356 

47 

9.65381 

48 

9.65406 

49 

9.65431 

50 

9.65456 

51 

9.65481 

52 

9.65506 

53 

9.65531 

54 

9.65556 

55 

9.65580 

56 

9.65605 

57 

9.65630 

58 

9.65655 

59 

9.65680 

60 

9.65705 

L.Tang. 

¥.'68818 

9.68850 

9.68882 

9.68914 

9.68946 

9.68978 

9.69010 

9.69042 

9.69074 

9.69106 

9.69138 

9.69170 

9.69202 

9.69234 

9.69266 

9.69298 

9.69329 

9.69361 

9.69393 

9.69425 

9.69457 

9.69488 

9.69520 

9.69552 

9.69584 

9.69615 

9.69647 

9.69679 

9.69710 

9.69742 

9.69774 

9.69805 

9.69837 

9.69868 

9.69900 

9.69932 
. 9.69963 
9.69995 
9.70026 
9.70058 

9.70089 

9.70121 

9.70152 

9.70184 

9.70215 

9.70247 

9.70278 

9.70309 

9.70341 

9.70372 

9.70404 

9.70435 

9.70466 

9.70498 

9.70529 

9.70560 

9.70592 

9.70623 

9.70654 

9.70685 

9.70717 

L.  Cotg. 

L.  Cotg. 

L.  Cos. 

0.31182 

9.95366 

0.31150 

9.95360 

0.31118 

9.95354 

0.31086 

9.95348 

0.31054 

9.95341 

0.31022 

9.95335 

0.30990 

9.95329 

0.30958 

9.95323 

0.30926 

9.95317 

0.30894 

9.95310 

0.30862 

9.95304 

0.30830 

9.95298 

0.30798 

9.95292 

0.30766 

9.95286 

0.30734 

9.95279 

0.30702 

9.95273 

0.30671 

9.95267 

0.30639 

9.95261 

0.30607 

9.95254 

0.30575 

9.95248 

0.30543 

9.95242 

0.30512 

9.95236 

0.30480 

9.95229 

0.30448 

9.95223 

0.30416 

9.95217 

0.30385 

9.95211 

0.30353 

9.95204 

0.30321 

9.95198 

0.30290 

9.95192 

0.30258 

9.95185 

0.30226 

9.95179 

0.30195 

9.95173 

0.30163 

9.95167 

0.30132 

9.95160 

0.30100 

9.95154 

0.30068 

9.95148 

0.30037 

9.95141 

0.30005 

9.95135 

0.29974 

9.95129 

0.29942 

9.95122 

0.29911 

9.95116 

0.29879 

9.95110 

0.29848 

9.95103 

0.29816 

9.95097 

0.29785 

9.95090 

0.29753 

9.95084 

0.29722 

9.95078 

0.29691 

9.95071 

0.29659 

9.95065 

0.29628 

9.95059 

0.29596 

9.95052 

0.29565 

9.95046 

0.29534 

9.95039 

0.29502 

9.95033 

0.29471 

9.95027 

0.29440 

9.95020 

■ 0.29408 

9.95014 

0.29?77 

9.95007 

0.29346 

9.95001 

0.29315 

9.94995 

0.29283 

9.94988 

L.Tang. 

L.  Sin. 

L.  Cos. 


d. 

26 

26 

26 

26 

25 

26 
26 
26 
26 

25 

26 
26 

25 

26 
26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 
25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
25 
25 
25 
25 

25 

26 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 

24 

25 
25 
25 
25 
25 


d.  c. 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

31 

32 
32 
32 
32 

31 

32 
32 
32 

31 

32 
32 

31 

32 
32 

31 

32 

31 

32 
32 

31 

32 

31 

32 

31 

32 

31 

32 

31 

32 
31 

31 

32 

31 

32 
31 

31 

32 
31 

31 

32 
31 
31 

31 

32 


d. 


60 

59 

58 

57 

56 

55 

54 

53 

52 

5i 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 


P.  P. 


32 

3.2 

3.7 

4.3 

4.8 

5.3 

10.7 
16.0 
21.3 

26.7 


31 

3.1 

3.6 

4.1 

4.7 

5.2 
10.3 
15.5 

20.7 

25.8 


6 

n 

3 

9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


24 

2.4 

2.8 

3.2 

3.6 

4.0 

8.0 
12.0 
16.0 
20.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


7 

0.7 

0.8 

0.9 

1.1 

1.2 

2.3 

3.5 

4.7 

5.8 


0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


P.  P. 


63° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

27° 


519 


/ 

L.  Sin. 

0 

9.65705" 

1 

9.65729 

2 

9.65754 

3 

9.65779 

4 

9.65804 

5 

9.65828 

6 

9.65853 

7 

9.65878 

8 

9.65902 

9 

9.65927 

10 

9.65952 

11 

9.65976 

12 

9.66001 

13 

9.66025 

14 

9.66050 

15 

9.66075 

16 

9.66099 

17 

9.66124 

18 

9.66148 

19 

9.66173 

20 

9.66197 

21 

9.66221 

22 

9.66246 

23 

9.66270 

24 

9.66295 

25 

9.66319 

26 

9.66343 

27 

9.66368 

28 

9.66392 

29 

9.66416 

30 

9.66441 

31 

9.66465 

32 

9.66489 

33 

9.66513 

34 

9.66537 

35 

9.66562 

36 

9.66586 

37 

9.66610 

38 

9.66634 

39 

9.66658 

40 

9.66682 

41 

9.66706 

42 

9.66731 

43 

9.66755 

44 

9.66779 

45 

9.66803 

46 

9.66827 

47 

9.66851 

48 

9.66875 

49 

9.66899 

50 

9.66922 

51 

9.66946 

52 

9.66970 

53 

9.66994 

54 

9.67018 

55 

9.67042 

56 

9.67066 

57 

9.67090 

58 

9.67113 

59 

9.67137 

60 

9.67161 

L.  Cos. 

L.Tang. 

9.70717 

9.70748 

9.70779 

9.70810 

9.70841 

9.70873 

9.70904 

9.70935 

9.70966 

9.70997 

9.71028 

9.71059 

9.71090 

9.71121 

9.71153 

9.71184 

9.71215 

9.71246 

9.71277 

9.71308 

9.71339 

9.71370 

9.71401 

9.71431 

9.71462 

9.71493 

9.71524 

9.71555 

9.71586 

9.71617 

9.71648 

9.71679 

9.71709 

9.71740 

9.71771 

9.71802 

9.71833 

9.71863 

9.71894 

9.71925 

9.71955 

9.71986 

9.72017 

9.72048 

9.72078 

9.72109 

9.72140 

9.72170 

9.72201 

9.72231 

9.72262 

9.72293 

9.72323 

9.72354 

9.72384 

9.72415 

9.72445 

9.72476 

9.72506 

9.72537 

9.72567 

L.  Cotg. 

d. 

24 

25 
25 
25 

24 

25 
25 

24 

25 
25 

24 

25 

24 

25 
25 

24 

25 

24 

25 
24 

24 

25 

24 

25 
24 

24 

25 
24 

24 

25 
24 
24 
24 

24 

25 
24 
24 
24 
24 
24 

24 

25 
24 
24 
24 
24 
24 
24 
24 

23 

24 
24 
24 
24 
24 
24 
24 

23 

24 
24 


d. 


d.  c. 

31 

31 

31 

31 

32 
31 
31 
31 
31 
31 
31 
31 

31 

32 
31 
31 
31 
31 
31 
31 
31 
31 

30 

31 
31 
31 
31 
31 
31 
31 
31 

30 

31 
31 
31 
31 

30 

31 
31 

30 

31 
31 
31 

30 

31 
31 

30 

31 

30 

31 
31 

30 

31 

30 

31 

30 

31 

30 

31 
30 


|L.  Cotg. 
0.29283 
0.29252 
0.29221 
0.29190 
0.29159 


0.29127 

0.29096 

0.29065 

0.29034 

0.29003 


0.28972 

0.28941 

0.28910 

0.28879 

0.28847 


0.28816 

0.28785 

0.28754 

0.28723 

0.28692 


0.28661 

0.28630 

0.28599 

0.28569 

0.28538 


0.28507 

0.28476 

0.28445 

0.28414 

0.28383 


0.28352 

0.28321 

0.28291 

0.28260 

0.28229 


0.28198 

0.28167 

0.28137 

0.28106 

0.28075 


0.28045 

0.28014 

0.27983 

0.27952 

0.27922 


0.27891 

0.27860 

0.27830 

0.27799 

0.27769 


0.27738 

0.27707 

0.27677 

0.27646 

0.27616 


0.27585 

0.27555 

0.27524 

0.27494 

0.27463 


0.27433 


d.  c.  L.Tang 


L.  Cos.  d. 
9.94988" 
9.94982 
9.94975 
9.94969 
9.94962 


9.94956 

9.94949 

9.94943 

9.91936 

9.94930 


9.94923 

9.94917 

9.94911 

9.94904 

9.94898 


9.94891 

9.94885 

9.94878 

9.94871 

9.94865 


9.94858 

9.94852 

9.94845 

9.94839 

9.94832 


9.94826 

9.94819 

9.94813 

9.94806 

9.94799 


9.94793 

9.94786 

9.94780 

9.94773 

9.94767 


9.94760 

9.94753 

9.94747 

9.94740 

9.94734 


9.94727 

9.94720 

9.94714 

9.94707 

9.94700 


9.94694 

9.94687 

9.94680 

9.94674 

9.94667 


9.94660 

9.94654 

9.94647 

9.94640 

9.94634 


9.94627 

9.94620 

9.94614 

9.94607 

9.94600 


9.94593 


L.  Sin.  d 


P.  P. 


32 

3.2 

3.7 

4.3 

4.8 

5.3 

10.7 
16.0 
21.3 

26.7 


31 

3.1 

3.6 

4.1 

4.7 

5.2 
10.3 
15.5 

20.7 

25.8 


6 

7 

•8 

9 

10 

20 

30 

40 

50 


30 

3.0 

3.5 

4.0 

4.5 

5.0 
10.0 

15.0 

20.0 
25.0 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


24 

2.4 

2.8 

3.2 

3.6 

4.0 

8.0 
12.0 
16.0 
20.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


23 

2.3 

2.7 
3.1 
3.5 

3.8 
7.7 

11.5 

15.3 

19.2 


6 

7 

8 
9 

10 

20 

30 

40 

50 


7 

0.7 

0.8 

0.9 

1.1 

1.2 

2.3 

3.5 

4.7 

5.8 


6 

0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


P.  P. 


62° 


520  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

28° 


' 1 

L.  Sin. 

0 

9.67161 

1 

9.67185 

2 

9.67208 

3 

9.67232 

4 

9.67256 

5 

9.67280 

6 

9.67303 

7 

9.67327 

8 

9.67350 

9 

9.67374 

10 

9.67398 

11 

9.67421 

12 

9.67445 

13 

9.67468 

14 

9.67492 

15 

9.67515 

16 

9.67539 

17 

9.67562 

18 

9.67586 

19 

9.67609 

20 

9„67633 

21 

9.67656 

22 

9.67680 

23 

9.67703 

24 

9.67726 

25 

9.67750 

26 

9.67773 

27 

9.67796 

28 

9.67820 

29 

9.67843 

30 

9.67866 

31 

9.67890 

32 

9.67913 

33 

9.67936 

34 

9.67959 

35 

9.67982 

36 

9.68006 

37 

9.68029 

38 

9.68052 

39 

9.68075 

40 

9.68098 

41 

9.68121 

42 

9.68144 

43 

9.68167 

44 

9.68190 

45 

9.68213 

46 

9.68237 

47 

9.68260 

48 

9.68283 

49 

9.68305 

50 

9.68328 

51 

9.68351 

52 

9.68374 

53 

9.68397 

54 

9.68420 

55 

9.68443 

56 

9.68466 

57 

9.68489 

58 

9.68512 

59 

9.68534 

60 

9.68557 

L.  Cos. 

P. 

P. 

31 

30 

1 6 

3.1 

3.0 

7 

3.6 

3.5 

8 

4.1 

4.0 

9 

4.7 

4.5 

10 

5.2 

5.0 

20 

10.3 

10.0 

30 

15.5 

15.0 

40 

20.7 

20.0 

50 

25.8 

25.0 

29 

6 

2.9 

7 

3.4 

8 

3.9 

9 

4.4 

10 

4.8 

20 

9.7  1 

30 

14.5 

40 

19.3 

50 

24.2 

24 

23 

6 

2.4 

2.3 

7 

2.8 

2.7 

8 

3.2 

3.1 

- . 9 

3.6 

3.5 

10 

4.0 

3.8 

20 

8.0 

7.7 

30 

12.0 

11.5  > 

40 

16.0 

15.3 

- 50 

20.0 

19.2 

22 

6 

2.2 

7 

2.6 

8 

2.9 

9 

3.3 

10 

3.7 

20 

7.3 

30 

11.0 

40 

14.7 

50 

18.3 

7 

6 

i 

6 

0.7 

0.6 

i 

7 

0.8 

0.7 

i 

8 

0.9 

0.8 

9 

1.1 

0.9 

* 10 

1.2 

1.0 

, 20 

2.3 

2.0 

t 30 

3.5 

3.0 

; 40 

4.7 

4.0 

» 50 

5.8 

5.0 

1 

d. 


L.Tang. 


24 

23 

24 
24 
24 

23 

24 

23 

24 
24 

23 

24 

23 

24 

23 

24 

23 

24 

23 

24 

23 

24 
23 

23 

24 
23 

23 

24 
23 

23 

24 
23 
23 
23 

23 

24 
23 
23 
23 
23 
23 
23 
23 
23 

23 

24 
23 
23 
22 
23 
23 
23 
23 
23 
23 
23 
23 
23 
22 
23 


d. 


9.72567 

9.72598 

9.72628 

9.72659 

9.72689 


9.72720 

9o72750 

9.72780 

9.72811 

9.72841 


9.72872 

9.72902 

9.72932 

9.72963 

9.72993 


9.73023 

9.73054 

9.73084 

9.73114 

9.73144 


9.73175 

9.73205 

9.73235 

9.73265 

9.73295 


d.  c. 


9.73326 

9.73356 

9.73386 

9.73416 

9.73446 


9.73476 

9.73507 

9.73537 

9.73567 

9.73597 


9.73627 

9.73657 

9.73687 

9.73717 

9.73747 


9.73777 

9.73807 

9.73837 

9.73867 

9.73897 


9.73927 

9.73957 

9.73987 

9.74017 

9.74047 


9.74077 

9.74107 

9.74137 

9.74166 

9.74196 


9.74226 

9.74256 

9.74286 

9.74316 

9.74345 


31 

30 

31 

30 

31 
30 

30 

31 

30 

31 
30 

30 

31 
30 

30 

31 
30 
30 

30 

31 
30 
30 
30 

30 

31 
30 
30 
30 
30 

30 

31 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 


9.74375 


L.  Cotg. 


L.  Cotg. 


30 

30 

30 

30 

29 

30 
30 
30 
30 
30 

29 

30 


0.27433 

0.27402 

0.27372 

0.27341 

0.27311 


9.94593 

9.94587 

9.94580 

9.94573 

9.94567 


0.27280 

0.27250 

0.27220 

0.27189 

0.27159 


0.27128 

0.27098 

0.27068 

0.27037 

0.27007 


0.26977 

0.26946 

0.26916 

0.26886 

0.26856 


0.26825 

0.26795 

0.26765 

0.26735 

0.26705 


0.26674 

0.26644 

0.26614 

0.26584 

0.26554 


0.26524 

0.26493 

0.26463 

0.26433 

0.26403 


0.26373 

0.26343 

0.26313 

0.26283 

0.26253 


0.26223 

0.26193 

0.26163 

0.26133 

0.26103 


0.26073 

0.26043 

0.26013 

0.25983 

0.25953 


0.25923 

0.25893 

0.25863 

0.25834 

0.25804 


0.25774 

0.25744 

0.25714 

0.25684 

0.25655 


0.25625 


d.  c.  L.Tang 

61° 


L.  Cos.  d. 


9.94560 

9.94553 

9.94546 

9.94540 

9.94533 


9.94526 

9.94519 

9.94513 

9.94506 

9.94499 


9.94492 

9.94485 

9.94479 

9.94472 

9.94465 


9.94458 

9.94451 

9.94445 

9.94438 

9.94431 


9.94424 

9.94417 

9.94410 

9.94404 

9.94397 


9.94390 

9.94383 

9.94376 

9.94369 

9.94362 


9.94355 

9.94349 

9.94342 

9.94335 

9.94328 


9.94321 

9.94314 

9.94307 

9.94300 

9.94293 


9.94286 

9.94279 

9.94273 

9.94266 

9.94259 


9.94252 

9.94245 

9.94238 

9.94231 

9.94224 


9.94217 

9.94210 

9.94203 

9.94196 

9.94189 


9.94182 


L.  Sin.  d 


6 

7 

7 

6 

7 

7 

7 

6 

7 

7 

7 

6 

7 

7 

7 

7 

6 

7 

7 

7 

7 

6 

7 

7 

7 

7 

7 

6 

7 

7 

7 

7 

7 

7 

7 

6 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

6 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 


10 


P.  P. 


52.1 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS . 


29° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

9.68557 

9.74375 

0.25625 

9.94182 

60 

1 

9.68580 

23 

9.74405 

30 

0.25595 

9.94175 

7 

59 

2 

9.68603 

23 

9.74435 

30 

0.25565 

9.94168 

7 

58 

3 

9.68625 

22 

9.74465 

30 

0.25535 

9.94161 

7 

57 

a 

ou 

O A 

4 

9.68648 

23 

Oq 

9.74494 

29 

QO 

0.25506 

9.94154 

7 

7 

56 

D 

7 

3.0 

3.5 

5 

9.68671 

9.74524 

0.25476 

9.94147 

by 

55 

8 

4.0 

6 

9.68694 

23 

9.74554 

30 

0.25446 

9.94140 

7 

54 

9 

4.5 

7 

9.68716 

22 

9.74583 

29 

0.25417 

9.94133 

7 

53 

10 

5.0 

8 

9.68739 

23 

9.74613 

30 

0.25387 

9.94126 

7 

52 

20 

10.0 

9 

9.68762 

23 

22 

9.74643 

30 

30 

0.25357 

9.94119 

7 

7 

51 

30 

15.0 

10 

9.68784 

9.74673 

0.25327 

9.94112 

50 

40 

20.0 

11 

9.68807 

23 

9.74702 

29 

0.25298 

9.94105 

7 

49 

50 

25.0 

12 

9.68829 

22 

9.74732 

30 

0.25268 

9.94098 

7 

48 

13 

9.68852 

23 

9.74762 

30 

0.25238 

9.94090 

8 

47 

14 

9.68875 

23 

99 

9.74791 

29 

30 

0.25209 

9.94083 

7 

7 

46 

29 

15 

9.68897 

9.74821 

0.25179 

9.94076 

« 

by 

45 

6 

2.9 

16 

9.68920 

23 

9.74851 

30 

0.25149 

9.94069 

7 

44 

1 

3.4 

17 

9.68942 

22 

9.74880 

29 

0.25120 

9.94062 

7 

43 

8 

3.9 

18 

9.68965 

23 

9.74910 

30 

0.25090 

9.94055 

7 

42 

9 

4.4 

19 

9.68987 

22  ) 
23 

9.74939 

29 

30 

0.25061 

9.94048 

7 

7 

41 

10 

4.8 

20 

9.69010 

9.749&9 

0.25031 

9.94041 

40 

20 

9.7 

21 

9.69032 

22 

9.74998 

29 

0.25002 

9.94034 

7 

39 

30 

14.5 

22 

9.69055 

23 

9.75028 

30 

0.24972 

9.94027 

7 

38 

40 

19.3 

23 

9.69077 

22 

9.75058 

30 

0.24942 

9.94020 

7 

37 

50 

24.2 

24 

9.69100 

23 

99 

9.75087 

29 

30 

0.24913 

9.94012 

8 

7 

36 

25 

9.69122 

9.75117 

0.24883 

9.94005 

fy 

35 

26 

9.69144 

22 

9.75146 

29 

0.24854 

9.93998 

7 

34 

23 

27 

9.69167 

23 

9.75176 

30 

0.24824 

9.93991 

7 

33 

6 

2.3 

28 

9.69189 

22 

9.75205 

29 

0.24795 

9.93984 

7 

32 

7 

2.7 

29 

9.69212 

23 

9.75235 

30 

0.24765 

9.93977 

7 

31 

8 

3.1 

22 

29 

*1 

30 

9.69234 

9.75264 

0.24736 

9.93970 

4 

by 

30 

1 A 

6.0 
o o 

31 

9.69256 

22 

9.75294 

30 

0.24706 

9.93963 

7 

29 

10 

3.8 

<7  >1 

32 

9.69279 

23 

9.75323 

29 

0.24677 

9.93955 

8 

28 

20 

OA 

7.7 

33 

9.69301 

22 

9.75353 

30 

0.24647 

9.93948 

7 

27 

30 

A(\ 

11.0 
1C  Q 

34 

9.69323 

22 

22 

9.75382 

29 

9Q 

0.24618 

9.93941 

7 

7 

26 

R0 

10.3 
IQ  9 

35 

9.69345 

9.75411 

0.24589 

9.93934 

f 

by 

25 

36 

9.69368 

23 

9.75441 

30 

0.24559 

9.93927 

7 

24 

37 

9.69390 

22 

9.75470 

29 

0.24530 

9.93920 

7 

23 

38 

9.69412 

22 

9.75500 

30 

0.24500 

9.93912 

8 

22 

ZZ 

39 

9.69434 

22 

22 

9.75529 

29 

29 

0.24471 

9.93905 

7 

7 

21 

6 

7 

2.2 
9 A 

40 

9.69456 

9.75558 

0.24442 

9.93898 

f 

ty 

20 

« 

Z.O 

2.9 

41 

9.69479 

23 

9.75588 

30 

0.24412 

9.93891 

7 

19 

l 

3 

3*3 

42 

9.69501 

22 

9.75617 

29 

0.24383 

9.93884 

7 

18 

10 

8.7 

43 

9.69523 

22 

9.75647 

30 

0.24353 

9.93876 

8 

17 

20 

7.3 

44 

9.69545 

22 

22 

9.75676 

29 

29 

0.24324 

9.93869 

7 

7 

16 

30 

11.0 

45 

9.69567 

9.75705 

0.24295 

9.93862 

i 

by 

15 

40 

14.7 

46 

9.69589 

22 

9.75735 

30 

0.24265 

9.93855 

7 

14 

50 

18.3 

47 

9.69611 

22 

9.75764 

29 

0.24236 

9.93847 

8 

13 

48 

9.69633 

22 

9.75793 

29 

0.24207 

9 93840 

7 

12 

49 

9.69655 

22 

22 

9.75822 

29 

qn 

0.24178 

9.93833 

7 

7 

11 

ft 

a 

50 

9.69677 

9.75852 

ou 

0.24148 

9.93826 

i 

10 

6 

0.8 

0)7 

51 

9.69699 

22 

9.75881 

29 

0.24119 

9.93819 

7 

9 

7 

0.9 

0.8 

52 

9.69721 

22 

9.75910 

29 

0.24090 

9.93811 

8 

8 

8 

1.1 

0.9 

53 

9.69743 

22 

9.75939 

29 

0.24061 

9.93804 

7 

7 

9 

1.2 

1.1 

54 

9.69765 

22 

22 

9.75969 

30 

29 

0.24031 

9.93797 

7 

8 

6 

10 

1.3 

1.2 

55 

9.69787 

9.75998 

0.24002 

9.93789 

5 

20 

2.7 

2.3 

56 

9.69809 

22 

9.76027 

29 

0.23973 

9.93782 

7 

4 

30 

4.0 

3.5 

57 

9.69831 

22 

9.76056 

29 

0.23944 

9.93775 

7 

3 

40 

5.3 

4.7 

58 

9.69853 

22 

9.76086 

30 

0.23914 

9.93768 

7 

2 

50 

6.7 

5.8 

59 

9.69875 

22 

22 

9.76115 

29 

29 

0.23885 

9.93760 

8 

7 

1 

60 

9.69897 

9.76144 

0.23856 

9.93753 

4 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

60° 


522  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

30° 


r 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.69897 

9.69919 

9.69941 

9.69963 

9.69984 

22 

22 

22 

21 

22 

22 

22 

22 

21 

22 

22 

22 

21 

22 

22 

21 

22 

21 

22 

22 

21 

22 

21 

22 

21 

22 

21 

22 

21 

22 

A 

22 

21 

22 

21 

21 

22 

21 

21 

22 

21 

21 

21 

22 

21 

21 

21 

22 

21 

- 21 
21 
21 
21 
22 

- 21 

21 

21 

21 

21 

91 

9.76144 

9.76173 

9.76202 

9.76231 

9.76261 

29 

29 

29 

30 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 

29 

30 
29 
29 
28 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
28 
29 
29 

29 

29 

29 

28 

29 

29 

29 

29 

28 

29 

29 

29 

( 28 
29 
29 
28 
29 
29 
29 

- 28 
29 
28 
29 
29 

Oft 

0.23856 

0.23827 

0.23798 

0.23769 

0.23739 

9.93753 

9.93746 

9.93738 

9.93731 

9.93724 

7 

8 
7 
7 

7 

8 
7 

7 

8 
7 

7 

8 

7 

8 
7 

7 

8 

7 
7. 

8 

7 

8 
7 

7 

8 

7 

8 

7 

8 
7 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 
7 

- 8 

7 

8 

7 

8 

- 8 

7 

8 

7 

8 

- 7 

60 

59 

58 

57 

56 

30  29 

6 3.0  2.9 

7 3.5  3.4 

8 4.0  3.9 

9 4.5  4.4 

10  5.0  4.8 

20  10.0  9.7 

30  15.0  14.5 
40  20.0  19.3 
50  25.0  24.2 

28 

6 2.8 

7 3.3 

8 3.7 

9 4.2 

10  4.7 

20  9.3 

30  14.0 
40  18.7 
50  23.3 

22 

6 2.2 

7 2.6 

8 2.9 

9 3.3 

10  3.7 

20  7.3 

30  11.0 
40  14.7 
50  18.3 

2^ 

6 2.1 

7 2.5 

8 2.8 

9 3.2 

10  3.5 

20  7.0 

30  10.5 
40  14.0 
50  17.5 

8 7 

6 0.8  0.7 

7 0.9  0.8 

8 1.1  0.9 

9 1.2  1.1 
10  1.3  1.2 
20  2.7  2.3 
30  4.0  3.5 
40  5.3  4.7 
50  6.7  5.8 

5 

6 

7 

8 
9 

9.70006 

9.70028 

9.70050 

9.70072 

9.70093 

9.76290 

9.76319 

9.76348 

9.76377 

9.76406 

0.23710 

0.23681 

0.23652 

0.23623 

0.23594 

9.93717 

9.93709 

9.93702 

9.93695 

9.93687 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.70115 

9.70137 

9.70159 

9.70180 

9.70202 

9.76435 

9.76464 

9.76493 

9.76522 

9.76551 

0.23565 

0.23536 

0.23507 

0.23478 

0.23449 

9.93680 

9.93673 

9.93665 

9.93658 

9.93650 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.70224 

9.70245 

9.70267 

9.70288 

9.70310 

9.76580 

9.76609 

9.76639 

9.76668 

9.76697 

0.23420 

0.23391 

0.23361 

0.23332 

0.23303 

9.93643 

9.93636 

9.93628 

9.93621 

9.93614 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.70332 

9.70353 

9.70375 

9.70396 

9.70418 

9.76725 

9.76754 

9.76783 

9.76812 

9.76841 

0.23275 

0.23246 

0.23217 

0.23188 

0.23159 

9.93606 

9.93599 

9.93591 

9.93584 

9.93577 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.70439 

9.70461 

9.70482 

9.70504 

9.70525 

9.76870 

9.76899 

9.76928 

9.76957 

9.76986 

0.23130 

0.23101 

0.23072 

0.23043 

0.23014 

9.93569 

9.93562 

9.93554 

9.93547 

9.93539 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.70547 

9.70568 

9.70590 

9.70611 

9.70633 

9.77015 

9.77044 

9.77073 

9.77101 

9.77130 

0.22985 

0.22956 

0.22927 

0.22899 

0.22870 

9.93532 

9.93525 

9.93517 

9.93510 

9.93502 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.70654 

9.70675 

9.70697 

9.70718 

9.70739 

9.77159 

9.77188 

9.77217 

9.77246 

9.77274 

0.22841 

0.22812 

0.22783 

0.22754 

0.22726 

9.93495 

9.93487 

9.93480 

9.93472 

9.93465 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.70761 

9.70782 

9.70803 

9.70824 

9.70846 

9.77303 

9.77332 

9.77361 

9.77390 

9.77418 

0.22697 

0.22668 

0.22639 

0.22610 

0.22582 

9.93457 

9.93450 

9.93442 

9.93435 

9.93427 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.70867 

9.70888 

9.70909 

9.70931 

9.70952 

• 9.77447 
9.77476 
9.77505 
9.77533 
9.77562 

0.22553 

0.22524 

0.22495 

0.22467 

0.22438 

9.93420 

9.93412 

9.93405 

9.93397 

9.93390 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

’ 9.70973 
9.70994 
9.71015 
9.71036 
9.71058 

9.77591 

9.77619 

9.77648 

9.77677 

9.77706 

0.22409 

0.22381 

0.22352 

0.22323 

0.22294 

9.93382 

9.93375 

9.93367 

9.93360 

9.93352 

lo 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.71079 

9.71100 

9.71121 

9.71142 

9.71163 

9.77734 

9.77763 

9.77791 

9.77820 

9.77849 

0.22266 

0.22237 

0.22209 

0.22180 

0.22151 

9.93344 

9.93337 

9.93329 

9.93322 

9.93314 

5 

4 

3 

2 

1 

60 

" 9771184 

9.77877 

AdCj 

0.22123 

9.93307 

0 

L.  Cos. 

d. 

L.  Cotg 

. d.  c. 

L.Tang 

. L.  Sin. 

d. 

/ 

P.  P. 

59° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  523 


31° 


f 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

9.71184 

9.71205 

9.71226 

9.71247 

9.71268 

21 

21 

21 

21 

21 

21 

21 

21 

21 

20 

21 

21 

21 

21 

21 

21 

20 

21 

21 

21 

20 

21 

21 

21 

20 

21 

21 

20 

21 

21 

20 

21 

20 

21 

20 

21 

20 

21 

21 

20 

20 

21 

20 

21 

20 

21 

20 

20 

21 

,20 

20 

21 

20 

20 

21 

20 

20 

21 

20 

20 

9.77877 

9.77906 

9.77935 

9.77963 

.9.77992 

29 

29 

28 

29 

28 

29 

28 

29 

29 

28 

29 

28 

29 

28 

29 

28 

29 

28 

28 

29 

28 

29 

28 

29 

28 

28 

29 

28 

29 

28 

28 

29 

28 

28 

29 

28 

28 

29 

28 

28 

28 

29 

28 

28 

28 

29 

28 

28 

28 

28 

29 

28 

28 

28 

28 

28 

29 

28 

28 

- 28 

0.22123 

0.22094 

0.22065 

0.22037 

0.22008 

9.93307 

9.93299 

9.93291 

9.93284 

9.93276 

8 

8 

7 

8 

7 

8 
8 

7 

8 
8 

7 

8 
8 

7 

8 
8 

7 

8 
8 

7 

8 
8 

7 

8 
8 

7 

8 
8 
8 

7 

8 
8 
8 

7 

8 
8 
8 
8 

7 

8 
8 
8 

7 

8 
8 
8 
8 
8 

7 

8 
8 
8 
8 
8 
8 

7 

8 
8 
8 
8 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

29 

6 2.9 

7 3.4 

8 3.9 

9 4.4 

10  4.8 

20  9.7 

30  14.5 
40  19.3. 

50  24.2 

28 

6 1 2.8 

7 3.3 

8 3.7 

9 4.2 

10  4.7 

20  9.3 

30  14.0 
40  18.7 
50  23.3 

21 

6 2.1 

7 2.5 

8 2.8 

9 3.2 

10  3.5 

20  7.0 

30  10.5 
40  14.0 
50  17.5 

20 

6 2.0 

7 2.3 

8 2.7 

9 3.0 

10  3.3 

20  6.7 

30  10.0 
40  13.3 
50  16.7 

8 7 

6 0.8  0.7 

7 0.9  0.8 

8 1.1  0.9 

9 1.2  1.1 
10  1.3  1.2 
20  2.7  2.3 
30  4.0  3.5 
40  5.3  4.7 
50  6.7  5.8 

9.71289 

9.71310 

9.71331 

9.71352 

.9.71373 

9.78020 

9.78049 

9.78077 

9.78106 

9.78135 

0.21980 

0.21951 

0.21923 

0.21894 

0.21865 

9.93269 

9.93261 

9.93253 

9.93246 

9.93238 

10 

11 

12 

13 

14 

9.71393 

9.71414 

9.71435 

9.71456 

9.71477 

9.78163 

9.78192 

9.78220 

9.78249 

9.78277 

0.21837 

0.21808 

0.21780 

0.21751 

0.21723 

9.93230 

9.93223 

9.93215 

9.93207 

9.93200 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.71498 

9.71519 

9.71539 

9.71560 

9.71581 

9.78306 

9.78334 

9.78363 

9.78391 

9.78419 

0.21694 

0.21666 

0.21637 

0.21609 

0.21581 

9.93192 

9.93184 

9.93177 

9.93169 

9.93161 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.71602 

9.71622 

9.71643 

9.71664 

9.71685 

9.78448 

9.78476 

9.78505 

9.78533 

9.78562 

0.21552 

0.21524 

0.21495 

0.21467 

0.21438 

9.93154 

9.93146 

9.93138 

9.93131 

9.93123 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.71705 

9.71726 

9.71747 

9.71767 

9.71788 

9.78590 

9.78618 

9.78647 

9.78675 

9.78704 

0.21410 

0.21382 

0.21353 

0.21325 

0.21296 

9.93115 

9.93108 

9.93100 

9.93092 

9.93084 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.71809 

9.71829 

9.71850 

9.71870 

9.71891 

9.78732 

9.78760 

9.78789 

9.78817 

9.78845 

0.21268 

0.21240 

0.21211 

0.21183 

0.21155 

9.93077 

9.93069 

9.93061 

9.93053 

9.93046 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.71911 

9.71932 

9.71952 

9.71973 

9.71994 

9.78874 

9.78902 

9.78930 

9.78959 

9.78987 

0.21126 

0.21098 

0.21070 

0.21041 

0.21013 

9.93038 

9.93030 

9.93022 

9.93014 

9.93007 

25 

24 

^23 

22 

21 

40 

41 

42 

43 

44 

9.72014 

9.72034 

9.72055 

9.72075 

9.72096 

9.79015 

9.79043 

9.79072 

9.79100 

9.79128 

0.20985 

0.20957 

0.20928 

0.20900 

0.20872 

9.92999 

9.92991 

9.92983 

9.92976 

9.92968 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.72116 

9.72137 

9.72157 

9.72177 

9.72198 

9.79156 

9.79185 

9.79213 

9.79241 

9.79269 

0.20844 

0.20815 

0.20787 

0.20759 

0.20731 

9.92960 

9.92952 

9.92944 

9.92936 

9.92929 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.72218' 

9.72238 

9.72259 

9.72279 

9.72299 

9.79297 

9.79326 

9.79354 

9.79382 

9.79410 

0.20703 

0.20674 

0.20646 

0.20618 

0.20590 

9.92921 

9.92913 

9.92905 

9.92897 

9.92889 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.72320 

9.72340 

9.72360 

9.72381 

9.72401 

9.79438 

9.79466 

9.79495 

9.79523 

9.79551 

0.20562 

0.20534 

0.20505 

0.20477 

0.20449 

9.92881 

9.92874 

9.92866 

9.92858 

9.92850 

5 

4 

3 

2 

1 

60 

9.72421 
L.  Cos. 

9.79579 

0.20421 

9.92842 

0 

d. 

L.  Cotg 

. d.  c. 

L.Tang. 

. L.  Sin. 

d. 

/ 

P.  P. 

58° 


524  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

32° 


/ 

L.  Sin. 

0 

9.72421 

1 

9.72441 

2 

9.72461 

3 

9.72482 

4 

9.72502 

5 

9.72522 

6 

9.72542 

7 

9.72562 

8 

9.72582 

9 

9.72602 

10 

9.72622 

11 

9.72643 

12 

9.72663 

13 

9.72683 

14 

9.72703 

15 

9.72723 

16 

9.72743 

17 

9.72763 

18 

9.72783 

19 

9.72803 

20 

9.72823 

21 

9.72843 

22 

9.72863 

23 

9.72883 

24 

9.72902 

25 

9.72922 

26 

9.72942 

27 

9.72962 

28 

9.72982 

29 

9.73002 

30 

9.73022 

31 

9.73041 

32 

9.73061 

33 

9.73081 

34 

9.73101 

35 

9.73121 

36 

9.73140 

37 

9.73160 

38 

9.73180 

39 

9.73200 

40 

9.73219 

41 

9.73239 

42 

9.73259 

43 

9.73278 

44 

9.73298 

45 

9.73318 

46 

9.73337 

47 

9.73357 

48 

9.73377 

49 

9.73396 

50 

9.73416 

51 

9.73435 

52 

9.73455 

53 

9.73474 

54 

9.73494 

55 

9.73513 

56 

9.73533 

57 

9.73552 

58 

9.73572 

59 

9.73591 

60 

9.73611 

L.Cos. 

d. 


L.Tang. 


20 

20 

21 

20 

20 

20 

20 

20 

20 

20 

21 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

19 

20 
20 
20 
20 
20 
20 

19 

20 
20 
20 
20 

19 

20 
20 
20 

19 

20 
20 

19 

20 
20 

19 

20 
20 

19 

20 

19 

20 

19 

20 

19 

20 

19 

20 

19 

20 


9.79579 

9.79607 

9.79635 

9.79663 

9.79691 


9.79719 

9.79747 

9.79776 

9.79804 

9.79832 


9.79860 

9.79888 

9.79916 

9.79944 

9.79972 


9.80000 

9.80028 

9.80056 

9.80084 

9.80112 


9.80140 

9.80168 

9.80195 

9.80223 

9.80251 


9.80279 

9.80307 

9.80335 

9.80363 

9.80391 


9.80419 

9.80447 

9.80474 

9.80502 

9.80530 


9.80558 

9.80586 

9.80614 

9.80642 

9.80669 


9.80697 

9.80725 

9.80753 

9.80781 

9.80808 


9.80836 

9.80864 

9.80892 

9.80919 

9.80947 


9.80975 

9.81003 

9.81030 

9.81058 

9.81086 

9.81113 

9.81141 

9.81169 

9.81196 

9.81224 


9.81252 


d.  c. 

28 

28 

28 

28 

28 

28 

29 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

27 

28 
28 
28 
28 
28 
28 
28 
28 
28 

27 

28 
28 
28 
28 
28 
28 

27 

28 
28 
28 
28 

27 

28 
28 
28 

27 

28 
28 
28 

27 

28 
28 

27 

28 
28 

27 

28 
28 


d.  L.  Cotg.  d.  c 


L.  Cotg. 

L.  Cos. 

0.20421 

9.92842 

0.20393 

9.92834 

0.20365 

9.92826 

0.20337 

9.92818 

0.20309 

9.92810 

0.20281 

9.92803 

0.20253 

9.92795 

0.20224 

9.92787 

0.20196 

9.92779 

0.20168 

9.92771 

0.20140 

9.92763 

0.20112 

9.92755 

0.20084 

9.92747 

0.20056 

9.92739 

0.20028 

9.92731 

0.20000 

9.92723 

0.19972 

9.92715 

0.19944 

9.92707 

0.19916 

9.92699 

0.19888 

9.92691 

0.19860 

9.92683 

0.19832 

9.92675 

0.19805 

9.92667 

0.19777 

9.92659 

0.19749 

9.92651 

0.19721 

9.92643 

0.19693 

9.92635 

0.19665 

9.92627 

0.19637 

9.92619 

0.19609 

9.92611 

0.19581 

9.92603 

0.19553 

9.92595 

0.19526 

9.92587 

0.19498 

9.92579 

0.19470 

9.92571 

0.19442 

9.92563 

0.19414 

9.92555 

0.19386 

9.92546 

0.19358 

9.92538 

0.19331 

9.92530 

0.19303 

9.92522 

0.19275 

9.92514 

0.19247 

9.92506 

0.19219 

9.92498 

0.19192 

9.92490 

0.19164 

9.92482 

0.19136 

9.92473 

0.19108 

9.92465 

0.19081 

9.92457 

0.19053 

9.92449 

0.19025 

9.92441 

0.18997 

9.92433 

0.18970 

9.92425 

0.18942 

9.92416 

0.18914 

9.92408 

0.18887 

9.92400 

0.18859 

9.92392 

0.18831 

9.92384 

0.18804 

9.92376 

0.18776 

9.92367 

0.18748 

9.92359 

L.Tang, 

. L.  Sin. 

8 

8 

8 

8 

7 

8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

9 

8 

8 

8 

8 

8 

8 

8 

8 

9 

8 

8 

8 

8 

8 

8 

9 

8 

8 

8 

8 

8 

9 

8 


P. 

P. 

29 

28 

6 

2.9 

2.8 

7 

3.4 

3.3 

8 

3.9 

3.7 

9 

4.4 

4.2 

10 

4.8 

4.7 

20 

9.7 

9.3 

30 

14.5 

14.0 

40 

19.3 

18.7 

50 

24.2 

23.3 

27 

6 

2.7 

7 

3.2 

8 

3.6 

9 

4.1 

10 

4.5 

20 

9.0 

30 

13.5 

40 

18.0 

50 

22.5 

21 

20 

6 

! 2.1 

2.0 

7 

2.5 

2.3 

8 

2.8 

2.7 

- 9 

3.2 

3.0 

10 

3.5 

3.3 

20 

7.0 

6.7 

30 

10.5 

10.0 

40 

14.0 

13.3 

- 50 

17.5 

16.7 

19 

6 

1.9 

7 

2.2 

8 

2.5 

9 

2.9 

10 

3.2 

20 

6.3 

30 

9.5 

40 

12.7 

50 

15.8 

9 

8 

7 

6 

0.9 

0.8 

0.7 

7 

1.1 

0.9 

0.8 

8 

1.2 

1.1 

0.9 

9 

1.4 

1.2 

1.1 

10 

1.5 

1.3 

1.2 

20 

3.0 

2.7 

2.3 

30 

4.5 

4.0 

3.5 

40 

6.0 

5.3 

4.7 

50 

7.5 

6.7 

5.8 

P. 

, I 

> 

57° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


525 


f 

L.  Sin. 

0 

9.73611 

1 

9,73630 

2 

9.73650 

3 

9.73669 

4 

9.73689 

5 

9.73708 

6 

9.73727 

7 

9.73747 

8 

9.73766 

9 

9.73785 

10 

9.73805 

11 

9.73824 

12 

9.73843 

13 

9.73863 

14 

9.73882 

15 

9.73901 

16 

9.73921 

17 

9.73940 

18 

9.73959 

19 

9.73978 

20 

9.73997 

21 

9.74017 

22 

9.74036 

23 

9.74055 

24 

9.74074 

25 

9.74093 

26 

9.74113 

27 

9.74132 

28 

9.74151 

29 

9.74170 

30 

9.74189 

31 

9.74208 

32 

9.74227 

33 

9.74246 

34 

9.74265 

35 

9.74284 

36 

9.74303 

37 

9.74322 

38 

9.74341 

39 

9.74360 

40 

9.74379 

41 

9.74398 

42 

9.74417 

43 

9.74436 

44 

9.74455 

45 

9.74474 

46 

9.74493 

47 

9.74512 

48 

9.74531 

49 

9.74549 

50 

9.74568 

51 

9.74587 

52 

9.74606 

53 

9.74625 

54 

9.74644 

55 

9.74662 

56 

9.74681 

57 

9.74700 

58 

9.74719 

59 

9.74737 

60 

9.74756 

L.  Cos. 

d. 


19 

20 

19 

20 
19 

19 

20 
19 

19 

20 
19 

19 

20 
19 

19 

20 
19 
19 
19 

19 

20 
19 
19 
19 

19 

20 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
18 
19 
19 
19 
19 
19 
18 
19 
19 
19 
18 
19 


L.Tang. 

d.  c.  : 

L.  Cotg. 

L.  Cos. 

9.81252 

0.18748 

9.92359 

9.81279 

27 

0.18721 

9.92351 

9.81307 

28 

0.18693 

9.92343 

9.81335 

28 

0.18665 

9.92335 

9.81362 

27 

OG 

0.18638 

9.92326 

9.81390 

Zo 

0.18610 

9.92318 

9.81418 

28 

0.18582 

9.92310 

9.81445 

27 

0.18555 

9.92302 

9.81473 

28 

0.18527 

9.92293 

9.81500 

27 

OG 

0.18500 

9.92285 

9.81528 

Zo 

0.18472 

9.92277 

9.81556 

28 

0.18444 

9.92269 

9.81583 

27 

0.18417 

9.92260 

9.81611 

28 

0.18389 

9.92252 

9.81638 

27 

OQ 

0.18362 

9.92244 

9.81666 

Zo 

0.18334 

9.92235 

9.81693 

27 

0.18307 

9.92227 

9.81721 

28 

0.18279 

9.92219 

9.81748 

27 

0.18252 

9.92211 

9.81776 

28 

07 

0.18224 

9.92202 

9.81803 

Zl 

0.18197 

9.92194 

9.81831 

28 

0.18169 

9.92186 

9.81858 

27 

0.18142 

9.92177 

9.81886 

28 

0.18114 

9.92169 

9.81913 

27 

OG 

0.18087 

9.92161 

9.81941 

Zo 

0.18059 

9.92152 

9.81968 

27 

0.18032 

9.92144 

9.81996 

28 

0.18004 

9.92136 

9.82023 

27 

0.17977 

9.92127 

9.82051 

28 

07 

0.17949 

9.92119 

9.82078 

Zl 

0.17922 

9.92111 

9.82106 

28 

0.17894 

9.92102 

9.82133 

27 

0.17867 

9.92094 

9.82161 

28 

0.17839 

9.92086 

9.82188 

27 

07 

0.17812 

9.92077 

9.82215 

Zl 

0.17785 

9.92069 

9.82243 

28 

0.17757 

9.92060 

9.82270 

27 

0.17730 

9.92052 

9.82298 

28 

0.17702 

9.92044 

9.82325 

27 

07 

0.17675 

9.92035 

9.82352 

Zl 

0.17648 

9.92027 

9.82380 

28 

0.17620 

9.92018 

9.82407 

27 

0.17593 

9.92010 

9.82435 

28 

0.17565 

9.92002 

9.82462 

27 

07 

0.17538 

9.91993 

9.82489 

Zl 

0.17511 

9.91985 

9.82517 

28 

0.17483 

9.91976 

9.82544 

27 

0.17456 

9.91968 

9.82571 

27 

0.17429 

9.91959 

9.82599 

28 

27 

0.17401 

9.91951 

9.82626 

0.17374 

9.91942 

9.82653 

27 

0.17347 

9.91934 

9.82681 

28 

0.17319 

9.91925 

9.82708 

27 

0.17292 

9.91917 

9.82735 

27 

07 

0.17265 

9.91908 

9.82762 

Zl 

0.17238 

9.91900 

9.82790 

28 

0.17210 

9.91891 

9.82817 

27 

0.17183 

9.91883 

9.82844 

27 

0.17156 

9.91874 

9.82871 

27 

- 28 

0.17129 

9.91866 

9.82899 

0.17101 

9.91857 

L.  Cotg 

. d.  c. 

L.Tang 

. L.  Sin. 

d. 


8 

8 

8 

9 

8 

8 

8 

9 

8 

8 

8 

9 

8 

8 

9 

8 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

9 

8 

8 

9 

8 

9 

8 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

~ d7 


60 

59 

58 

57 

56_ 

55 

54 

53 

52 

51 


35 
34 
33 
32 
31 

36 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

a 

ii 

to 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 


P.  P. 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


20 

2.0 

2.3 

2.7 
3.0 

3.3 

6.7 
10.0 
13.3 
16.7 


19 

1.9 

2.2 

2.5 

2.9 

3.2 

6.3 

9.5 

12.7 

15.8 


18 

1.8 

2.1 

2.4 

2.7 

3.0 

6.0 

9.0 

12.0 

15.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


9 

0.9 

1.1 

1.2 

1.4 

1.5 

3.0 

4.5 

6.0 

7.5 


0.8 

0.9 

1.1 

1.2 

1.3 

2.7 
4.0 

5.3 

6.7 


P.  P. 


5SC 


526  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

34° 


t 

L.  Sin. 

0 

9.74756 

1 

9.74775 

2 

9.74794 

3 

9.74812 

4 

9.74831 

5 

9.74850 

6 

9.74868 

7 

9.74887 

8 

9.74906 

9 

9.74924 

10 

9.74943 

11 

9.74961 

12 

9.74980 

13 

9.74999 

14 

9.75017 

15 

9.75036 

16 

9.75054 

17 

9.75073 

18 

9.75091 

19 

9.75110 

20 

9.75128 

21 

9.75147 

22 

9.75165 

23 

9.75184 

24 

9.75202 

25 

9.75221 

26 

9.75239 

27 

9.75258 

28 

9.75276 

29 

9.75294 

30 

9.75313 

31 

9.75331 

32 

9.75350 

33 

9.75368 

34 

9.75386 

35 

9.75405 

36 

9.75423 

37 

9.75441 

38 

9.75459 

39 

9.75478 

40 

9.75496 

41 

9.75514 

42 

9.75533 

43 

9.75551 

44 

9.75569 

45 

9.75587 

46 

9.75605 

47 

9.75624 

48 

9.75642 

49 

9.75660 

50 

9.75678 

51 

9.75696 

52 

9.75714 

53 

9.75733 

54 

9.75751 

55 

9.75769 

56 

9.75787 

57 

9.75805 

58 

9.75823 

59 

9.75841 

60 

9.75859 

d.  L.Tang. 


L.  Cos. 


19 

19 

18 

19 

19 

18 

19 

19 

18 

19 

18 

19 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

18 

19 

18' 
19 
18 
18 
19 
18 
18 
18 
19 
18 
18 
19 
18 
18 
18 
18 
19 
18  • 
18 
18 
18 
18 
19 
18 
18 
18 
18 
18 
18 
18 


9.82899 

9.82926 

9.82953 

9.82980 

9.83008 


9.83035 

9.83062 

9.83089 

9.83117 

9.83144 


9.83171 

9.83198 

9.83225 

9.83252 

9.83280 


9.83307 

9.83334 

9.83361 

9.83388 

9.83415 


9.83442 

9.83470 

9.83497 

9.83524 

9.83551 


9.83578 

9.83605 

9.83632 

9.83659 

9.83686 


9.83713 

9.83740 

9.83768 

9.83795 

9.83822 


9.83849 

9.83876 

9.83903 

9.83930 

9.83957 


9.83984 

9.84011 

9.84038 

9.84065 

9.84092 


9.84119 

9.84146 

9.84173 

9.84200 

9.84227 


9.84254 

9.84280 

9.84307 

9.84334 

9.84361 


9.84388 

9.84415 

9.84442 

9.84469 

9.84496 


9.84523 


L.  Cotgf. 


27 

27, 

27 

28 
27 
27 

27 

28 
27 
27 
27 
27 

27 

28 
27 
27 
27 
27 
27 

27 

28 
27 
27 
27 
27 
27 
27 
27 
27 
27 

27 

28 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
26 
27 
27 
27 
27 
27 
27 
27 
27 
27 


L.  Cotg. 

L.  Cos. 

0.17101 

0.17074 

0.17047 

0.17020 

0.16992 

9.91857 

9.91849 

9.91840 

9.91832 

9.91823 

0.16965 

0.16938 

0.16911 

0.16883 

0.16856 

9.91815 

9.91806 

9.91798 

9.91789 

9.91781 

0.16829 

0.16802 

0.16775 

0.16748 

0.16720 

9.91772 

9.91763 

9.91755 

9.91746 

9.91738 

0.16693 

0.16666 

0.16639 

0.16612 

0.16585 

9.91729 

9.91720 

9.91712 

9.91703 

9.91695 

0.16558 

0.16530 

0.16503 

0.16476 

0.16449 

9.91686 

9.91677 

9.91669 

9.91660 

9.91651 

0.16422 

0.16395 

0.16368 

0.16341 

0.16314 

9.91643 

9.91634 

9.91625 

9.91617 

9.91608 

0.16287 

0.16260 

0.16232 

0.16205 

0.16178 

9.91599 

9.91591 

9.91582 

9.91573 

9.91565 

0.16151 

0.16124 

0.16097 

0.16070 

0.16043 

9.91556 

9.9154? 

9.91538 

9.91530 

9.91521 

0.16016 

0.15989 

0.15962 

0.15935 

0.15908 

9.91512 

9.91504 

9.91495 

9.91486 

9.91477 

0.15881 

0.15854 

0.15827 

0.15800 

0.15773 

9.91469 

9.91460 

9.91451 

9.91442 

9.91433 

0.15746 

0.15720 

0.15693 

0.15666 

0.15639 

9.91425 

9.91416 

9.91407 

9.91398 

9.91389 

0.15612 

0.15585 

0.15558 

0.15531 

0.15504 

9.91381 

9.91372 

9.91363 

9.91354 

9.91345 

0.15477 

9.91336 

L.Tang. 

L.  Sin. 

d. 


8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

9 

8 

9 

8 

9 

9 

8 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

9 

8 

9 

9 

8 

9 

9 

9 

8 

9 

9 

9 

9 

8 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 


d. 


55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 


P.  P. 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


13 

1.9 

2.2 

2.5 

2.9 

3.2 

6.3 

9.5 

12.7 

15.8 


18 

1.8 

2.1 

2.4 

2.7 

3.0 

6.0 

9.0 

12.0 

15.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


9 

0.9 

1.1 

1.2 

1.4 

1.5 

3.0 

4.5 

6.0 

7.5 


0.8 

0.9 

1.1 

1.2 

1.3 

2.7 
4.0 

5.3 

6.7 


P.  P. 


55° 


f 

L.  Sin. 

0 

9.75859 

1 

9.75877 

2 

9.75895 

3 

9.75913 

4 

9.75931 

5 

9.75949 

6 

9.75967 

7 

9.75985 

8 

9.76003 

9 

9.76021 

10 

9.76039 

11 

9.76057 

12 

9.76075 

13 

9.76093 

14 

9.76111 

15 

9.76129 

16 

9.76146 

17 

9.76164 

18 

9.76182 

19 

9.76200 

20 

9.76218 

21 

9.76236 

22 

9.76253 

23 

9.76271 

24 

9.76289 

25 

9.76307 

26 

9.76324 

27 

9.76342 

28 

9.76360 

29 

9.76378 

30 

9.76395 

31 

9.76413 

32 

9.76431 

33 

9.76448 

34 

9.76466 

35 

9.76484 

36 

9.76501 

37 

9.76519 

38 

9.76537 

39 

9.76554 

40 

9.76572 

41 

9.76590 

42 

9.76607 

43 

9.76625 

44 

9.76642 

45 

9.76660 

46 

9.76677 

47 

9.76695 

48 

9.76712 

49 

9.76730 

50 

9.76747 

51 

9.76765 

52 

9.76782 

53 

9.76800 

54 

9.76817 

55 

9.76835 

56 

9.76852 

57 

9.76870 

58 

9.76887 

59 

9.76904 

60 

9.76922 

L.  Cos. 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS . 

35°  


527 


d. 


L.Tang.  d.  c.  L.  Cotg. 


18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

17 

18 
18 
18 
18 
18 

17 

18 
18 
18 

17 

18 
18 
18 

17 

18 
18 

17 

18 
18 

17 

18 
18 

17 

18 
18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 
17 

17 

18 


9.84528 

9.84550 

9.84576 

9.84603 

9.84630 


9.84657 

9.84684 

9.84711 

9.84738 

9.84764 


9.84791 

9.84818 

9.84845 

9.84872 

9.84899 


9.84925 

9.84952 

9.84979 

9.85006 

9.85033 


9.85059 

9.85086 

9.85113 

9.85140 

9.85166 


9.85193 

9.85220 

9.85247 

9.85273 

9.85300 


9.85327 

9.85354 

9.85380 

9.85407 

9.85434 


9.85460 

9.85487 

9.85514 

9.85540 

9.85567 


9.85594 

9.85620 

9.85647 

9.85674 

9.85700 


9.85727 

9.85754 

9.85780 

9.85807 

9.85834 


9.85860 

9.85887 

9.85913 

9.85940 

9.85967 


9.85993 

9.86020 

9.86046 

9.86073 

9.86100 


9.86126 


d.  L.  Cotg. 


27 

26 

27 

27 

27 

27 

27 

27 

26 

27 

27 

27 

27 

27 

26 

27 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

26 

27 

27 

26 

27 

26 

27 

27 

26 


0.15477 

0.15450 

0.15424 

0.15397 

0.15370 


0.15343 

0.15316 

0.15289 

0.15262 

0.15236 


0.15209 

0.15182 

0.15155 

0.15128 

0.15101 


0.15075 

0.15048 

0.15021 

0.14994 

0.14967 


0.14941 

0.14914 

0.14887 

0.14860 

0.14834 


0.14807 

0.14780 

0.14753 

0.14727 

0.14700 


L.  Cos. 


9.91336 

9.91328 

9.91319 

9.91310 

9.91301 


9.91292 

9.91283 

9.91274 

9.91266 

9.91257 


9.91248 

9.91239 

9.91230 

9.91221 

9.91212 


d. 


9.91203 

9.91194 

9.91185 

9.91176 

9.91167 


9.91158 

.9.91149 

9.91141 

9.91132 

9.91123 


0.14673 

0.14646 

0.14620 

0.14593 

0.14566 


0.14540 

0.14513 

0.14486 

0.14460 

0.14433 


0.14406 

0.14380 

0.14353 

0.14326 

0.14300 


9.91114 

9.91105 

9.91096 

9.91087 

9.91078 


9.91069 

9.91060 

9.91051 

9.91042 

9.91033 


9.91023 

9.91014 

9.91005 

9.90996 

9.90987 


0.14273 

0.14246 

0.14220 

0.14193 

0.14166 


0.14140 

0.14113 

0.14087 

0.14060 

0.14033 


0.14007 

0.13980 

0.13954 

0.13927 

0.13900 


d.  c. 


0.13874 
I L.Tang 


9.90978 

9.90969 

9.90960 

9.90951 

9.90942 


9.90933 

9.90924 

9.90915 

9.90906 

9.90896 


9.90887 

9.90878 

9.90869 

9.90860 

9.90851 


9.90842 

9.90832 

9.90823 

9.90814 

9.90805 


9.90796 


L.  Sin. 


8 

9 

9 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 
9 
9 
9 

10 
9 
9 
9 
9 
9 
9 
9 
9 

9 
9 
9 
9 
9 

10 
9 
9 

9 
9 
9 
9 

10 
9 
9 
9 
9 


60 

59 

58 

57 

56^ 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 


P.  P. 


27 

26 

6 

2.7 

2.6 

7 

3.2 

3.0 

8 

3.6 

3.5 

9 

4.1 

3.9 

10 

4.5 

4.3 

20 

9.0 

8.7 

30 

13.5 

13.0 

40 

18.0 

17.3 

50 

22.5 

21.7 

18 

6 

1.8 

7 

2.1 

8 

2.4 

9 

2.7 

10 

3.0 

20 

6.0 

30 

9.0 

40 

12.0 

50 

15.0 

17 

1.7 
2.0 
2.3 
2.6 

2.8 
5.7 
8.5 

11.3 

14.2 


10 

1.0 

1.2 

1.3 
1.5 

1.7 

3.3 
5.0 

6.7 

8.3 


9 

8 

6 

0.9 

0.8 

7 

1.1 

0.9 

8 

1.2 

1.1 

9 

1.4 

1.2 

10 

1.5 

1.3 

20 

3.0 

2.7 

30 

4.5 

4.0 

40 

6.0 

5.3 

50 

7.5 

6.7 

P.  P. 


54° 


528  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

36° 


L.  Sin. 


d. 


L.Tang. 


d.  c. 


L.  Cotg. 

L.  Cos. 

d. 

0.13874 

9.90796 

60 

0.13847 

9.90787 

9 

59 

0.13821 

9.90777 

10 

58 

0.13794 

9.90768 

9 

57 

0.13768 

9.90759 

9 

q 

56 

0.13741 

9.90750 

«7 

A 

55 

0.13715 

9.90741 

9 

54 

0.13688 

9.90731 

10 

53 

0.13662 

9.90722 

9 

52 

0.13635 

9.90713 

9 

q 

51 

0.13608 

9.90704 

V 

-?  rv 

50 

0.13582 

9.90694 

iO 

49 

0.13555 

9.90685 

9 

48 

0.13529 

9.90676 

9 

47 

0.13502 

9.90667 

9 

10 

46 

0.13476 

9.90657 

-LV/ 

A 

45 

0.13449 

9.90648 

9 

a 

44 

0.13423 

9.90639 

9 

43 

0.13397 

9.90630 

9 

42 

0.13370 

9.90620 

10 

q 

41 

0.13344 

9.90611 

A 

40 

0.13317 

9.90602 

9 

1 A 

39 

0.13291 

9.90592 

10 

38 

0.13264 

9.90583 

9 

37 

0.13238 

9.90574 

9 

9 

36 

0.13211 

9.90565 

35 

0.13185 

9.90555 

10 

34 

0.13158 

9.90546 

9 

A 

33 

0.13132 

9.90537 

9 

32 

0.13106 

9.90527 

10 

9 

31 

0.13079 

9.90518 

30 

0.13053 

9.90509 

9 

29 

0.13026 

9.90499 

10 

A 

28 

0.13000 

9.90490 

9 

27 

0.12973 

9.90480 

10 

9 

26 

0.12947 

9.90471 

25 

0.12921 

9.90462 

9 

24 

0.12894 

9.90452 

10 

23 

0.12868 

9.90443 

9 

22 

0.12842 

9.90434 

9 

10 

21 

0.12815 

9.90424 

20 

0.12789 

9.90415 

9 

19 

0.12762 

9.90405 

10 

18 

0.12736 

9.90396 

9 

17 

0.12710 

9.90386 

10 

9 

16 

0.12683 

9.90377 

15 

0.12657 

9.90368 

9 

14 

0.12631 

9.90358 

10 

13 

0.12604 

9.90349 

9 

12 

0.12578 

9.90339 

10 

9 

11 

0.12552 

9.90330 

10 

0.12525 

9.90320 

10 

9 

0.12499 

9.90311 

9 

*1  A 

8 

0.12473 

9.90301 

10 

7 

0.12446 

9.90292 

9 

10 

6 

0.12420 

9.90282 

5 

0.12394 

9.90273 

9 

4 

0.12367 

9.90263 

10 

3 

0.12341 

9.90254 

9 

2 

0.12315 

9.90244 

10 

9 

1 

0.12289 

9.90235 

0 

L.Tang. 

L.  Sin 

| d.. 

/ 

P.  P. 


20 

21 

22 

23 

24 


25 

26 

27 

28 
29 

30” 

31 

32 

33 

34 

35 

36 

37 

38 

39 


40 

41 

42 

43 

44 


45 

46 

47 
48' 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 


9.76922 

9.76939 

9.76957 

9.76974 

9.76991 


9.77009 

9.77026 

9.77043 

9.77061 

9.77078 


9.77095 

9.77112 

9.77130 

9.77147 

9.77164 


9.77181 

9.77199 

9.77216 

9.77233 

9.77250 


9.77268 

9.77285 

9.77302 

9.77319 

9.77336 


9.77353 

9.77370 

9.77387 

9.77405 

9.7/422 


9.77439 

9.77456 

9.77473 

9.77490 

977507 


9.77524 

9.77541 

9.77558 

9.77575 

9.77592 


9.77609 

9.77626 

9.77643 

9.77660 

9.77677 


9.77694 

9.77711 

9.77728 

9.77744 

9.77761 


9.77778 

9.77795 

9.77812 

9.77829 

9.77846 


9.77862 

9.77879 

9.77896 

9.77913 

9.77930 


60 


9.77946 
L.  Cos. 


17 

18 
17 

17 

18 
17 

17 

18 
17 
17 

17 

18 
17 
17 

17 

18 
17 
17 

17 

18 
17 
17 
17 
17 
17 
17 

17 

18 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
16 
17 
17 
17 
17 
17 
17 
16 

17 

17 

17 

17 

16 


9.86126 

9.86153 

9.86179 

9.86206 

9.86232 


9.86259 

9.86285 

9.86312 

9.86338 

9.86365 


9.86392 

9.86418 

9.86445 

9.86471 

9.86498 


9.86524 

9.86551 

9.86577 

9.86603 

9.86630 


9.86656 

9.86683 

9.86709 

9.86736 

9.86762 

9.86789 

9.86815 

9.86842 

9.86868 

9.86894 


9.86921 

9=86947 

9.86974 

9.87000 

9.87027 


9.87053 

9.87079 

9.87106 

9.87132 

9.87158 


9.87185 

9.87211 

9.87238 

9.87264 

9.87290 


9.87317 

9.87343 

9.87369 

9.87396 

9.87422 


9.87448 

9.87475 

9.87501 

9.87527 

9.87554 


9.87580 

9.87606 

9.87633 

9.87659 

9.87685 


9.87711 


27 

26 

27 

26 

27 

26 

27 

26 

27 

27 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

27 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

26 

27 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

26 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


18 

1.8 

2.1 

2.4 

2.7 

3.0 

6.0 

9.0 


40  12.0 
50  i 15.0 


6 

7 

8 
9 

10 

20 

30 

40 

50 


17 

1.7 
2.0 
2.3 
2.6 

2.8 
5.7 
8.5 

11.3 

14.2 


16 

1.6 

1.9 

2.1 

2.4 

2.7 

5.3 

8.0 

10.7 

13.3 


iO 

1.0 

1.2 

1.3 
1.5 

1.7 

3.3 
5.0 

6.7 

8.3 


9 

0.9 

1.1 

1.2 

1.4 

1.5 

3.0 

4.5 

6.0 

7.5 


d.  L.  Cotg, 


d.  c. 


P.  P. 


53c 


logarithms  of  trigonometric  functions. 


529 


/ I 

L.  Sin.  c 

0 

9.77946  n 

1 

9.77963 

2 

9.77980  } 

3 

9.77997 

4 

9.78013 

5 

9.78030  . 

6 

9.78047  ] 

7 

9.78063  ; 

8 

9.78080  : 

9 

9.78097  : 

10 

9.78113  ; 

11 

9.78130 

12 

9.78147 

13 

9.78163 

14 

9.78180 

15 

9.78197 

16  1 

9.78213 

17 

9.78230 

18 

9.78246 

19 

9.78263 

20 

9.78280 

21 

9.78296 

22 

9.78313 

23 

9.78329 

24 

9.78346 

25 

9.78362 

26 

9.78379 

27 

9.78395 

28 

9.78412 

29 

; 9.78428 

30 

9.78445 

31 

9.78461 

32 

9.78478 

33 

9.78494 

34  1 

9.78510 

35 

9.78527 

36 

9.78543 

37 

9.78560 

38 

9.78576 

39 

9.78592 

40 

9.78609 

41 

9.78625 

42 

9.78642 

43 

9.78658 

44 

9.78674 1 

45 

9.78691" 

46 

9.78707 

47 

9.78723 

48 

9.78739 

49 

9.78756 

50 

| 9.78772 

51 

9.78788 

52 

9.78805 

53 

9.78821 

54 

9.78837 

55 

9.78853 

56 

9.78869 

57 

9.78886 

58 

. 9.78902 

59 

i 9.78918 

60 

i 9.78934 

16 

17 

16 

17 

17 

16 

17 

16 

17 

16 

17 

16 

17 

16 

17 

16 

17 

16 

16 

17 

16 

17 

16 

16 

17 

16 

17 

16 

16 

17 

16 

16 

16 

17 

16 


d. 


L.Tang.  d. 

9.87711  r 
9.87738  i 
9.87764  i 
9.87790  ; 

9.87817  t 

9.87843  J 
9.87869  ; 

9.87895  ; 

9.87922  ; 

9.87948  ; 

9.87974  i 
9.88000  ; 

9.88027  ; 

9.88053  ; 

9.88079  ; 

9.88105 

9.88131 

9.88158 

9.88184 

9.88210 

9.88236 

9.88262 

9.88289 

9.88315 

9.88341 

9.88367 

9.88393 

9.88420 

9.88446 

9.88472 

9.88498 

9.88524 

9.88550 

9.88577 

9.88603 

9.88629 

9.88655 

9.88681 

9.88707 

9.88733 

9.88759 

9.88786 

9.88812 

9.88838 

9.88864 

9.88890 

9.88916 

9.88942 

9.88968 

9.88994 

9.89020 
9.89046 
9.89073 
' 9.89099 

1 9.89125 

’ 9.89151 

» 9.89177 

' 9.89203 

> 9.89229 

> 9.89255 

3 9.89281 

L.  Cotg 


.c.  I 

j.  Cotg.  ] 

L.  Cos. 

d. 

P. 

P. 

0.12289 

9.90235 

i 

60 

27- 

0.12262 

9.90225 

10 

59 

26 

0.12236 

9.90216 

9 

58 

27 

26 

0.12210 

9.90206 

10 

57 

6 

2.7 

27 

0.12183 

9.90197 

9 

10 

56 

7 

3.2 

26 

0.12157 

9.90187 

55 

8 

3.6 

26 

0.12131 

9.90178 

9 

54 

9 

4.1 

26 

0.12105 

9.90168 

10 

53 

10 

4.5 

27 

0.12078 

9.90159 

9 

52 

20 

9.0 

26 

0.12052 

9.90149 

10 

10  - 

51 

30 

13.5 

2b 

0.12026 

9.90139 

50 

40 

18.0 

26 

0.12000 

9.90130 

9 

49 

50 

22.5 

27 

0.11973 

9.90120 

10 

48 

26 

0.11947 

9.90111 

9 

47 

26 

0.11921 

9.90101 

10 

10 

46 

26 

Zb 

0.11895 

9.90091 

45 

6 

2.6 

26 

0.11869 

9.90082 

9 

44 

7 

3.0 

27 

0.11842 

9.90072 

10 

43 

8 

3.5 

26 

0.11816 

9.90063 

9 

42 

9 

3.9 

26 

0.11790 

9.90053 

10 

41 

10 

4.3 

26 

10 

20 

0.11764 

9.90043 

40 

o ./ 

1 o A 

26 

0.11738 

9.90034 

9 

39 

30 

13.0 

27 

0.11711 

9.90024 

10 

38 

40 

17.3 

HI  *7  j 

26 

0.11685 

9.90014 

10 

37 

50 

21.7 

26 

26 

0.11659 

9.90005 

9 

10 

36 

N 

0.11633 

9.89995 

35 

26 

0.11607 

9.89985 

10 

34 

17 

27 

0.11580 

9.89976 

9 

33 

6 

1.7 

26 

0.11554 

9.89966 

10 

32 

7 

2.0 

26 

0.11528 

9.89956 

10 

q 

31 

8 

Q 

2.3 
9 fi 

Zo 

0.11502 

9.89947 

U 
-1  A 

30 

10 

2.8 

26 

0.11476 

9.89937 

10 

29 

20 

5.7 

26 

0.11450 

9.89927 

10 

28 

30 

8.5 

27 

0.11423 

9.89918 

9 

27 

40 

11.3 

26 
O a 

0.11397 

9.89908 

10 

10 

26 

50 

14.2 

ZO 

0.11371 

9.89898 

25 

26 

0.11345 

9.89888 

10 

24 

.26 

0.11319 

9.89879 

9 

23 

ic 

26 

0.11293 

9.89869 

10 

22 

o 

lb 

1 A 

26 

OA 

0.11267 

9.89859 

10 

10 

21 

b 

7 

i.b 

1.9 

Zb 

0.11241 

9.89849 

20 

8 

2.1 

27 

0.11214 

9.89840 

9 

19 

9 

2.4 

26 

0.11188 

9.89830 

10 

18 

10 

2.7 

26 

0.11162 

9.89820 

10 

17 

20 

5.3 

26 

OA 

0.11136 

9.89810 

10 

9 

16 

30 

8.0 

Zb 

0.11110 

9.89801 

15 

40 

10.7 

26 

0.11084 

9.89791 

10 

14 

50 

i 13.3 

26 

0.11058 

9.89781 

10 

13 

26 

0.11032 

9.89771 

10 

12 

26 

OA 

0.11006 

9.89761 

10 

Q 

11 

10 

9 

Zb 

0.10980 

9.89752" 

-f  A 

10 

6 

1.0 

0.9 

26 

0.10954 

9.89742 

10 

9 

7 

1.2 

1.1 

27 

0.10927 

9.89732 

10 

8 

8 

1.3 

1.2 

26 

0.10901 

9.89722 

10 

7 

9 

1.5 

1.4 

26 

OA 

0.10875 

9.89712 

10 

' 10 

6 

10 

1.7 

1.5 

ZO 

0.10849 

9.89702 

5 

20 

3.3 

3.0 

26 

0.10823 

9.89693 

i 9 

4 

30 

5.0 

4.5 

26 

0.10797 

9.89683 

1 K 

3 

40 

6.7 

6.0 

26 

0.10771 

9.89673 

; In 

2 

50 

8.3 

7.5 

26 
o Ct 

0.10745 

> 9.89663 

5 10 

1 

ZO 

0.10719 

1 9.8965* 

i 10 

0 

d.  c 

. L.Tang 

f.  L.  Sin 

. d. 

/ 

P.  P. 

52° 


530  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS . 

38° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.78934 

9.78950 

9.78967 

9.78983 

9.78999 

16 

17 

16 

16 

16 

16 

16 

16 

16 

16 

9.89281 

9.89307 

9.89333 

9.89359 

9.89385 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

0.10719 

0.10693 

0.10667 

0.10641 

0.10615 

9.89653 

9.89643 

9.89633 

9.89624 

9.89614 

10 

10 

9 

! 10 
j 10 

10 
: io 
! io 
! 10 
10 

60 

59 

58 

57 

56 

26 

6 2.6 

7 3.0 

8 I 3.5 

9 j 3.9 

10  4.3 

20  8.7 

30  13.0 

25 

2.5 
2.9 
I 3.3 
1 3.8 
! 4.2 
8.3 
12.5 

5 

6 

7 

8 
9 

9.79015 

9.79031 

9.79047 

9.79063 

9.79079 

9.80411 

9.89437 

9.89463 

9.89489 

9.89515 

0.10589 

0.10563 

0.10537 

0.10511 

0.10485 

9.89604 

9.89594 

9.89584 

9.89574 

9.89564 

55 

54 

53 

52 

51 

10 

9.79095 

9.89541 

0.10459 

9.89554 

50 

40  17.3 

16.7 

11 

9.79111 

16 

9.89567 

26 

0.10433 

9.89544 

10 

49 

50  | 21.7 

20.S 

12 

9.79128 

17 

9.89593 

26 

0.10407 

9.89534 

! 10 

48 

13 

9.79144 

16 

9.89619 

26 

0.10381 

9.89524 

1 10 

47 

14 

9.79160 

16 

16 

9.89645 

26 

OA 

0.10355 

9.89514 

10 

10 

46 

17 

15 

9.79176 

9.89671 

0.10329 

9.89504 

45 

6 17 

16 

9.79192 

16 

9.89697 

26 

0.10303 

9.89495 

9 

44 

7 ? 5 

> 0 

17 

9.79208 

16 

9.89723 

26 

0.10277 

9.89485 

! 10 

43 

8 2.3 

18 

9.79224 

16 

9.89749 

26 

0.10251 

9.S9475 

i 10 

42 

9 2.6 

19 

9.79240 

16 

16 

9.89775 

26 

26 

0.10225 

9.89465 

1 10 
! 10 

41 

io  *: 

>.8 

20 

9.79256 

9.89801 

0.10199 

9.89455 

40 

20  ! 5.7 

21 

9.79272 

16 

9.89827 

26 

0.10173 

9.S9445 

1 10 

39 

30  | 8.5 

22 

9.79288 

16 

9.89S53 

26 

0.10147 

9.89435 

j 10 

38 

40  j 11.3 

23 

9.79304 

16 

9.89879 

26 

0.10121 

9.89425 

i 10 

37 

50  j 14.2 

24 

9.79319 

15 

16 

9.89905 

26 

26 

0.10095 

9.89415 

I 10 
10 

36 

25 

9.79335 

9.89931 

0.10069 

9.89405 

35 

26 

9.79351 

16 

9.89957 

26 

0.10043 

9.89395 

10 

34 

16 

15 

27 

9.79367 

16 

9.89983 

26 

0.10017 

9.89385 

10 

33 

6 1.6 

1.5 

28 

9.79383 

16 

9.90009 

26 

0.09991 

9.89375 

10 

32 

7 1.9 

1.8 

29 

9.79399 

16 

9.90035  I 

26 

j 0.09965 

9.89364 

! 11 

31 

8 2.1 

2.0 

16 

1 Ofx 

! 10 

30 

9.79415 

9.90061 

zo 

! 0.09939 

9.89354 

30 

9 2.4 

| 2.3 

31 

9.79431  ! 

16 

9.90086 

25 

0.09914 

9.S9344 

! 10 

29 

10  2.7 

: 2.5 

32 

9.79447  ! 

16 

9.90112 

26 

i 0.09888 

9.89334 

j 10 

28 

20  i o.3 

; 5.0 

33 

9.79463 

16 

9.90138 

j 26 

0.09862 

9.89324 

! 10 

27 

30  8.0 

* 7.5 

34 

9.79478 

15 

16 

9.90164  ! 

26 

26 

i 0.09836 

9.89314 

j 10 
10 

26 

40  10.7 
50  , 13.3  | 

10.0 

12.5 

35 

9.79494  1 

9.90190  | 

i 0.09810 

9.89304 

25 

36 

9.79510  1 

16 

9.90216  ! 

26 

! 0.09784 

9.89294 

10 

24 

37 

9.79526 

16 

9.90242  1 

1 0.09758 

9.89284 

10 

23 

38 

9.79542 

16 

9.90268  | 

26 

| 0.09732 

9.89274 

10 

22 

II 

39 

9.79558 

16 

9.90294  | 

26 

0.09706 

9.89264 

10 

21 

6 1.1 

15 

10 

T 1 Q 

40 

9.79573  | 

9.90320  j 

zo 

0.09680 

9.89254 

20 

i j 1.0 
<2  1 ^ 

41 

9.79589  | 

16 

9.90346 

26 

0.09654 

9.89244  ! 

10 

19 

O 1.0 

Q 1 7 

42 

9.79605 

16 

9.90371  I 

25 

! 0.09629 

9.89233 

11 

18 

St  j A.  / 
10  1 ^ 

43 

9.79621 

16 

9.90397  | 

26 

0.09603 

9.89223 

10 

17 

1U  ; J..O 

20  ^ 7 

44 

9.79636 

15 

16 

9.90423  | 

26 

•>A 

0.09577 

9.89213  ! 

10 

10 

16 

_u  o.  / 

30 ' 5.5 

45 

9.79652  ! 

9.90449  j 

ZD 

0.09551 

9.89203  | 

15 

40  7. 

3 

46 

9.79668 

16 

9.90475 

26 

0.09525 

9.89193 

10 

14 

50  j 9. 

o 

47 

9.79684 

16 

9.90501 

26 

0.09499 

9.89183 

10 

13 

48 

9.79699  | 

15 

9.90527 

26 

0.09473 

9.89173  i 

10 

12 

49 

9.79715 

16 

16 

9.90553 

26  j 
25  | 

0.09447 

9.89162  I 

11 

10 

11 

10 

9 

50 

9.79731  i 

9.90578 

0.09422 

9.89152 

10 

6 1 1.0 

0.9 

51 

9.79746  1 

15 

9.90604 

26  i 

0.09396 

9.89142  i 

10 

9 

7 1.2  | 

1.1 

52 

9.79762  ! 

16 

9.90630 

26 

0.09370 

9.89132  i 

10 

8 

8 1 1.3 

1.2 

53 

9.79778 

16 

9.90656 

26  i 

0.09344 

9.89122  i 

10 

7 

9 1.5 

1.4 

54 

9.79793  | 

15 

16 

9.90682  | 

26 

26 

0.09318 

9.89112 

10 

11 

6 

10  j 1.7 

1.5 

55 

9.79809  i 

9.90708 

0.09292 

9.89101 

5 

20  ! 3.3 

3.0 

56 

9.79825  1 

16 

9.90734 

26 

0.09266 

9.89091  i 

10 

4 

30  1 5.0 

4.5 

57 

9.79840  | 

15 

9.90759  ! 

25 

0.09241 

9.S9081 

10 

3 

40  6.7 

6.0 

58 

9.79856  i 

16 

9.90785  j 

26 

0.09215 

9.89071 

10 

2 

50  | 8.3 

7.6 

59 

9.79872  ! 

16 

15 

9.90811  1 

26  . 

0.09189 

9.89060  ! 

11 

10 

1 

60 

9.79887 

9.90837 

— U , 

0.09163 

9.89050 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

51° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 


531 


/ 

L.  Sin. 

0 

9.79887 

1 

9.79903 

2 

9.79918 

3 

9.79934 

4 

9.79950 

5 

9.79965 

6 

9.79981 

7 

9.79996 

8 

9.80012 

9 

9.80027 

10 

9.80043 

11 

9.80058 

12 

9.80074 

13 

9.80089 

14 

9.80105 

15 

9.80120 

16 

9.80136 

17 

9.80151 

18 

9V80166 

19 

9.80182 

20 

9.80197 

21 

9.80213 

22 

9.80228 

23 

9.80244 

24 

9.80259 

25 

9.80274 

26 

9.80290 

27 

9.8G305 

28 

9.80320 

29 

9.80336 

30 

9.80351 

31 

9.80366 

32 

9.80382 

33 

9.80397 

34 

9.80412 

35 

9.80428 

36 

9.80443 

37 

9.80458 

38 

9.80473 

39 

9.80489 

40 

9.80504 

41 

9.80519 

42 

9.80534 

43 

9.80550 

44 

9.80565 

45 

9.80580 

46 

9.80595 

47 

9.80610 

48 

9.80625 

49 

9.80641 

50 

9.80656 

51 

9.80671 

52 

9.80686 

53 

9.80701 

54 

9.80716 

55 

9.80731 

56 

9.80746 

57 

9.80762 

58 

9.80777 

59 

9.80792 

60 

9.80807 

L.  Cos. 

d. 

16 

15 

16 
16 

15 

16 

15 

16 

15 

16 

15 

16 

15 

16 

15 

16 
15 

15 

16 

15 

16 

15 

16 
15 

15 

16 
15 

15 

16 
15 

15 

16 
15 

15 

16 
15 
15 

15 

16 
15 
15 

15 

16 
15 
15 
15 
15 

15 

16 
15 
15 
15 
15 
15 
15 

15 

16 
15 
15 


L.Tang.  d 

“9790837 

9.90863 

9.90889 

9.90914 

9.90940 

9.90966 

9.90992 

9.91018 

9.91043 

9.91069 

9.91095 

9.91121 

9.91147 

9.91172 

9.91198 

9.91224 

9.91250 

9.91276 

9.91301 

9.91327 

9.91353 

9.91379 

9.91404 

9.91430 

9.91456 

9.91482 

9.91507 

9.91533 

9.91559 

9.91585 

9.91610 

9.91636 

9.91662 

9.91688 

9.91713 

9.91739 

9.91765 

9.91791 

9.91816 

9.91842 

9.91868 

9.91893 

9.91919 

9.91945 

9.91971 

9.91996 

9.92022 

9.92048 

9.92073 

9.92099 

9.92125 

9.92150 

9.92176 

9.92202 

9.92227 

9.92253 

9.92279 

9.92304 

9.92330 

9.92356 

9.92381 

L.  Cotg. 

26 

26 

25 

26 
26 
26 
26 

25 

26 
26 
26 
26 

25 

26 
26 
26 
26 

25 

26 
26 
26 

25 

26 
26 
26 

25 

26 
26 
26 

25 

26 
26 
26 

25 
. 26 

26 
26 

25 

26 
26 

25 

26 
26 
26 

25 

26 
26 

25 

26 
26 

25 

26 
26 

25 

26 
26 

25 

26 
26 
25 


L.  Cotg. 

L.  Cos.  c 

0.09163  " 

9.89050  . 

0.09137 

9.89040  ] 

0.09111 

9.89030  } 

0.09086 

9.89020  } 

0.09060 

9.89009  1 

0.09034 

9.88999  , 

0.09008 

9.88989 

0.08982 

9.88978 

0.08957 

9.88968 

0.08931 

9.88958 

0.08905 

9.88948  . 

0.08879 

9.88937  3 

0.08853 

9.88927  : 

0.08828 

9.88917  : 

0.08802 

9.8^906  : 

0.08776 

9.88896  ! 

0.08750 

9.88886  : 

0.08724 

9.88875  : 

0.08699 

9.88865  : 

0.08673 

9.88855 

0.08647 

9.88844 

0.08621 

9.88834 

0.08596 

9.88824 

0.08570 

9.88813 

0.08544 

9.88803 

0.08518 

9.88793 

0.08493 

9.88782 

0.08467 

9.88772 

0.08441 

9.88761 

0.08415 

9.88751 

0.08390 

9.88741 

0.08364 

9.88730 

0.08338 

9.88720 

0.08312 

9.88709 

0.08287 

9.88699 

0.08261 

9.88688 

0.08235 

9.88678 

0.08209 

9.88668 

0.08184 

9.88657 

0.08158 

9.88647 

0.08132 

9.88636 

0.08107 

9.88626 

0.08081 

9.88615 

0.08055 

9.88605 

0.08029 

9.88594 

0.08004 

9.88584 

0.07978 

9.88573 

0.07952 

9.88563 

0.07927 

9.88552 

0.07901 

9.88542 

0.07875 

9.88531 

0.07850 

9.88521 

0.07824 

9.88510 

0.07798 

9.88499 

0.07773 

9.88489 

0.07747 

9.88478 

0.07721 

9.88468 

0.07696 

9.88457 

0.07670 

9.88447 

0.07644 

9.88436 

0.07619 

9.88425 

3.  L.Tang 

. L.  Sin. 

60 

59 

58 

57 

_56 

55 

54 

53 

52 

51 


50 

49 

48 

47 

46 


P.  P. 


10 

10 

11 

10 

10 

11 

10 

10 

11 

10 

11 

10 

10 

11 

10 

11 

10 

11 

10 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

11 

10 

11 

10 

11 

10 

11 

11 

d. 


35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


16 

1.6 

1.9 

2.1 

2.4 

2.7 

5.3 

8.0 

10.7 

13.3 


6 

7 

8 
9 

10 

20 

30 

40 

50 


15 

1.5 
1.8 
2.0 
2.3 

2.5 
5.0 

7.5 
10.0 
12.5 


6 

7 

8 
9 

10 

20 

30 

40 

50 


II 

1.1 

1.3 

1.5 

1.7 

1.8 

3.7 

5.5 

7.3 
9.2 


10 

1.0 

1.2 

1.3 
1.5 

1.7 

3.3 
5.0 

6.7 

8.3 


P.  P. 


50° 


532 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 


40° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.80807 

9.80822 

9.80837 

9.80852 

9.80867 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

14  . 

15 
15 
15 
15 
15 
15 
15 

14 

15 
15 
15 
15 

14 

15 
15 
15 
15 

14 

15 
15 

14 

15 
15 
15 

14 

15 
15 

14 

15 
15 

14 

15 
15 

14 

15 

14 

15 
15 

14 

15 

14 

15 
14 

9.92381 

9.92407 

9.92433 

9.92458 

9.92484 

26 

26 

25 

26 
26 

25 

26 
26 

25 

26 

25 

26 
26 

25 

26 
26 

25 

26 

25 

26 
26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 
25 

0.07619 

0.07593 

0.07567 

0.07542 

0.07516 

9.88425 

9.88415 

9.88404 

9.88394 

9.88383 

10 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

11 

11 

11 

60 

59 

58 

57 

56 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 
40  17.3 
50  21.7 

25 

6 2.5 

7 2.9 

8 3.3 

9 3.8 

10  4.2 

20  8.3  ! 

30  12.5 
40  16.7 
50  20.8 

15 

6 1.5  | 

7 1.8 

8 2.0 

9 2.3 

10  2.5 

20  5.0 

30  7.5 

40  10.0 
50  12.5 

14  ! 

6 1.4 

7 1.6 

8 1.9 

9 2.1 

10  2.3 

20’  4.7 

30  7.0 

40  9.3 

50  11.7 

II  10 

6 1.1  1.0 

7 1.3  1.2 

8 1.5  1.3 

9 1.7  1.5 
10  1.8  1.7 

20  3.7  3.3  j 
30  5.5  5.0 
40  7.3  6.7 
50  9.2  8.3 

5 

6 

7 

8 
9 

9.80882 

9.80897 

9.80912 

9.80927 

9.80942 

9.92510 

9.92535 

9.92561 

9.92587 

9.92612 

0.07490 

0.07465 

0.07439 

0.(57413 

0.07388 

9.88372 

9.88362 

9.88351 

9.88340 

9.88330 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.80957 

9.80972 

9.80987 

9.81002 

9.81017 

9.92638 

9.92663 

9.92689 

9.92715 

9.92740 

0.07362 

0.07337 

0.07311 

0.07285 

0.07260 

9.88319 

9.88308 

9.88298 

9.88287 

9.88276 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.81032 

9.81047 

9.81061 

9.81076 

9.81091 

9.92766 

9.92792 

9.92817 

9.92843 

9.92868 

0.07234 

0.07208 

0.07183 

0.07157 

0.07132 

9.88266 

9.88255 

9.88244 

9.88234 

9.88223 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.81106 

9.81121 

9.81136 

9.81151 

9.81166 

9.92894 

9.92920 

9.92945 

9.92971 

9.92996 

0.07106 

0.07080 

0.07055 

0.07029 

0.07004 

9.88212 

9.88201 

9.88191 

9.88180 

9.88169 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.81180 

9.81195 

9.81210 

9.81225 

9.81240 

9.93022 

9.93048 

9.93073 

9.93099 

9.93124 

0.06978 

0.06952 

0.06927 

0.06901 

0.06876 

9.88158 

9.88148 

9.88137 

9.88126 

9.88115 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.81254 

9.81269 

9.81284 

9.81299 

9.81314 

9.93150 

9.93175 

9.93201 

9.93227 

9.93252 

0.06850 

0.06825 

0.06799 

0.06773 

0.06748 

9.88105 

9.88094 

9.88083 

9.88072 

9.88061 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.81328 

9.81343 

9.81358 

9.81372 

9.81387 

9.93278 

9.93303 

9.93329 

9.93354 

9.93380 

0.06722 

0.06697 

0.06671 

0.06646 

0.06620 

9.88051 

9.88040 

9.88029 

9.88018 

9.88007 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.81402 

9.81417 

9.81431 

9.81446 

9.81461 

9.93406 

9.93431 

9.93457 

9.93482 

9.93508 

0.06594 

0.06569 

0.06543 

0.06518 

0.06492 

9.87996 

9.87985 

9.87975 

9.87964 

9.87953 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.81475 

9.81490 

9.81505 

9.81519 

9.81534 

9.93533 

9.93559 

9.93584 

9.93610 

9.93636 

0.06467 

0.06441 

0.06416 

0.06390 

0.06364 

9.87942 

9.87931 

9.87920 

9.87909 

9.87898 

15 

14 

13 

12 

11 

50 

51 

1 52 

53 

54 

9.81549 

9.81563 

9.81578 

9.81592 

9.81607 

9.93661 

9.93687 

9.93712 

9.93738 

9.93763 

0.06339 

0.06313 

0.06288 

0.06262 

0.06237 

9.87887 

9.87877 

9.87866 

9.87855 

9.87844 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

60 

9.81622 

9.81636 

9.81651 

9.81665 

9.81680 

9.93789 

9.93814 

9.93840 

9.93865 

9.93891 

0.06211 

0.06186 

0.06160 

0.06135 

0.06109 

9.87833 

9.87822 

9.87811 

9.87800 

9.87789 

5 

4 

3 

2 

1 

9.81694 

9.93916 

0.06084 

9.87778 

0 

L.  Cos. 

~~A. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

49° 


1 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


533 


/ 

L.  Sin. 

0 

9.81694 

1 

9.81709 

2 

9.81723 

3 

9.81738 

4 

9.81752 

5 

9.81767 

6 

9.81781 

7 

9.81796 

8 

9.81810 

9 

9.81825 

10 

9.81839 

11 

9.81854 

12 

9.81868 

13 

9.81882 

14 

9.81897 

15 

9.81911 

16 

9.81926 

17 

9.81940 

18 

9.81955 

19 

9.81969 

20 

9.81983 

21 

9.81998 

22 

9.82012 

23 

9.82026 

24 

9.82041 

25 

9.82055 

26 

9.82069 

27 

9.82084 

28 

9.82098 

29 

9.82112 

30 

9.82126 

31 

9.82141 

32 

9.82155 

33 

9.82169 

34 

9.82184 

35 

9.82198 

36 

9.82212 

37 

9.82226 

38 

9.82240 

39 

9.82255 

40 

9.82269 

41 

9.82283 

42 

9.82297 

43 

9.82311 

44 

9.82326 

45 

9.82340 

46 

9.82354 

47 

9.82368 

48 

9.82382 

49 

9.82396 

50 

9.82410 

51 

9.82424 

52 

9.82439 

53 

9.82453 

54 

9.82467 

55 

9.82481 

56 

9.82495 

57 

9.82509 

58 

9.82523 

59 

9.82537 

60 

9.82551 

L.  Cos. 

d.  L.Tang. 


15 

14 

15 

14 

15 

14 

15 

14 

15 

14 

15 
14 

14 

15 

14 

15 

14 

15 
14 

14 

15 
14 

14 

15 
14 

14 

15 
14 
14 

14 

15 
14 

14 

15 
14 
14 
14 

14 

15 
14 
14 
14 

14 

15 
14 
14 
14 
14 
14 
14 

14 

15 
14 
14 
14 
14 
14 
14 
14 
14 


9.93916 

9.93942 

9.93967 

9.93993 

9.94018 


9.94044 

9.94069 

9.94095 

9.94120 

9.94146 

9.94171 

9.94197 

9.94222 

9.94248 

9.94273 


9.94299 

9.94324 

9.94350 

9.94375 

9.94401 


9.94426 

9.94452 

9.94477 

9.94503 

9.94528 


9.94554 

9.94579 

9.94604 

9.94630 

9.94655 


9.94681 

9.94706 

9.94732 

5.94757 

9.94783 


d.c.  J 

L.  Cotg. 

L.  Cos. 

d. 

0.06084 

9.87778 

60 

26 

0.06058 

9.87767 

11 

59 

25 

0.06033 

9.87756 

11 

58 

26 

0.06007 

9.87745 

11 

57 

25 

0.05982 

9.87734 

11 

11 

56 

2b 

0.05956 

9.87723 

55 

25 

0.05931 

9.87712 

11 

54 

26 

0.05905 

9.87701 

11 

53 

25 

0.05880 

9.87690 

11 

52 

26 

0.05854 

9.87679 

11 

11 

51 

Zo 

0.05829 

9.87668 

50 

26 

0.05803 

9.87657 

11 

49 

25 

0.05778 

9.87646 

11 

48 

26 

0.05752 

9.87635 

11 

47 

25 

26 

0.05727 

9.87624 

11 

11 

46 

0.05701 

9.87613 

45 

25 

0.05676 

9.87601 

12 

44 

26 

0.05650 

9.87590 

11 

43 

25 

0.05625 

9.87579 

11 

42 

26 

25 

0.65599 

9.87568 

11 

41 

0.05574 

9.87557 

-LX 
1 1 

40 

26 

0.05548 

9.87546 

11 

39 

25 

0.05523 

9.87535 

11 

38 

26 

0.05497 

9.87524 

11 

37 

25 

0.05472 

9.87513 

11 

12 

36 

Zo 

0.05446 

9.87501 

35 

25 

0.05421 

9.87490 

11 

34 

25 

0.05396 

9.87479 

11 

33 

26 

0.05370 

9.87468 

11 

32 

25 

0.05345 

9.87457 

11 
11 
1 o 

31 

ZO 

0.05319 

9.87446 

30 

25 

0.05294 

9.87434 

12 

29 

26 

0.05268 

9.87423 

11 

28 

25 

0.05243 

9.87412 

11 

27 

26 
- 25 

0.05217 

9.87401 

11 
11 
1 o 

26 

0.05192 

9.87390 

25 

26 

0.05166 

9.87378 

12 

24 

i 25 

0.05141 

9.87367 

11 
1 1 

23 

25 

0.05116 

9.87356 

11 

22 

i 1 

0.05090 

9.87345 

11 
11 
1 o 

21 

> ^ 

0.05065 

9.87334 

20 

26 

0.05039 

9.87322 

12 

19 

i 25 

0.05014 

9.87311 

11 

18 

» 26 

0.04988 

9.87300 

1] 

17 

r 25 

0.04963 

9.87288 

12 

11 

16 

> 25 

0.04938 

9.87277 

15 

i 26 

0.04912 

9.87266 

11 

14 

> 25 

0.04887 

9.87255 

11 
1 o 

13 

> It 

0.04861 

9.87243 

12 

12 

1 26 

0.04836 

9.87232 

11 

11 

11 

) It 

0.04810 

9.87221 

1 o 

10 

0.04785 

9.87209 

12 
i -| 

9 

) 25 

0.04760 

9.87198 

11 

8 

5 It 

0.04734 

9.87187 

11 

7 

1 26 

0.04709 

9.87175 

12, 

11 

6 

7 it 

0.04683 

9.87164 

5 

2 25 

0.04658 

9.87153 

11 

4 

3 ?6 

0.04632 

9.87141 

12 

3 

i 25 

0.04607 

9.87130 

11 

2 

8 25 

0.04582 

9.87119 

11 

- 12 

, 1 

4 26 

0.04556 

9.87107 

0 

d.  c. 

L.Tang 

. L.  Sin. 

d. 

/ 

P.  P. 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


6 

7 

8 
9 

10 

20 

30 

40 

50 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


15 

1.5 
1 8 
2.0 
2.3 

2.5 
5.0 

7.5 
10.0 
12.5 


6 

7 

8 
9 

10 

20 

30 

40 

50 


14 

1.4 

1.6 

1.9 

2:1 

2.3 
4.7 
7.0 

9.3 
11.7 


6 

7 

8 
9 

10 

20 

30 

40 

50 


12 

1.2 

1.4 

1.6 

1.8 

2.0 

4.0 

6.0 
8.0 

10.0 


P.  P. 


II 

1.1 

1.3 

1.5 

1.7 

1.8 
3.7 

5.5 

7.3 
9.2 


48c 


534  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


42° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

. P. 

0 

9.82551 

9.95444 

0.04556 

9.87107 

60 

1 

9.82565 

14 

9.95469 

2 5 

0.04531 

9.87096 

11 

59 

2 

9.82579 

14 

9.95495 

26 

0.04505 

9.87085 

11 

58 

0 c 

3 

9.82593 

14 

9.95520 

25 

0.04480 

9.87073 

12 

57 

R 

CO 

O R 

4 

9.82607 

14 

1 A 

9.95545 

25 

26 

0.04455 

9.87062 

11 

12 

56 

0 

7 

Z.D 

3.0 

5 

9.82621 

9.95571 

0.04429 

■9.87050 

55 

8 

3.5 

6 

9.82635 

14 

9.95596 

25 

0.04404 

9.87039 

11 

54 

9 

3.9 

7 

9.82649 

14 

9,95622 

26 

0.0437<S 

9.87028 

11 

53 

10 

4.3 

8 

9.82663 

14 

9.95647 

2i> 

0.04353 

9.87016 

12 

52 

20 

8.7 

9 

9.82677 

14 
r a 

9.95672 

25 

26 

0.04328 

9.87005 

11 

12 

51 

30 

13.0 

10 

9.82691 

9.95698 

0.04302 

9.86993 

50 

40 

17.3 

11 

9.82705 

14 

9.95723 

25 

0.04277 

9.86982 

11 

49 

50 

21.7 

12 

9.82719 

14 

9.95748 

25 

0.04252 

9.86970 

12 

48 

13 

9.82733 

14 

9.95774 

26 

0.04226 

9.86959 

11 

47 

14 

9.82747 

14 

1, A 

9.95799 

25 

0.04201 

9.86947 

12 

11 

46 

25 

15 

9.82761 

9.95825 

0.04175 

9.86936 

45 

6 

2.5 

16 

9.82775 

14 

9.95850 

25 

0.04150 

9.86924 

12 

44 

7 

2.9 

17  - 

9.82788 

13 

9.95875 

25 

0.04125 

9.86913 

11 

43 

8 

3.3 

18 

9.82802 

14 

9.95901 

26 

0.04099 

9.86902 

11 

42 

9 

3.8 

19 

9.82816 

14 

9.95926 

25 

0.04074 

9.86890 

12 

41 

10 

4.2 

26 

11 

20 

9.82830 

9.95952 

0.04048 

9.86879 

40 

ZO 

S.3 

21 

9.82844 

14 

9.95977 

25 

0.04023 

9.86867 

12 

39 

30 

12.5 

22 

9.82858 

14 

9.96002 

25 

0.03998 

9.86855 

12 

38 

40 

16.7 

23 

9.82872 

14 

9.96028 

26 

0.03972 

9.86844 

11 

37 

50 

20.8 

24 

9.82885 

13 

14 

9.96053 

25 

25 

0.03947 

9.86832 

12 

11 

36 

25 

9.82899 

9.96078 

0.03922 

9.86821 

35 

26 

9.82913 

14 

9.96104 

26 

0.03896 

9.86809 

12 

34 

14 

27 

9.82927 

14 

9.96129 

25 

0.03871 

9.86798 

11 

33 

6 

1.4 

28 

9.82941 

14 

9.96155 

26 

0.03845 

9.86786 

12 

32 

7 

1.6 

29 

9.82955 

14 

iq 

9.96180 

25 

25 

0.03820 

9.86775 

11 

12 

31 

8 

1.9 

O 1 

30 

9.82968 

AO 

9.96205 

0.03795 

9.86763 

30 

i n 

Z.A 

9 ^ 

31 

9.82982 

14 

9.96231 

26 

0.03769 

9.86752 

11 

29 

±u 

on 

A 7 

32 

9.82996 

14 

9.96256 

25 

0.03744 

9.86740 

12 

28 

4k.  / 

7 0 

33 

9.83010 

14 

9.96281 

25 

0.03719 

9.86728 

12 

27 

ou 

d.0 

/ .u 
Q ^ 

34 

9.83023 

13 

14 

9.96307 

26 

25 

OK 

0.03693 

9.86717 

11 

19 

26 

50 

t/.O 

11.7 

35 

9.83037 

Art 

i a 

9.96332 

0.03668 

9.86705 

A<£ 

25 

36 

9.83051 

14 

9.96357 

25 

0.03643 

9.86694 

11 

24 

37 

9.83065 

14 

9.96383 

26 

0.03617 

9.86682 

12 

23 

38 

9.83078 

13 

9.96408 

25 

0.03592 

9.86670 

12 

22 

13 

39 

9.83092 

14 

14 

9.96433 

25 

26 

0.03567 

9.86659 

11 

12 

21 

6 

7 

1.3 

1.5 

40 

9.83106 

9.96459 

0.03541- 

9.86647 

20 

8 

L7 

11 

9.83120 

14 

9.96484 

25 

0.03516 

9.86635 

12 

19 

9 

2.0 

12 

9.83133 

13 

9.96510 

26 

0.03490 

9.86624 

11 

18 

10 

2.2 

43 

9.83147 

14 

9.96535 

25 

0.03465 

9.86612 

12 

17 

20 

4.3 

44 

9.83161 

14 

-iq 

9.96560 

25 

26 

0.03440 

9.86600 

12 

11 

16 

30 

6.5 

45 

9.83174 

_LO 

9.96586 

0.03414 

9.86589 

15 

40 

8.7 

46 

9.83188 

14 

9.96611 

25 

0.03389 

9.86577 

12 

14 

50 

10.8 

47 

9.83202 

14 

9.96636 

25 

0.03364 

9.86565 

12 

13 

48 

9.83215 

13 

9.96662 

26 

0.03338 

9.86554 

11 

12 

49 

9.83229 

14 

IQ 

9.96687 

25 

25 

0.03313 

9.86542 

12 

19 

11 

12 

II 

50 

9.83242 

i-O 

i a 

9.96712 

0.03288 

9.86530 

AZi 

10 

6 

1.2 

1.1 

51 

9.83256 

14 

9.96738 

26 

0.03262 

9.86518 

12 

9 

7 

1.4 

1.3 

52 

9.83270 

14 

9.96763 

25 

0.03237 

9.86507 

11 

8 

8 

1.6 

1.5 

53 

9.83283 

13 

9.96788 

25 

0.03212 

9.86495 

12 

7 

9 

1.8 

1.7 

54 

9.83297 

14 

13 

9.96814 

26 

25 

0.03186 

9.86483 

12 

11 

6 

10 

2.0 

1.8 

55 

9.83310 

9.96839 

0.03161 

9.86472 

5 

20 

4.0 

3.7 

56 

9.83324 

14 

9.96864 

25 

0.03136 

9.86460 

12 

4 

30 

6.0 

5.5 

57 

9.83338 

14 

9.96890 

26 

0.03110 

9.86448 

12 

3 

40 

8.0 

7.3 

58 

9.83351 

13 

9.96915 

25 

0.03085 

9.86436 

12 

2 

50 

10.0 

9.2 

59 

9.83365 

14 

IQ 

9.96940 

25 

26 

0.03060 

9.86425 

11 

12 

1 

60 

9.83378 

AO 

9.96966 

0.03034 

9.86413 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

47° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


535 


/ 

L.  Sin.  - 

0 ' 

9.83378 

1 ' 

9.83392 

2 1 

9.83405 

3 1 

9.83419 

4 1 

9.83432 

5 

9.83446 

6 

9.83459 

7 

9.83473 

8 

9.83486 

9 

9.83500 

10 

9.83513 

11 

9.83527 

12 

9.83540 

13 

9.83554 

14 

9.83567 

15 

9.83581 

16 

9.83594 

17 

9.83608 

18 

9.83621 

19 

9.83634 

20 

9783648 

21 

9.83661 

22 

9.83674 

23 

9.83688 

24 

9.83701 

25 

9.83715 

26 

9.83728 

27 

9.83741 

28 

9.83755 

29 

9.83768 

30 

9.83781 

31 

9.83795 

32 

9.83808 

33 

9.83821 

34 

9.83834 

35 

9.83848 

36 

9.83861 

37 

9.83874 

38 

9.83887 

39 

9.83901 

40 

9.83914 

41 

9.83927 

42 

9.83940 

43 

9.83954 

44 

9.83967 

45 

9.83980 

46 

9.83993 

47 

9.84006 

48 

9.84020 

49 

9.84033 

50 

9.84046 

51 

9.84059 

52 

9.84072 

53 

9.84085 

54 

9.84098 

55 

9.84112 

56 

9.84125 

57 

9.84138 

58 

9.84151 

59 

i 9.84164 

60 

9.84177 

L.  Cos. 

d. 


L.Tang. 


14 

13 

14 

13 

14 

13 

14 

13 

14 

13 

14 

13 

14 

13 

14 

13 

14 
13 

13 

14 
13 

13 

14 

13 

14 
13 

13 

14 
13 

13 

14 
13 
13 

13 

14 
13 
13 

13 

14 
13 
13 

13 

14 
13 
13 
13 

13 

14 
13 
13 
13 
13 
13 

13 

14 
13 
13 
13 
13 
13 

d7 


9.97092 

.97118 

.97143 

97168 

.97193 


96966 

96991 

97016 

97042 

.97067 


.97219 

.97244 

97269 

.97295 

.97320 


.97345 

.97371 

.97396 

.97421 

.97447 


9.97472 

9.97497 

9.97523 

9.97548 

9.97573 


d.c.  I 

j.  cotg.  ; 

L.  Cos.  d 

0.03034 

9.86413 

25 

0.03009 

9.86401  J; 

25 

0.02984 

9.86389  j; 

26 

0.02958 

9.86377 

25 

QC 

0.02933 

9.86366 

ZD 

0.02908 

9.86354 

26 

0.02882 

9.86342  }: 

25 

0.02857 

9.86330  }: 

25 

0.02832 

9.86318  J; 

25 

0.02807 

9.86306 

26 

0.02781 

9.86295  " 

25 

0.02756 

9.86283  1; 

25 

0.02731 

9.86271  } 

26 

0.02705 

9.86259  } 

25 

ore 

0.02680 

9.86247  J 

Zo 

0.02655 

9.86235  , 

26 

0.02629 

9.86223  } 

25 

0.02604 

9.86211  } 

25 

0.02579 

9.86200  \ 

26 
- 25 

0.02553 

9.86188  | 

0.02528 

9.86176  . 

25 

0.02503 

9.86164  { 

26 

0.02477 

9.86152  } 

25 

0.02452 

9.86140  } 

25 

ore 

0.02427 

9.86128  * 

25 

26 

0.02402 

9.86116  1 

0.02376 

9.86104  ] 

; 25 

0.02351 

9.86092 

25 

0.02326 

9.86080 

; 26 
ore 

0.02300 

9.86068  3 

Zu 

; 25 

0.02275 

9.86056  ; 

0.02250 

9.86044  : 

; 26 

0.02224 

9.86032  : 

25 

0.02199 

9.86020  : 

1 t 

0.02174 

9.86008  : 

L 25 
1 

0.02149 

9.85996  : 

0.02123 

9.85984 

l 25 

0.02098 

9.85972 

j 25 

0.02073 

9.85960 

5 25 

0.02047 

9.85948 

25 

0.02022 

9.85936 

0.01997 

9.85924 

0.01971 

9.85912 

4 25 

0.01946 

9.85900 

9 95 

0.01921 

9.85888 

4 25 

o 25 

0.01896 

9.85876 

0.01870 

9.85864 

5 25 

0.01845 

9.85851 

0 25 

0.01820 

9.85839 

16  25 

0.01794 

9.85827 

i 1 

0.01769 

9.85815 

0.01744 

9.85803 

d 25 

0.01719 

9.85791 

)7  26 

0.01693 

9.85779 

*2.  |5 

0.01668 

9.85766 

>7  25 

S3  26 

0.01643 

. 9.85754 

0.01617 

9.85742 

)8  25 

0.01592 

! 9.85730 

S3  25 

0.01567 

r 9.85718 

58  26 

0.01542 

! 9.85706 

84  26 

0.01516 

I 9.85693 

tg.  d.c 

. L.Tang 

r.  L.  Sin. 

12 

12 

12 

12 

12 

12 

12 

12 

13 

12 

12 

12 

12 

12 

12 

13 

12 

12 

12 

12 

12 

13 

d. 


P. 

P. 

30 

59 

58 

57 

6 

26 

2.6 

56 

7 

3.0 

55 

8 

3.5 

54 

9 

3.9 

53 

10 

4.3 

52 

20 

8.7 

51 

30 

13.0 

50 

40 

17.3 

49 

50 

21.7 

48 

47 

46 

25 

45 

6 

2.5 

44 

7 

2.9 

43 

8 

3.3 

42 

9 

3.8 

41 

10 

4.2 

40 

39 

38 

37 

20 

8.3 

30 

12.5 

40 

16.7 

50 

20.8 

36 

35 

14 

34 

33 

6 

1.4 

32 

7 

1.6 

31 

8 

1.9 

9 

2.1 

~3cT 

10 

2.3 

29 

20 

4.7 

28 

30 

7.0 

27 

40 

9.3 

26 

50 

11.7 

25 

24 

23 

22 

21 

6 

7 

13 

1.3 

1.5 

20 

8 

1.7 

19 

9 

2.0 

18 

10 

2.2 

17 

20 

4.3 

16 

30 

i 6.5 

15 

40 

i 8.7 

14 

50 

i 10.8 

13 

12 

11 

12 

II 

10 

6 

1.2 

1.1 

9 

7 

1.4 

1.3 

8 

8 

1.6 

1.5 

7 

9 

1.8 

1.7 

6 

10 

2.0 

1.8 

5 

" 20 

4.0 

3.7 

4 

30 

6.0 

5.5 

3 

; 40 

8.0 

7.3 

2 

1 

1 50 

10.0 

9.2 

0 

i 

t 

P.  P. 

46° 


536 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


44° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.84177 

9.84190 

9.84203 

9.84216 

9.84229 

13 

13 

13 

13 

13 

13 

14 
13 
13 
13 
13 
13 
13 
13 
13 
12 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
12 
13 
13 

13 

13 

13 

33 

12 

13 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

12 

13 

13 

12 

13 

13 

9.98484 

9.98509 

9.98534 

9.98560 

9.98585 

25 

25 

26 
25 
25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 
25 

0.01516 

0.01491 

0.01466 

0.01440 

0.01415 

9.85693 

9.85681 

9.85669 

9.85657 

9.85645 

12 

12 

12 

12 

13 

12 

12 

12 

13 

12 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

13 

12 

12 

13 

12 

13 

12 

13 

12 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

13 

12 

13 

12 

13 

12 

13 

13 

12 

13 

12 

60 

59 

58 

57 

56 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 
40  17.3 
50  21.7 

25 

6 2.5 

7 2.9 

8 3.3 

9 3.8 

10  4.2 

20  8.3 

30  12.5 
40  16.7 
50  20.8 

14 

6 1.4 

7 1.6 

8 1.9 

9 2.1 

10  2.3 

20  4.7 

30  7.0 

40  9.3 

50  11.7 

13 

6 1.3 

7 1.5 

8 1.7  ! 

9 2.0 

10  2.2 
20  4.3 

30  6.5 

40  8.7 

50  10.8 

12 

6 1.2 

7 1.4 

8 1.6 

9 1.8 

10  2.0  | 
20  4.0 

30  6.0 

40  8.0 

50  10.0 

5 

6 

7 

8 
9 

9.84242 

9.84255 

9.84269 

9.84282 

9.84295 

9.98610 

9.98635 

9.98661 

9.98686 

9.98711 

0.01390 

0.01365 

0.01339 

0.01314 

0.01289 

9.85632 

9.85620 

9.85608 

9.85596 

9.85583 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.84308 

9.84321 

9.84334 

9.84347 

9.84360 

9.98737 

9.98762 

9.98787 

9.98812 

9.98838 

0.01263 

0.01238 

0.01213 

0.01188 

0.01162 

9.85571 

9.85559 

9.85547 

9.85534 

9.85522 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.84373 

9.84385 

9.84398 

9.84411 

9.84424 

9.98863 

9.98888 

9.98913 

9.98939 

9.98964 

0.01137 

0.01112 

0.01087 

0.01061 

0.01036 

9.85510 

9.85497 

9.85485 

9.85473 

9.85460 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.84437 

9.84450 

9.84463 

9.84476 

9.84489 

9.98989 

9.99015 

9.99040 

9.99065 

9.99090 

0.01011 

0.00985 

0.00960 

0.00935 

0.00910 

9.85448 

9.85436 

9.85423 

9.85411 

9.85399 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.84502 

9.84515 

9.84528 

9.84540 

9.84553 

9.99116 

9.99141 

9.99166 

9.99191 

9.99217 

0.00884 

0.00859 

0.00834 

0.00809 

0.00783 

9.85386 

9.85374 

9.85361 

9.85349 

9.85337 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.84566 

9.84579 

9.84592 

9.84605 

9.84618 

9.99242 

9.99267 

9.99293 

9.99318 

9.99343 

0.00758 

0.00733 

0.00707 

0.00682 

0.00657 

9.85324 

9.85312 

9.85299 

9.85287 

9.85274 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.84630 

9.84643 

9.84656 

9.84669 

9.84682 

9.99368 

9.99394 

9.99419 

9.99444 

9.99469 

0.00632 

0.00606 

0.00581 

0.00556 

0.00531 

9.85262 

9.85250 

9.85237 

9.85225 

9.85212 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.84694 

9.84707 

9.84720 

9.84733 

9.84745 

9.99495 

9.99520 

9.99545 

9.99570 

9.99596 

0.00505 

0.00480 

0.00455 

0.00430 

0.00404 

9.85200 

9.85187 

9.85175 

9.85162 

9.85150 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.84758 

9.84771 

9.84784 

9.84796 

9.84809 

9.99621 

9.99646 

9.99672 

9.99697 

9.99722 

0.00379 

0.00354 

0.00328 

0.00303 

0.00278 

9.85137 

9.85125 

9.85112 

9.85100 

9.85087 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.84822 

9.84835 

9.84847 

9.84860 

9.84873 

9.99747 

9.99773 

9.99798 

9.99823 

9.99848 

0.00253 

0.00227 

0.00202 

0.00177 

0.00152 

9.85074 

9.85062 

9.85049 

9.85037 

9.85024 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.84885 

9.84898 

9.84911 

9.84923 

9.84936 

9.99874 

9.99899 

9.99924 

9.99949 

9.99975 

0.00126 

0.00101 

0.00076 

0.00051 

0.00025 

9.85012 

9.84999 

9.84986 

9.84974 

9.84961 

5 

4 

3 

2 

1 

60 

9.84949 

0.00000 

0.00000 

9.S4949 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

45° 


TEA  VERSE  TABLES. 


537 


TRAVERSE  TABLES. 

To  use  the  tables,  find  the  number  of  degrees  In  the  left-hand  column  if 
thfA  onp-lp  hp  Ipss  than  45°  and  in  the  right-hand  column  if  greater  than  45  . 
The  numbers  on  the  same  line  running  across  the  page  are  the  latitudes  and 
rlpnartures  for  that  angle  and  for  the  respective  distances,  1,  2, 3,  4,  5, 6,  7,  8, 9, 
wlSch  annear  at  the  top  and  bottom  of  the  pages.  Thus,  if  the  bearing  of  a 
Hne  be 10° and ^the  distance  4,  the  latitude  will  be  3.939  and  the  departure 
0 695‘  with  the  same  bearing,  and  the  distance  8,  the  latitude  will  be  7.878  and 
?i?e  < departure^ 1 38?  The  latitude  and  departure  for  80  is  10  times  the  latitude 
and  departure  for  8,  and  is  found  by  moving  the  decimal  point  one  place  to 
the  right*  that  for  500  is  100  times  the  latitude  and  departure  ior  5,  and  is  found 
by two  places  to  the  right  and  so  on , gy  njo^g 
the  decimal  point  one,  two,  or  more  places  to  the  right,  the  latitude  ana 
dpnarture  mav  be  found  for  any  multiple  of  any  number  given  m the  table. 
Tn  finding-  the  latitude  and  departure  for  any  number  such  as  453,  the  number 
is 1re?olve¥tato^ “number!,  viz.:  400, 50  3,  and  the  latitude  and  departure 
for  each  taken  from  the  table  and  then  added  together. 

and  departure,  neglecting 

for  the  first  figure  of  the  given  distance;  write  under  them  the  latitude  and  depar- 
ture  for  the  second  figure , setting  them  one  place  farther  to  the  right;  un^J'JieJf1) 
rtlnce  the  latitude  and  departure  for  the  third  figure , setting  them  one  place  still 
farther  to  thfrightand  so  continue  until  all  the  figures  of  tte  given  distance  have 
been  used  • add  these  latitudes  and  departures , and  point  off  on  the  right  of  their 
sums  a number  of  decimal  places  equal  to  the  number  of 

the  tables  being  used  are  carried;  the  resulting  numbers  will  be  the  latitude  and 

in  feet,  links , chains , or  whatever  unit  of  measure- 

xImple^'a  bearing  is  16°  and  the  distance  725  ft.;  what  is  the  latitude 
and  departure? 

Distances.  Latitudes.  Departures. 

700  6729  1®??1 

20  °147S 

5 4806  1378 

7~25  6 9 6.9  3 6 1 9 9.7  8 8 

Taking  the  nearest  whole  numbers  and  rejecting  the  decimals,  we  find 

theV7hirfoaocdcu^r\hl  given  nuU“  next  figure  must  he  set  fcro 

P'The^elringfs* £ Tnf^d'isUnle^Tft  "required,  the  latitude  and 

departure.  Latitudes.  Departures. 

900  8345  3371 


6490 


2622 


907  8 4 0.990  339.722 

TTptp  the  nlace  of  0 both  in  the  distance  column  and  in  the  latitude  and 

faffisTiM  ^«h7w^e|a|j  goj  Van 

fhe&rr^ 

and  the  departure  of  any  bearing,  as  30°,  is  the  1 ol  i ts  compimne  , 

60°  Where  the  bearings  are  given  m smaller  fractions  ot  degrees  tnan  s 
found  in  the  table,  the  latitudes  and  departures  can  be  found  by  inter- 
polation. 


538 


LATITUDES  AND  DEPARTURES. 


Bearing. 

1 

2 

3 

4 

5 

Bearing. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

0° 

1.000 

0.000 

2.000 

0.000 

3.000 

1 

0.000 

4.000 

0.000 

5.000 

90° 

0* 

1.000 

0.004 

2.000 

0.009 

3.000 

0.013 

4.000 

0.017 

5.000 

89f 

0* 

1.000 

0.009 

2.000 

0.017 

3.000 

0.026 

4.000 

0.035 

5.000 

89* 

Of 

1.000 

0.013 

2.000 

0.026 

3.000 

0.039 

4.000 

0.052 

5.000 

89* 

1° 

1.000 

0.017 

2.000 

0.035 

3.000 

0.052 

3.999 

0.070 

4.999 

89° 

l* 

1.000 

0.022 

2.000 

0.044 

2.999 

0.065 

3.999 

0.087 

4.999 

88f 

l* 

1.000 

0.026 

1.999 

0.052 

2.999 

0.079 

3.999 

0.105 

4.998 

88* 

if 

1.000 

0.031 

1.999 

0.061 

2.999 

0.092 

3.998 

0.122 

4.998 

88* 

2° 

0.999 

0.035 

1.999 

0.070 

2.998 

0.105 

3.998 

0.140 

4.997 

88° 

2* 

0.999 

0.039 

1.998 

0.079 

2.998 

0.118 

3.997 

0.157 

4.996 

87f 

2* 

0.999 

0.044 

1.998 

0.087 

2.997 

0.131 

3.996 

0.174 

4.995 

87* 

2f 

0.999 

0.048 

1.998 

0.096 

2.997 

0.144 

3.995 

0.192 

4.994 

87* 

3° 

0.999 

0.052 

1.997 

0.105 

2.996 

0.157 

3.995 

0.209 

4.993 

87° 

3* 

0.998 

0.057 

1.997 

0.113 

2.995 

0.170 

3.994 

0.227 

4.992 

86f 

3* 

0.998 

0.061 

1.996 

0.122 

2.994 

0.183 

3.993 

0.244 

4.991 

86* 

Bf 

0.998 

0.065 

1.996 

0.131 

2.994 

0.196 

3.991 

0.262 

4.989 

86* 

4° 

0.998 

0.070 

1.995 

0.140 

2.993 

0.209 

3.990 

0.279 

4.988 

86° 

4* 

0.997 

0.074 

1.995 

0.148 

2.992 

0.222 

3.989 

0.296 

4.986 

85f 

4* 

0.997 

0.078 

1.994 

0.157 

2.991 

0.235 

3.988 

0.314 

4.985 

85* 

4f 

0.997 

0.083 

1.993 

0.166 

2.990 

0.248 

3.986 

0.331 

4.983 

85* 

5° 

.0.996 

0.087 

1.992 

0.174 

2.989 

0.261 

3.985 

0.349 

4.981 

85° 

5* 

0.996 

0.092 

1.992 

0.183 

2.987 

0.275 

3.983 

0.366 

4.979 

84f 

5* 

0.995 

0.096 

1.991 

0.192 

2.986 

0.288 

3.982 

0.383 

4.977 

84* 

5f 

0.995 

0.100 

1.990 

0.200 

2.985 

0.301 

3.980 

0.401 

4.975 

84* 

6° 

0.995 

0.105 

1.989 

0.209 

2.984 

0.314 

3.978 

0.418 

4.973 

84a 

6* 

0.994 

0.109 

1.988 

0.218 

2.982 

0.327 

3.976 

0.435 

4.970 

83f 

6* 

0.994 

0.113 

1.987 

0.226 

2.981 

0.340 

3.974 

0.453 

4.968 

83* 

6f 

0.993 

0.118 

1.986 

0.235 

2.979 

0.353 

3.972 

0.470 

4.965 

83* 

7° 

0.993 

0.122 

1.985 

0.244 

2.978 

0.366 

3.970 

0.487 

4.963 

83° 

7* 

0.992 

0.126 

1.984 

0.252 

2.976 

0.379 

3.968 

0.505 

4.960 

82f 

n 

0.991 

0.131 

1.983 

0.261 

2.974 

0.392 

3.966 

0.522 

4.957 

82* 

7f 

0.991 

0.135 

1.982 

0.270 

2.973 

0.405 

3.963 

0.539 

4.954 

82* 

8° 

0.990 

0.139 

1.981 

0.278 

2.971 

0.418 

3.961 

0.557 

4,951 

82° 

8* 

0.990 

0.143 

1.979 

0.287 

2.969 

0.430 

3.959 

0.574 

4.948 

81f 

8* 

0.989 

0.148 

1.978 

0.296 

2.967 

0.443 

3.956 

0.591 

4.945 

81* 

8f 

0.988 

0.152 

1.977 

0.304 

2.965 

0.456 

3.953 

0.608 

4.942 

81* 

9° 

0.988 

0.156 

1.975 

0.313 

2.963 

0.469 

3.951 

0.626 

4.938 

81° 

9* 

0.987 

0.161 

1.974 

0.321 

2.961 

0.482 

3.948 

0.643 

4.935 

80f 

9* 

0.986 

0.165 

1.973 

0.330 

2.959 

0.495 

3.945 

0.660 

4.931 

80* 

9f 

0.986 

0.169 

1.971 

0.339 

2.957 

0.508 

3.942 

0.677 

4.928 

80* 

10° 

0.985 

0.174 

1.970 

0.347 

2.954 

0.521 

3.939 

0.695 

4.924 

80° 

io* 

0.984 

0.178 

1.968 

0.356 

2.952 

0.534 

3.936 

0.712 

4.920 

79f 

10| 

0.983 

0.182 

1.967 

0.364 

2.950 

0.547 

3.933 

0.729 

4.916 

79* 

lOf 

0.982 

0.187 

1.965 

0.373 

2.947 

0.560 

3.930 

0.746 

4.912 

79* 

,,o 

0.982 

0.191 

1.963 

0.382 

2.945 

0.572 

3.927 

0.763 

4.908 

79° 

1H 

0.981 

0.195 

1.962 

0.390 

2.942 

0.585 

3.923 

0.780 

4.904 

78f 

Hi 

0.980 

0.199 

1.960 

0.399 

2.940 

0.598 

3.920 

0.797 

4.900 

78* 

-lif 

0.979 

0.204 

1.958 

0.407 

2.937 

0.611 

3.916 

0.815 

4.895 

78* 

12° 

0.978 

0.208 

1.956 

0.416 

2.934 

0.624 

3.913 

0.832 

4.891 

78° 

12* 

0.977 

0.212 

1.954 

0.424 

2.932 

0.637 

3.909 

0.849 

4.886 

77f 

12* 

0.976 

0.216 

1.953 

0.433 

2.929 

0.649 

3.905 

0.866 

4.881 

77* 

12f 

0.975 

0.221 

1.951 

0.441 

2.926 

0.662 

3.901 

0.883 

4.877 

77* 

13° 

0.974 

0.225 

1.949 

0.450 

2.923 

0.675 

3.897 

0.900 

4.872 

77° 

bub 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

bi 

c 

*lZ 

co 

69 

as 

1 

2 

3 

4 

5 

CO 

<L> 

CD 

LATITUDES  AND  DEPARTURES. 


539 


feb 

c 

5 

6 

7 

8 

9 

th 

C 

'u 

1— 

40 

a> 

CD 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

CO 

0° 

0.000 

6.000 

0.000 

7.000 

0.000 

8.000 

0.000 

9.000 

0.000 

90° 

0- 

0 022 

6.000 

0.026 

7.000 

0.031 

8.000 

0.035 

9.000 

0.039 

89$ 

01 

0 044 

6.000 

0.052 

7.000 

0.061 

8.000 

0.070 

9.000 

0.079 

89$ 

f n 

0 065 

5.999 

0.079 

6.999 

0.092 

7.999 

0.105 

8.999 

0.118 

89$ 

1° 

0 087 

5.999 

0.105 

6.999 

0.122 

7.999 

0.140 

8.999 

0.157 

89° 

1 1 

0 109 

5.999 

0.131 

6.998 

0.153 

7.998 

0.175 

8.998 

0.196 

88$ 

1 1 

0 131 

5.998 

0.157 

6.998 

0.183 

7.997 

0.209 

8.997 

0.236 

88$ 

13 

0 153 

5.997 

0.183 

6.997 

0.214 

7.996 

0.244 

8.996 

0.275 

88$ 

2° 

0 174 

5.996 

0.209 

6.996 

0.244 

7.995 

0.279 

8.995 

0.314 

88° 

2i 

0 196 

5.995 

0.236 

6.995 

0.275 

7.994 

0.314 

8.993 

0.353 

87$ 

Oi 

0 218 

5.994 

0.262 

6.993 

0.305 

7.992 

0.349 

8.991 

0.393 

87i 

91 

0 240 

5.993 

0.288 

6.992 

0.336 

7.991 

0.384 

8.990 

0.432 

87$ 

3° 

0 262 

5.992 

0.314 

6.990 

0.366 

7.989 

0.419 

8.988 

0.471 

8 7° 

31 

0 283 

5.990 

0.340 

6.989 

0.397 

7.987 

0.454 

8.986 

0.510 

86$ 

31 

0 305 

5.989 

0.366 

6.987 

0.427 

7.985 

0.488 

8.983 

0.549 

86i 

0 327 

5.987 

0.392 

6.985 

0.458 

7.983 

0.523  ■ 

8.981 

0.589 

86$ 

4° 

0 349 

5.985 

0.419 

6.983 

0.488 

7.981 

0.558 

8.978 

0.628 

86° 

41 

0 371 

5.984 

0.445 

6.981 

0.519 

7.978 

0.593 

8.975 

0.667 

85$ 

41 

0 392 

5.982 

0.471 

6.978 

0.549 

7.975 

0.628 

8.972 

0.706 

85$ 

41 

0.414 

5.979 

0.497 

6.976 

0.580 

7.973 

0.662 

8.969 

0.745 

85$ 

5° 

0.436 

5.977 

0.523 

6.973 

0.610 

7.970 

0.697 

8.966 

0.784 

85° 

51 

0.458 

5.975 

0.549 

6.971 

0.641 

7.966 

0.732 

8.962 

0.824 

84$ 

51 

0.479 

5.972 

0.575 

6.968 

0.671 

7.963 

0.767 

8.959 

0.863 

84$ 

0.501 

5.970 

0.601 

6.965 

0.701 

7.960 

0.802 

8.955 

0.902 

84$ 

6° 

0.523 

5.967 

0.627 

6.962 

0.732 

7.956 

0.836 

8.951 

0.941 

84° 

6i 

0.544 

5.964 

0.653 

6.958 

0.762 

7.952 

0.871 

8.947 

0.980 

83$ 

0.566 

5.961 

0.679 

6.955 

0.792 

7.949 

0.906 

8.942 

1.019 

83$ 

u9 

A3. 

0.588 

5.958 

0.705 

6.951 

0.823 

7.945 

0.940 

8.938 

1.058 

83$ 

V»4 

7° 

0.609 

5.955 

0.731 

6.948 

0.853 

7.940 

0.975 

8.933 

1.097 

83° 

7± 

0.631 

5.952 

0.757 

6.944 

0.883 

7.936 

1.010 

8.928 

1.136 

82$ 

7 i 

0.653 

5.949 

0.783 

6.940 

0.914 

7.932 

1.044 

8.923 

1.175 

82$ 

73- 

0.674 

5.945 

0.809 

6.936 

0.944 

7.927 

1.079 

8.918 

1.214 

82$ 

8° 

0.696 

5.942 

0.835 

6.932 

0.974 

7.922 

1.113 

8.912 

1.253 

82° 

84 

0.717 

5.938 

0.861 

6.928 

1.004 

7.917 

1.148 

8.907 

1.291 

81$ 

°4 

8$ 

0.739 

5.934 

0.887 

6.923 

1.035 

7.912 

1.182 

8.901 

1.330 

81$ 

°a 

8$ 

0.761 

5.930 

0.913 

6.919 

1.065 

7.907 

1.217 

8.895 

1.369 

81$ 

°4 

9° 

0.782 

5.926 

0.939 

6.914 

1.095 

7.902 

1.251 

8.889 

1.408 

8 1^ 

9$ 

0.804 

5.922 

0.964 

6.909 

1.125 

7.896 

1.286 

8.883 

1.447 

80$ 

gi- 

0.825 

5.918 

0.990 

6.904 

1.155 

7.890 

1.320 

8.877 

1.485 

80$ 

“Q 

9$ 

0.847 

5.913 

1.016 

6.899 

1.185 

7.884 

1.355 

8.870 

1.524 

• — - — ■ 

80$ 

10° 

0.868 

5.909 

1.042 

6.894 

1.216 

7.878 

1.389 

8.863 

1.563 

80° 

10$ 

0.890 

5.904 

1.068 

6.888 

1.246 

7.872 

1.424 

8.856 

1.601 

79$ 

10^ 

0.911 

5.900 

1.093 

6.883 

1.276 

7.866 

1.458 

8.849 

1.640 

79$ 

10$ 

0.933 

5.895 

1.119 

6.877 

1.306 

7.860 

1.492 

8.842 

1.679 

79$ 

1 1° 

0.954 

5 890 

1.145 

6.871 

1.336 

7.853 

1.526 

8.835 

1.717 

79° 

111 

0.975 

5.885 

1.171 

6.866 

1.366 

7.846 

1.561 

8.827 

1.756 

78$ 

Hi 

0.997 

5.880 

1.196 

6.859 

1.396 

7.839 

1.595 

8.819 

1.794 

78$ 

111 

1.018 

5.874 

1.222 

6.853 

1.425 

7.832 

1.629 

8.811 

1.833 

12° 

1.040 

5.869 

1.247 

6.847 

1.455 

7.825 

1.663 

8.803 

1.871 

78° 

12$ 

1.061 

5.863 

1.273 

6.841 

1.485 

7.818 

1.697 

8.795 

1.910 

77$ 

12i 

1.082 

5.858 

1.299 

6.834 

1.515 

7.810 

1.732 

8.787 

1.948 

77$ 

12$ 

1.103 

5.852 

1.324 

6.827 

1.545 

7.803 

1.766 

8.778 

1.986 

77$ 

mm  — ft 

13° 

1.125 

5.846 

1.350 

6.821 

1.575 

7.795 

1.800 

8.769 

2.025 

77° 

bh 

c 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 Lat. 

bb 

c 

_ 

k_ 

40 

42 

CD 

5 

6 

7 

8 

9 

a> 

CD 

540 


LATITUDES  AND  DEPARTURES. 


tio 

«= 

1 

2 

3 

4 

5 

bi 

«D 

JD 

CO 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

to 

0> 

CO 

13° 

0.974 

0.225 

1.949 

0.450 

2.923 

0.675 

3.897 

0.900 

4.872 

77° 

131 

0.973 

0.229 

1.947 

0.458 

2.920 

0.688 

3.894 

0.917 

4.867 

76$ 

13i 

0.972 

0.233 

1.945 

0.467 

2.917 

0.700 

3.889 

0.934 

4.862 

761 

13$ 

0.971 

0.238 

1.943 

0.475 

2.914 

0.713 

3.885 

0.951 

4.857 

761 

14° 

0.970 

0.242 

1.941 

0.484 

2.911 

0.726 

3.881 

0.968 

4.851 

76° 

141 

0.969 

0.246 

1.938 

0.492 

2.908 

0.738 

3.877 

0.985 

4.846 

75$ 

14i 

0.968 

0.250 

1.936 

0.501 

2.904 

0.751 

3.873 

1.002 

4.841 

751 

14$ 

0.967 

0.255 

1.934 

0.509 

2.901 

0.764 

3.868 

1.018 

4.835 

751 

15° 

0.966 

0.259 

1.932 

0.518 

2.898 

0.776 

3.864 

1.035 

4.830 

75° 

151 

0.965 

0.263 

1.930 

0.526 

2.894 

0.789 

3.859 

1.052 

4.824 

74$ 

151 

0.964 

0.267 

1.927 

0.534 

2.891 

0.802 

3.855 

1.069 

4.818 

741 

15$ 

0.962 

0.271 

1.925 

0.543 

2.887 

0.814 

3.850  ' 

1.086 

4.812 

741 

16° 

0.961 

0.276 

1.923 

0.551 

2.884 

0.827 

3.845 

1.103 

4.806 

74° 

161 

0.960 

0.280 

1.920 

0.560 

2.880 

0.839 

3.840 

1.119 

4.800 

'CO 

Mu 

161 

0.959 

0.284 

1.918 

0.568 

2.876 

0.852 

3.835 

1.136 

4.794 

731 

16$ 

0.958 

0.288 

1.915 

0.576 

2.873 

0.865 

3.830 

1.153 

4.788 

731 

17° 

0.956 

0.292 

1.913 

0.585 

2.869 

0.877 

3.825 

1.169 

4.782 

73° 

m 

0.955 

0.297 

1.910 

0.593 

2.865 

0.890 

3.820 

1.186 

4.775 

72$ 

171 

0.954 

0.301 

1.907 

0.601 

2.861 

0.902 

3.815 

1.203 

4.769 

721 

17$ 

0.952 

0.305 

1.905 

0.610 

2.857 

0.915 

3.810 

1.220 

4.762 

721 

18° 

0.951 

0.309 

1.902 

0.618 

2.853 

0.927 

3.804 

1.236 

4.755 

72° 

181 

0.950 

0.313 

1.899 

0.626 

2.849 

0.939 

3.799 

1.253 

4.748 

71$ 

181 

0.948 

0.317 

1.897 

0.635 

2.845 

0.952 

3.793 

1.269 

4.742 

711 

18| 

0.947 

0.321 

1.894 

0.643 

2.841 

0.964 

3.788 

1.286 

4.735 

711 

19° 

0.946 

0.326 

1.891 

0.651 

2.837 

0.977 

3.782 

1.302 

4.728 

71° 

191 

0.944 

0.330 

1.888 

0.659 

2.832 

0.989 

3.776 

1.319 

4.720 

70$ 

m 

0.943 

0.334 

1.885 

0.668 

2.828 

1.001 

3.771 

1.335 

4.713 

701 

19$ 

0.941 

0.338 

1.882 

0.676 

2.824 

1.014 

3.765 

1.352 

4.706 

701 

20° 

0.940 

0.342 

1.879 

0.684 

2.819 

1.026 

3.759 

1.368 

4.698 

70° 

201 

0.938 

0.346 

1.876 

0.692 

2.815 

1.038 

3.753 

1.384 

4.691 

69$ 

20i 

0.937 

0.350 

1.873 

0.700 

2.810 

1.051 

3.747 

1.401 

4.683 

691 

20f 

0.935 

0.354 

1.870 

0.709 

2.805 

1.063 

3.741 

1.417 

4.676 

691 

21° 

0.934 

0.358 

1.867 

0.717 

2.801 

1.075 

3.734 

1.433 

4.668 

69° 

2H 

0.932 

0.362 

1.864 

0.725 

2.796 

1.087 

3.728 

1.450 

4.660 

68$ 

211 

0.930 

0.367 

1.861 

0.733 

2.791 

1.100 

3.722 

1.466 

4.652 

681 

21$ 

0.929 

0.371 

1.858 

0.741 

2.786 

1.112 

3.715 

1.482 

4.644 

681 

22° 

0.927 

0.375 

1.854 

0.749 

2.782 

1.124 

3.709 

1.498 

4.636 

68° 

22i 

0.926 

0.379 

1.851 

0.757 

2.777 

1.136 

3.702 

1.515 

4.628 

67$ 

22i 

0.924 

0.383 

1.848 

0.765 

2.772 

1.148 

3.696 

1.531 

4.619 

671 

22$ 

0.922 

0.387 

1.844 

0.773 

2.767 

1.160 

3.689 

1.547 

4.611 

671 

23° 

0.921 

0.391 

1.841 

0.781 

2.762 

1.172 

3.682 

1.563 

4.603 

67° 

23i 

0.919 

0.395 

1.838 

0.789 

2.756 

1.184 

3.675 

1.579 

4.594 

66$ 

23i 

0.917 

0.399 

1.834 

0.797 

2.751 

1.196 

3.668 

1.595 

4.585 

661 

23$ 

0.915 

0.403 

1.831 

0.805 

2.746 

1.208 

3.661 

1.611 

4.577 

661 

24° 

0.914 

0.407 

1.827 

0.813 

2.741 

1.220 

3.654 

1.627 

4.568 

66° 

24i 

0.912 

0.411 

1.824 

0.821 

2.735 

1.232 

3.647 

1.643 

4.559 

65$ 

24i 

0.910 

0.415 

1.820 

0.829 

2.730 

1.244 

3.640 

1.659 

4.550 

651 

24$ 

0.908 

0.419 

1.816 

0.837 

2.724 

1.256 

3.633 

1.675 

4.541 

651 

25° 

0.906 

0.423 

1.813 

0.845 

2.719 

1.268 

3.625 

1.690 

4.532 

65° 

25i 

0.904 

0.427 

1.809 

0.853 

2.713 

1.280 

3.618 

1.706 

4.522 

64$ 

25i 

0.903 

0.431 

1.805 

0.861 

2.708 

1.292 

3.610 

1.722 

4.513 

641 

25$ 

0.901 

0.434 

1.801 

0.869 

2.702 

1.303 

3.603 

1.738 

4.503 

641 

26° 

0.899 

0.438 

1.798 

0.877 

2.696 

1.315 

3.595 

1.753 

4.494 

64° 

bfi 

c 

&_ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

bi 

c 

u 

CO 

«> 

CO 

' 

2 

3 

4 

5 

<0 

<D 

CO 

LATITUDES  AND  DEPARTURES. 


541 


tub 

c 

5 

6 

7 

8 

9 

Bearing. 

1— 

to 

03 

00 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

13° 

13* 

13* 

13* 

14° 

14* 

14* 

14* 

1.125 

1.146 

1.167 

1.188 

1.210 

1.231 

1.252 

1.273 

5.846 

5.840 

5.834 

5.828 

5.822 

5.815 

5.809 

5.802 

1.350 

1.375 

1.401 

1.426 

1.452 

1.477 

1.502 

1.528 

6.821 

6.814 

6.807 

6.799 

6.792 

6.785 

6.777 

6.769 

1.575 

1.604 

1.634 

1.664 

1.693 

1.723 

1.753 

1.782 

7.795 

7.787 

7.779 

7.771 

7.762 

7.754 

7.745 

7.736 

1.800 

1.834 

1.868 

1.902 

1.935 

1.969 

2.003 

2.037 

8.769 

8.760 

8.751 

8.742 

8.733 

8.723 

8.713 

8.703 

2.025 

2.063 

2.101 

2.139 

2.177 

2.215 

2.253 

2.291 

77° 

76* 

76* 

76* 

76° 

75* 

75* 

75* 

15° 

1§* 

15* 

15* 

16° 

16* 

16* 

16* 

17° 

17* 

17* 

17* 

18° 

18* 

18* 

18* 

19° 

19* 

19* 

19* 

1.294 

1.315 

1.336 

1.357 

1.378 

1.399 

1.420 

1.441 

1.462 

1.483 

1.504 

1.524 

1.545 

1.566 

1.587 

1.607 

1.628 

1.648 

1.669 

1.690 

5.796 

5.789 

5.782 

5.775 

5.768 

5.760 

5.753 

5.745 

5.738 

5.730 

5.722 

5.714 

5.706 

5.698 

5.690 

5.682 

5.673 

5.665 

5.656 

5.647 

1.553 

1.578 

1.603 

1.629 

1.654 

1.679 

1.704 

1.729 

1.754 

1.779 

1.804 

1.829 

1.854 

1.879 

1.904 

1.929 

1.953 

1.978 

2.003 

2.028 

6.761 

6.754 

6.745 

6.737 

6.729 

6.720 

6.712 

6.703 

6.694 

6.685 

6.676 

6.667 

6.657 

6.648 

6.638 

6.629 

6.619 

6.609 

6.598 

6.588 

1.812 

1.841 

1.871 

1.900 

1.929 

1.959 

1.988 

2.017 

2.047 

2.076 

2.105 

2.134 

2.163 

2.192 

2.221 

2.250 

2.279 

2.308 

2.337 

2.365 

7.727 

7.718 

7.709 

7.700 

7.690 

7.680 

7.671 

7.661 

7.650 

7.640 

7.630 

7.619 

7.608 

7.598 

7.587 

7.575 

7.564 

7.553 

7.541 

7.529 

2.071 

2.104 

2.138 

2.172 

2.205 

2.239 

2.272 

2.306 

2.339 

2.372 

2.406 

2.439 

2.472 

2.505 

2.538 

2.572 

2.605 

2.638 

2.670 

2.703 

8.693 

8.683 

8.673 

8.662 

8.651 

8.640 

8.629 

8.618 

8.607 

8.595 

8.583 

8.572 

8.560 

8.547 

8.535 

8.522 

8.510 

8.497 

8.484 

8.471 

2.329 

2.367 

2.405 

2.443 

2.481 

2.518 

2.556 

2.594 

2.631 

2.669 

2.706 

2.744 

2.781 

2.818 

2.856 

2.893 

2.930 

2.967 

3.004 

3.041 

75° 

74* 

74* 

74* 

74° 

73* 

73* 

73* 

73° 

72* 

72* 

72* 

72° 

71* 

71* 

71* 

71° 

70* 

70* 

70* 

20° 

1.710 

5.638 

2.052 

6.578 

2.394 

7.518 

2.736 

8.457 

3.078 

7 0° 

20* 

1.731 

5.629 

2.077 

6.567 

2.423 

7.506 

2.769 

8.444 

3.115 

69* 

20* 

1.751 

5.620 

2.101 

6.557 

2.451 

7.493 

2.802 

8.430 

3.152 

69* 

204 

1.771 

5.611 

2.126 

6.546 

2.480 

7.481 

2.834 

8.416 

3.189 

69* 

■“”4 

21° 

1.792 

5.601 

2.150 

6.535 

2.509 

7.469 

2.867 

8.402 

3.225 

69° 

214 

1.812 

5.592 

2.175 

6.524 

2.537 

7.456 

2.900 

8.388 

3.262 

68* 

21  i 

1.833 

5.582 

2.199 

6.513 

2.566 

7.443 

2.932 

8.374 

3.299 

68* 

214 

1.853 

5.573 

2.223 

6.502 

2.594 

7.430 

2.964 

8.359 

3.335 

68* 

22° 

1.873 

5.563 

2.248 

6.490 

2.622 

7.417 

2.997 

8.345 

3.371 

68° 

224 

1.893 

5.553 

2.272 

6.479 

2.651 

7.404 

3.029 

8.330 

3.408 

67* 

22* 

1.913 

5.543 

2.296 

6.467 

2.679 

7.391 

3.061 

8.315 

3.444 

. 67* 

22* 

1.934 

5.533 

2.320 

6.455 

2.707 

7.378 

3.094 

8.300 

! 3.480 

67* 

23°- 

1.954 

5.523 

2.344 

6.444 

2.  / o5 

7.364 

3.126 

8.285 

3.517 

67° 

234 

1.974 

5.513 

2.368 

6.432 

2.763 

7.350 

3.158 

8.269 

3.553 

66* 

"'4 

23* 

1.994 

5.502 

2.392 

6.419 

2.791 

7.336 

3.190 

8.254 

3.589 

66  * 

23* 

2.014 

5.492 

2.416 

6.407 

2.819 

7.322 

3.222 

8.238 

3.625 

66* 

24° 

2.034 

5.481 

2.440 

6.395 

2.847 

7.308 

3.254 

8.222 

3.661 

66° 

24* 

2.054 

5.471 

2.464 

6.382 

2.875 

7.294 

3.286 

8.206 

3.696 

65* 

24* 

2.073 

5.460 

2.488 

6.370 

2.903 

7.280 

3.318 

8.190 

3.732 

652 

24* 

2.093 

5.449 

2.512 

6.357 

2.931 

7.265 

3.349 

8.173 

3.768 

65* 

25° 

2.113 

5.438 

2.536 

6.344 

2.958 

7.250 

3.381 

8.157 

3.804 

65° 

25* 

2.133 

5.427 

2.559 

6.331 

2.986 

7.236 

3.413 

8.140 

3.839 

64* 

25* 

2.153 

5.416 

2.583 

6.318 

3.014 

7.221 

3.444 

8.123 

3.8  / 5 

64* 

25* 

2.172 

5.404 

2.607 

6.305 

3.041 

7.206 

3.476 

8.106 

3.910 

64* 

26° 

2.192 

5.393 

2.630 

6.292 

3.069 

7.190 

3.507 

8.089 

3.945 

64° 

bi> 

c 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

fci 

c 

u 

k— 

<0 

03 

CO 

5 

6 

7 

. 

8 

9 

CO 

0> 

00 

542 


LATITUDES  AND  DEPARTURES. 


Bearing. 

. 

2 

3 

4 

5 

Bearing. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

26° 

0.899 

0.438 

1.798 

0.877 

2.696 

1.315 

3.595 

1.753 

4.494 

64° 

26* 

0.897 

0,442 

1.794 

0.885 

2.691 

1.327 

3.587 

1.769 

4.484 

63* 

26* 

0.895 

0.446 

1.790 

0.892 

2.685 

1.339 

3.580 

1.785 

4.475 

63* 

26* 

0.893 

0.450 

1.786 

0.900 

2.679 

1.350 

3.572 

1.800 

4.465 

63* 

27° 

0.891 

0.454 

1.782 

0.908 

2.673 

1.362 

3.564 

1.816 

4.455 

63° 

27* 

0.889 

0.458 

1.778 

0.916 

2.667 

1.374 

3.556 

1.831 

4.445 

62* 

27* 

0.887 

0.462 

1.774 

0.923 

2.661 

1.385 

3.548 

1.847 

4.435 

62* 

27* 

0.885 

0.466 

1.770 

0.931 

2.655 

1.397 

3.540 

1.862 

4.425 

62* 

28° 

0.883 

0.469 

1.766 

0.939 

2.649 

1.408 

3.532 

1.878 

4.415 

62° 

28* 

0.881 

0.473 

1.762 

0.947 

2.643 

1.420 

3.524 

1.893 

4.404 

61* 

28  g- 

0.879 

0.477 

1.758 

0.954 

2.636 

1.431 

3.515 

1.909 

4.394 

61* 

28* 

0,877 

0.481 

1.753 

0.962 

2.630 

1.443 

3.507 

1.924 

4.384 

61* 

29° 

0.875 

0.485 

1.749 

0.970 

2.624 

1.454 

3.498 

1.939 

4.373 

61° 

29* 

0.872 

0.489 

1.745 

0.977 

2.617 

1.466 

3.490 

1.954 

4.362 

60* 

29* 

0.870 

0.492 

1.741 

0.985 

2.611 

1.477 

3.481 

1.970 

4.352 

60* 

29* 

0.868 

0.496 

1.736 

0.992 

2.605 

1.489 

3.473 

1.985 

4.341 

60* 

30° 

0.866 

0.500 

1.732 

1.000 

2.598 

1.500 

3.464 

2.000 

4.330 

60° 

30* 

0.864 

0.504 

1.728 

1.008 

2.592 

1.511 

3.455 

2.015 

4.319 

59* 

30* 

0.862 

0.508 

1.723 

1.015 

2.585 

1.523 

3.447 

2.030 

4.308 

59* 

30* 

0.859 

0.511 

1.719 

1.023 

2.578 

1.534 

3.438 

2.045 

4.297 

59* 

31° 

6.857 

0.515 

1.714 

1.030 

2.572 

1.545 

3.429 

2.060 

4.286 

59° 

31* 

0.855 

0.519 

1.710 

1.038 

2.565 

1.556 

3.420 

2.075 

4.275 

58* 

31* 

0.853 

0.522 

1.705 

1.045 

2.558 

1.567 

3.411 

2.090 

4.263 

58* 

31* 

0.850 

0.526 

1.701 

1.052 

2.551 

1.579 

3.401 

2.105 

4.252 

58* 

32° 

0.848 

0.530 

1.696 

1.060 

2.544 

1.590 

3.392 

2.120 

4.240 

58° 

32* 

0.846 

0.534 

1.691 

1.067 

2.537 

1.601 

3.383 

2.134 

4.229 

57* 

32* 

0.843 

0.537 

1.687 

1.075 

2.530 

1.612 

3.374 

2.149 

4.217 

57* 

32* 

0.841 

0.541 

1.682 

1.082 

2.523 

1.623 

3.364 

2.164 

4.205 

57* 

33° 

0.839 

0.545 

1.677 

1.089 

2.516 

1.634 

3.355 

2.179 

4.193 

57° 

33* 

0.836 

0.548 

1.673 

1.097 

2.509 

1.645 

3.345 

2.193 

4.181 

56* 

33* 

0.834 

0.552 

1.668 

1.104 

2.502 

1.656 

3.336 

2.208 

4.169 

56* 

33* 

0.831 

0.556 

1.663 

1.111 

2.494 

1.667 

3.326 

2.222 

4.157 

56* 

34° 

0.829 

0.559 

1.658 

1.118 

2.487 

1.678 

3.316 

2.237 

4.145 

56° 

34* 

0.827 

0.563 

1.653 

1.126 

2.480 

1.688 

3.306 

2.251 

4.133 

55* 

34* 

0.824 

0.566 

1.648 

1.133 

2.472 

1.699 

3.297 

2.266 

4.121 

55* 

34* 

0.822 

0.570 

1.643 

1.140 

2.465 

1.710 

3.287 

2.280 

4.108 

55* 

35° 

0.819 

0.574 

1.638 

1.147 

2.457 

1.721 

3.277 

2.294 

4.096 

55° 

35* 

0.817 

0.577 

1.633 

1.154 

2.450 

1.731 

3.267 

2.309 

4.083 

54* 

35* 

0.814 

0.581 

1.628 

1.161 

2.442 

1.742 

3.257 

2.323 

4.071 

54* 

35* 

0.812 

0.584 

1.623 

1.168 

2.435 

1.753 

3.246 

2.337 

4.058 

54* 

36° 

0.809 

0.588 

1.618 

1.176 

2,427 

1.763 

3.236 

2.351 

4.045 

54° 

36* 

0.806 

0.591 

1.613 

1.183 

2.419 

1.774 

3.226 

2.365 

4.032 

53* 

36* 

0.804 

0.595 

1.608 

1.190 

2.412 

1.784 

3.215 

2.379 

4.019 

53* 

36* 

0.801 

0.598 

1.603 

1.197 

2.404 

1.795 

3.205 

2.393 

4.006 

53* 

37° 

0.799 

0.602 

1.597 

1.204 

2.396 

1.805 

3.195 

2.407 

3.993 

53° 

37* 

0.796 

0.605 

1.592 

1.211 

2,388 

1.816 

3.184 

2.421 

3.980 

52* 

37* 

0.793 

0.609 

1.587 

1.218 

2.380 

1.826 

3.173 

2.435 

3.967 

52* 

37* 

0.791 

0.612 

1.581 

1.224 

2.372 

1.837 

3.163 

2.449 

3.953 

52* 

38° 

0.788 

0.616 

1.576 

1.231 

2.364 

1.847 

3.152 

2.463 

3.940 

52° 

38* 

0.785 

0.619 

1.571 

1.238 

2.356 

1.857 

3.141 

2.476 

3.927 

51* 

38* 

0.783 

0.623 

1.565 

1.245 

2.348 

1.868 

3.130 

2.490 

3.913 

51* 

38* 

0.780 

0.626 

1.560 

1.252 

2.340 

1.878 

3.120 

2.504 

3.899 

51* 

39° 

0.777 

0.629 

1.554 

1.259 

2.331 

1.888 

3.109 

2.517 

3.886 

51° 

eh 

c 

i_ 

Dep. 

Ld;t« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

tab 

c 

CO 

<o 

CD 

1 

2 

3 

4 

5 

CO 

<U 

CQ 

LATITUDES  AND  DEPARTURES. 


fa b 
c 

5 

6 

7 

8 

9 

Bearing. 

hm 

CO 

£ 

Dep. 

Ls/t  • 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

26° 

26* 

26* 

26* 

27° 

27* 

27* 

27* 

28° 

28* 

28* 

28* 

M° 

29* 

29* 

29* 

2.192 

2.211 

2.231 

2.250 

2.270 

2.289 

2.309 

2.328 

2.347 

2.367 

2.386 

2.405 

2.424 

2.443 

2.462 

2.481 

5.393 

5.381 

5.370 

5.358 

5.346 

5.334 

5.322 

5.310 

5.298 

5.285 

5.273 

5.260 

5.248 

5.235 

5.222 

5.209 

2.630 

2.654 

2.677 

2.701 

2.724 

2.747 

2.770 

2.794 

2.817 

2.840 

2.863 

2.886 

2.909 

2.932 

2.955 

2.977 

6.292 

6.278 

6.265 

6.251 

6.237 

6.223 

6.209 

6.195 

6.181 

6.166 

6.152 

6.137 

6.122 

6.107 

6.093 

6.077 

3.069 

3.096 

3.123 

3.151 

3.178 

3.205 

3.232 

3.259 

3.286 

3.313 

3.340 

3.367 

3.394 

3.420 

3.447 

3.474 

7.190 

7.175 

7.160 

7.144 

7.128 

7.112 

7.096 

7.080 

7.064 

7.047 

7.031 

7.014 

6.997 

6.980 

6.963 

6.946 

3.507 

3.538 

3.570 

3.601 

3.632 

3.663 

3.694 

3.725 

3.756 

3.787 

3.817 

3.848 

3.878 

3.909 

3.939 

3.970 

8.089 

8.072 

8.054 

8.037 

8.019 

8.001 

7.983 

7.965 

7.947 

7.928 

7.909 

7.891 

7.872 

7.852 

7.833 

7.814 

3.945 

3.981 

4.016 

4.051 

4.086 

4.121 

4.156 

4.190 

4.225 

4.260 

4.294 

4.329 

4.363 

4.398 

4.432 

4.466 

64° 

63* 

63* 

63* 

63° 

62* 

62* 

62* 

62° 

61* 

61* 

61° 

30° 

30* 

30* 

30* 

31° 

31* 

31* 

31* 

32° 

| 

33* 

34° 

3 

34* 

2.500 

2.519 

2.538 

2.556 

2.575 

2.594 

2.612 

2.631 

2.650 

2.668 

2.686 

2.705 

2.723 

2.741 

2.760 

2.778 

2.796 

2.814 

2.832 

2.850 

5.196 

5.183 

5.170 

5.156 

5.143 

5.129 

5.116 

5.102 

5.088 

5.074 

5.060 

5.046 

5.032 

5.018 

5.003 

4.989 

4.974 

4.960 

4.945 

4.930 

3.000 
3.023 
3.045 
3.068 
3.090 
3.113 
3.135 
3.157 
3.180 
3.202 
• 3.224 
3.246 
3.268 
3.290 
3.312 
3.333 
3.355 
3.377 
3.398 
3.420 

6.062 

6.047 

6.031 

6.016 

6.000 

5.984 

5.968 

5.952 

5.936 

5.920 

5.904 

5.887 

5.871 

5.854 

5.837 

5.820 

5.803 

5.786 

5.769 

5.752 

3.500 

3.526 

3.553 

3.579 

3.605 

3.631 

3.657 

3.683 

3.709 

3.735 

3.761 

3.787 

3.812 

3.838 

3.864 

3.889 

3.914 

3.940 

3.965 

3.990 

6.928 

6.911 

6.893 

6.875 

6.857 

6.839 

6.821 

6.803 

6.784 

6.766 

6.747 

6.728 

6.709 

6.690 

6.671 

6.652 

6.632 

6.613 

6.593 

6.573 

4.000 

4.030 

4.060 

'4.090 

4.120 

4.150 

4.180 

4.210 

4.239 

4.269 

4.298 

4.328 

4.357 

4.386 

4.416 

4.445 

4.474 

4.502 

4.531 

4.560 

7.794 

7.775 

7.755 

7.735 

7.715 

7.694 

7.674 

7.653 

7.632 

7.612 

7.591 

7.569 

7.548 

7.527 

7.505 

7.483 

7.461 

7.439 

7.417 

7.395 

4.500 

4.534 

4.568 

4.602 

4.635 

4.669 

4.702 

4.736 

4.769 

4.802 

4.836 

4.869 

4.902 

4.935 

4.967 

5.000 

5.033 

5.065 

5.098 

5.130 

60° 

59* 

59* 

59* 

59° 

58* 

If 

Ooj 

58° 

57* 

57* 

57* 

57° 

56* 

56* 

56* 

56° 

55* 

55* 

55*__ 

35° 

38® 

37° 

37* 

37* 

37* 

38° 

it 

38* 

39° 

2.868 

2.886 

2.904 

2.921 

2.939 

2.957 

2.974 

2.992 

3.009 

3.026 

3.044 

3.061 

3.078 

3.095 

3.113 

3.130 

3.147 

4.915 

4.900 

4.885 

4.869 

4.854 

4.839 

4.823 

4.808 

4.792 

4.776 

4.760 

4.744 

4.728 

4.712 

4.696 

4.679 

4.663 

3.441 

3.463 

3.484 

3.505 

3.527 

3.548 

3.569 

3.590 

3.611 

3.632 

3.653 

3.673 

3.694 

3.715 

3.735 

3.756 

3.776 

5.734 

5.716 

5.699 

5.681 

5.663 

5.645 

5.627 

5.609 

5.590 

5.572 

5.554 

5.535 

5.516 

5.497 

5.478 

5.459 

5.440 

4.015 

4.040 

4.065 

4.090 

4.115 

4.139 

4.164 

4.188 

4.213 

4.237 

4.261 

4.286 

4.310 

4.334 

4.358 

4.381 

4.405 

6.553 

6.533 

6.513 

6.493 

6.472 

6.452 

6.431 

6.410 

6.389 

6.368 

6.347 

6.326 

6.304 

6.283 

6.261 

6.239 

6.217 

4.589 

4.617 

4.646 

4.674 

4.702 

4.730 

4.759 

4.787 

4.815 

4.842 

4.870 

4.898 

4.925 

4.953 

4.980 

5.007 

5.035 

7.372 

7.350 

7.327 

7.304 

7.281 

7.258 

7.235 

7.211 

7.188 

7.164 

7.140 

7.116 

7.092 

7.068 

7.043 

7.019 

6.994 

5.162 

5.194 

5.226 

5.258 

5.290 

5.322 

5.353 

5.385 

5.416 

5.448 

5.479 

5.510 

5.541' 

5.572 

5.603 

5.633 

5.664 

55° 

54* 

54* 

54* 

54° 

53* 

53* 

53* 

53° 

52* 

52* 

52* 

52° 

51* 

51* 

51* 

51° 

fab 

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Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

fab 

c 

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6 

7 

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LATITUDES  AND  DEPARTURES. 


da 

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Lat. 

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Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

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0.777 

0.629 

1.554 

1.259 

2.331 

1.888 

3.109 

2.517 

3.886 

51° 

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0.774 

0.633 

1.549 

1.265 

2.323 

1.898 

3.098 

2.531 

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1.543 

1.272 

2.315 

1.908 

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2.544 

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0.769 

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1.538 

1.279 

2.307 

1.918 

3.075 

2.558 

3.844 

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0.766 

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1.532 

1.286 

2.298 

1.928 

3.064 

2.571 

3.830 

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0.646 

1.526 

1.292 

2.290 

1.938 

3.053 

2.584 

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1.521 

1.299 

2.281 

1.948 

3.042 

2.598 

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1.515 

1.306 

2.273 

1.958 

3.030 

2.611 

3.788 

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0.755 

0.656 

1.509 

1.312 

2.264 

1.968 

3.019 

2.624 

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1.504 

1.319 

2.256 

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3.007 

2.637 

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0.663 

1.498 

1.325 

2.247 

1.988 

2.996 

2.650 

3.745 

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0.746 

0.666 

1.492 

1.332 

2.238 

1.998 

2.984 

2.664 

3.730 

48£ 

42° 

0.743 

0.669 

1.486 

1*338 

2.229 

2.007 

2.973 

2.677 

3.716 

48° 

42 £ 

0.740 

0.672 

1.480 

1.345 

2.221 

2.017 

2.961 

2.689 

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0.737 

0.676 

1.475 

1.351 

2.212 

2.027 

2.949 

2.702 

3.686 

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0.734 

0.679 

1.469 

1.358 

2.203 

2.036 

2.937 

2.715 

3.672 

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0.731 

0.682 

1.463 

1.364 

2.194 

2.046 

2.925 

2.728 

3.657 

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43£ 

0.728 

0.685 

1.457 

1.370 

2.185 

2.056 

2.913 

2.741 

3.642 

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0.688 

1.451 

1.377 

2.176 

2.065 

2.901 

2.753 

3.627 

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0.722 

0.692 

1.445 

1.383 

2.167 

2.075 

2.889 

2.766 

3.612 

46£ 

44° 

0.719 

0.695 

1.439 

1.389 

2.158 

2.084 

2.877 

2.779 

3.597 

46° 

44£ 

0.716 

0.698 

1.433 

1.396 

2.149 

2.093 

2.865 

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0.713 

0.701 

1.427 

1.402 

2.140 

2.103 

2.853 

2.804 

3.566 

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44£ 

0.710 

0.704 

1.420 

1.408 

2.131 

2.112 

2.841 

2.816 

3.551 

45£ 

45° 

0.707 

0.707 

1.414 

1.414 

2.121 

2.121 

2.828 

2.828 

3.536 

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Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Bear- 

ing. 

do 

C 

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6 

7 

8 

9 

bi 

c 

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CO 

03 

00 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

CD 

SO 

39° 

3.147 

4.663 

3.776 

5.440 

4.405 

6.217 

5.035 

6.994 

5.664 

“Ti5" 

39£ 

3.164 

4.646 

3.796 

5.421 

4.429 

6.195 

5.062 

6.970 

5.694 

50£ 

39k 

3.180 

4.630 

3.816 

5.401 

4.453 

6.173 

5.089 

6.945 

5.725 

50| 

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3.197 

4.613 

3.837 

5.382 

4.476 

6.151 

5.116 

6.920 

5.755 

50£ 

40° 

3.214 

4.596 

3.857 

5.362 

4.500 

6.128 

5.142 

6.894 

5,785 

50° 

40£ 

3.231 

4.579 

3.877 

5.343 

4.523 

6.106 

5.169 

6.869 

5.’815 

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3.247 

4.562 

3.897 

5.323 

4.546 

6.083 

5.196 

6.844 

5.845 

49k 

40£ 

3.264 

4.545 

3.917 

5.303 

4.569 

6.061 

5.222 

6.818 

5.875 

49£ 

41° 

3.280' 

4.528 

3.936 

5.283 

4.592 

6.038 

5.248 

6.792 

5.905 

49° 

41£ 

3.297 

4.511 

3.956 

5.263 

4.615 

6.015 

5.275 

6.767 

5.934 

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3.313 

4.494 

3.976 

5.243 

4.638 

5.992 

5.301 

6.741 

5.964 

43k 

41£ 

3.329 

4.476 

3.995 

5.222 

4.661 

5.968 

5.327 

6.715 

5.993 

48£ 

42° 

3.346 

4.459 

4.015 

5.202 

4.684 

5.945 

5.353 

6.688 

6.022 

48° 

42£ 

3.362 

4.441 

4.034 

5.182 

4.707  • 

5.922 

5.379 

6.662 

6.051 

47} 

42! 

3.378 

4.424 

4.054 

5.161 

4.729 

5.898 

5.405 

6.635 

6.080 

47  k 

42f 

3.394 

4.406 

4.073 

5.140 

4.752 

5.875 

5.430 

6.609 

6.109 

47£ 

43° 

3.410 

4.388 

4.092 

5.119 

4.774 

5.851 

5.456 

6.582 

6.138 

47° 

43£ 

3.426 

4.370 

4.111 

5.099 

4.796 

5.827 

5.481 

6.555 

6.167 

46} 

43! 

3.442 

4.352 

4.130 

5.078 

4.818 

5.803 

5.507 

6.528 

6.195 

46! 

43£ 

3.458 

4.334 

4.149 

5.057 

4.841 

5.779 

5.532 

6.501 

6.224 

46£ 

44° 

3.473 

4.316 

4.168 

5.035 

4.863 

5.755 

5.557 

6.474 

6.252 

46° 

44£ 

3.489 

4.298 

4.187 

5.014 

4.885 

5.730 

5.582 

6.447 

6.280 

45} 

44! 

3.505 

4.280 

4.206 

4.993 

4.906 

5.706 

5.607 

6.419 

6.308 

45! 

44£ 

3.520 

4.261 

4.224 

4.971 

4.928 

5.681 

5.632 

6.392 

6.336 

45£ 

45° 

3.536 

4.243 

4.243 

4.950 

4.950 

5.657 

5.657 

6.364 

6.364 

45° 

Bear- 

ing. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Bear- 

ing. 

CIRCUMFERENCES,  AND  AREAS. 


545 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 
CIRCUMFERENCES,  AND  AREAS. 


No. 

Square. 

Cube. 

3q.  Root.  1 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 
21 
22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

1 

4 

9 

16 

25 

36 

49 

64 

81 

100 

121 

144 

169 

196 

225 

256 

289 

324 

361 

400 

441 

484 

529 

576 

625 

676 

729 

784 

841 

900 

961 

1.024 
1,089 
1,156 
1,225 
1,296 
1,369 
1,444 
1,521 
1,600 
1,681 
1,764 
1,849 
1,936 

2.025 
2,116 
2,209 
2,304 
2,401 
2,500 
2,601 
2,704 
2,809 
2,916 

3.025 

1 

8 

27 

64 

125 

216 

343 

512 

729 

1,000 

1,331 

1,728 

2,197 

2,744 

3.375 
4,096 
4,913 
5,832 
6,859 
8,000 
9,261 

10,648 

12,167 

13,824 

15,625 

17,576 

19,683 

21,952 

24,389 

27.000 
29,791 
32,768 
35,937 
39,304 
42,875 
46,656 
50,653 
54.872 
59,319 

64.000 
68,921 
74,088 
79,507 
85,184 
91,125 
97,336 

103,823 

110,592 

117,649 

125.000 
132,651 
140,608 
148,877 
157,464 

166.375 

1.0000 

1.4142 

1.7321 

2.0000 

2.2361 

2.4495 

2.6458 

2.8284 

3.0000 

3.1623 

3.3166 

3.4641 

3.6056 

3.7417 

3.8730 

4.0000 
4.1231 
4.2426 
4.3589 
4.4721 
4.5826 
4.6904 
4.7958 
4.8990 

5.0000 
5.0990 
5.1962 
5.2915 
5.3852 
5.4772 
5.5678 
5.6569 
5.7446 
5.8310 
5.9161 
6.0000 
6.0828 
6.1644 
6.2450 
6.3246 
6.4031 
6.4807 
6.5574 
6.6332 
6.7082 
6.7823 
6.8557 
6.9282 
7.0000 
7.0711 
7.1414 
7.2111 
7.2801 
7.3485 
7.4162 

1.0000  ] 
1.2599 
1.4422 
1.5874 
1.7100 
1.8171 
1.9129 
2.0000 
2.0801 
2.1544 
2.2240 
2.2894 
2.3513 
2.4101 
2.4662 
2.5198 
2.5713 
2.6207 
2.6684 
2.7144 
2.7589 
2.8020 
' 2.8439 
2.8845 
2.9240 
2.9625 
3.0000 
3.0366 
3.0723 
3.1072 
3.1414 
3.1748 
3.2075 
3.2396 
3.2717 
3.3019 
3.3322 
3.3620 
3.3912 
3.4200 
3.4482 
3.4760 
3.5034 
3.5303 
3.5569 
3.5830 
3.6088 
3.6342 
3.6593 
3.6840 
3.7084 
3.7325 
3.7563 
3.7798 
3.8030 

L.000000000 

.500000000 

.333333333 

.250000000 

.200000000 

.166666667 

.142857143 

.125000000 

.111111111 

.100000000 

.090909091 

.083333333 

.076923077 

.071428571 

.066666667 

.062500000 

.058823529 

.055555556 

.052631579 

.050000000 

.047619048 

.045454545 

.043478261 

.041666667 

.040000000 

.038461538 

.037037037 

.035714286 

.034482759 

.033333333 

.032258065 

.031250000 

.030303030 

.029411765 

.028571429 

.027777778 

.027027027 

.026315789 

.025641026 

.025000000 

.024390244 

.023809524 

.023255814 

.022727273 

.022222222 

.021739130 

.021276600 

.020833333 

.020408163 

.020000000 

.019607843 

.019230769 

.018867925 

.018518519 

.018181818 

3.1416 

6.2832 

9.4248 

12.5664 

15.7080 

18.850 

21.991 

25.133 

28.274 

31.416 

34.558 

37-699 

40.841 

43.982 

47.124 

50.265 

53.407 

56.549 

59.690 

62.832 

65.973 

69.115 

72.257 

75.398 

78.540 

81.681 

84.823 

87.965 

91.106 

94.248 

97.389 

100.53 

103.67 

106.81 

109.96 

113.10 

116.24 

119.38 

122.52 

125.66 

128.81 

131.95 

135.09 

138.23 

141.37 

144.51 

147.65 
150.80 
153.94 
157.08 
160.22 
163.36 
166.50 

169.65 
172.79 

0.7854 

3.1416 

7.0686 

12.5664 

19.635 

28.274 

38.485 

50.266 

63.617 

78.540 

95.033 

113.10 

132.73 

153.94 
176.71 
201.06 
226.98 

254.47 

283.53 
314.16 
346.36 
380.13 

415.48 
452.39 
490.87 
530.93 
572.56 
615.75 
660.52 
706.86 
754.77 
804.25 
855.30 
907.92 
962.11 

1,017.88 

1.075.21 
1,134.11 
1,194.59 
1,256.64 
1,320.25 
1,385.44 
1,452.20 

1.520.53 
1,590.43 
1,661.90 

1.734.94 
1,809.56 
1,885.74 
1,963.50  1 

2.042.82 
2,123.72 
2,206.18 

2.290.22  ! 

2.375.83 

546 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS , 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

56 

3,136 

175,616 

7.4833 

3.8259 

.017857143 

175.93 

2,463.01 

57 

3,249 

185,193 

7.5498 

3.8485 

.017543860 

179.07 

2,551.76 

58 

3,364 

195,112 

7.6158 

3.8709 

.017241379 

182.21 

2,642.08 

59 

3,481 

205,379 

7.6811 

3.8930 

.016949153 

185.35 

2,733.97 

60 

3,600 

216,000 

7.7460 

3.9149 

.016666667 

188.50 

2,827.43 

61 

3,721 

226,981 

7.8102 

3.9365 

.016393443 

191.64 

2,922.47 

62 

3,844 

238,328 

7.8740 

3.9579 

.016129032 

194.78 

3,019.07 

63 

3,969 

250,047 

7.9373 

3.9791 

.015873016 

197.92 

3,117.25 

64 

4,096 

262,144 

8.0000 

4.0000 

.015625000 

201.06 

3,216.99 

65 

4,225 

274,625 

8.0623 

4.0207 

.015384615 

204.20 

3,318.31 

66 

4,356 

287,496 

8.1240 

4.0412 

.015151515 

207.34 

3,421.19 

67 

4,489 

300,763 

8.1854 

4.0615 

.014925373 

210.49 

3,525.65 

68 

4,624 

314,432 

8.2462 

4.0817 

.014705882 

213.63 

3,631.68 

69 

4^761 

328,509 

8.3066 

4.1016 

.014492754 

216.77 

3,739.28 

70 

4,900 

343,000 

8.3666 

4.1213 

.014285714 

219.91 

3,848.45 

71 

5,041 

357,911 

8.4261 

4.1408 

.014084517 

223.05 

3,959.19 

72 

5,184 

373,248 

8.4853 

4.1602 

.013888889 

226.19 

4,071.50 

73 

5,329 

389,017 

8.5440 

4.1793 

.013698630 

229.34 

4,185.39 

74 

5,476 

405,224 

8.6023 

4.1983 

.013513514 

232.48 

4,300.84 

75 

5,625 

421,875 

8.6603 

4.2172 

.013333333 

235.62 

4,417.86 

76 

5,776 

438,976 

8.7178 

4.2358 

.013157895 

238.76 

4,536.46 

77 

5*929 

456,533 

8.7750 

4.2543 

.012987013 

241.90 

4,656.63 

78 

6,084 

474,552 

8.8318 

4.2727 

.012820513 

245.04 

4,778.36 

79 

6,241 

493,039 

8.8882 

4.2908 

.012658228 

248.19 

4,901.67 

80 

6,400 

512,000 

8.9443 

4.3089 

.012500000 

251.33 

5,026.55 

81 

6,561 

531,441 

9.0000 

4.3267 

.012345679 

254.47 

5,153.00 

82 

6,724 

551,368 

9.0554 

4.3445 

.012195122 

257.61 

5,281.02 

83 

6i  889 

571,787 

9.1104 

4.3621 

.012048193 

260.75 

5,410.61 

84 

7,056 

592,704 

9.1652 

4.3795 

.011904762 

263.89 

5,541.77 

85 

7,225 

614,125 

9.2195 

4.3968 

.011764706 

267.04 

5,674.50 

86 

7,396 

636,056 

9.2736 

4.4140 

.011627907 

270.18 

5,808.80 

87 

7,569 

658,503 

9.3274 

4.4310 

.011494253 

273.32 

5,944.68 

88 

7,744 

681,472 

9.3808 

4.4480 

.011363636 

276.46 

6,082.12 

89 

7.921 

704,969 

9.4340 

4.4647 

.011235955 

279.60 

6,221.14 

90 

8,100 

729,000 

9.4868 

4.4814 

.011111111 

282.74 

6,361.73 

91 

8,281 

753,571 

9.5394 

4.4979 

.010989011 

285.88 

6,503.88 

92 

8,464 

778,688 

9.5917 

4.5144 

.010869565 

289.03 

6,647.61 

93 

8,649 

804,357 

9.6437 

4.5307 

.010752688 

292.17 

6,792.91 

94 

8,836 

830,584 

9.6954 

4.5468 

.010638298 

295.31 

6,939.78 

95 

9,025 

857,375 

9; 7468 

4.5629 

.010526316 

298.45 

7,088.22 

96 

9,216 

884,736 

9.7980 

4.5789 

.410416667 

301.59 

7,238.23 

97 

9,409 

912,673 

9.8489 

4.5947 

.010309278 

304.73 

7,389.81 

98 

9,604 

941,192 

9.8995 

4.6104 

.010204082 

307.88 

7,542.96 

99 

9,801 

970,299 

9.9499 

4.6261 

.010101010 

311.02 

7,697.69 

100 

10,000 

1,000,000 

10.0000 

4.6416 

.010000000 

314.16 

7,853.98 

101 

10,201 

1,030,301 

10.0499 

4.6570 

.009900990 

317.30 

8,011.85 

102 

10,404 

1,061,208 

10.0995 

4.6723 

.009803922 

320.44 

8,171.28 

103 

10,609 

1,092,727 

10.1489 

4.6875 

.009708738 

323.58 

8,332.29 

104 

10,816 

1,124,864 

10.1980 

4.7027 

.009615385 

326.73 

8,494.87 

105 

11,025 

1,157,625 

10.2470 

4.7177 

.009523810 

329.87 

8,659.01 

106 

11,236 

1,191,016 

10.2956 

4.7326 

.009433962 

333.01 

8,824.73 

107 

11,449 

1,225,043 

10.3441 

4.7475 

.009345794 

336.15 

8.992.02 

108 

11,664 

1,259,712 

10.3923 

4.7622 

.009259259 

339.29 

9,160.88 

109 

11,881 

1,295,029 

10.4403 

4.7769 

.009174312 

342.43 

9,331.32 

110 

12,100 

1,331,000 

10.4881 

4.7914 

.009090909 

345.58 

9,503.32 

111 

12,321 

1,367,631 

10.5357 

4.8059 

.009009009 

348.72 

9,676.89 

112 

12,544 

1,404,928 

10.5830 

4.8203 

.008928571 

351.86 

9,852.03 

113 

12,769 

1,442,897 

10.6301 

4.8346 

.008849558 

355.00 

10,028.75 

114 

12,996 

1,481,544 

10.6771 

4.8488 

.008771930 

358.14 

10,207.03 

115 

13,225 

1,520,875 

10.7238 

4.8629 

.008695652 

361.28 

10,386.89 

116 

13,456 

1,560,896 

10.7703 

4.8770 

.008020690 

364.42 

10,568.32 

117 

13,689 

1,601,613 

10.8167 

4.8910 

.008547009 

367.57 

10,751.32 

118 

13,924 

1,643,032 

10.8628 

4.9049 

.008474576 

370.71 

10,935.88 

CIRCUMFERENCES,  AND  AREAS. 


547 


I1 

No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

119 

120 
121 
122 

123 

124 

125 

126 

127 

128 

129 

130 

131 

132 

133 

134 

135 

136 

137 

138 

139 

140 

141 

142 

143 

144 

145 

146 

147 

148 

149 

150 

151 

152 

153 

154 

155 

156 

157 

158 

159 

160 
161 
162 

163 

164 

165 

166 

167 

168 

169 

170 

171 

172 

173 

174 

175 

176 

177 

178 

179 

180 
181 

14.161 
14,400 

14.641 
14,834 

15.129 
15,376 
15,625 
15,876 

16.129 
16,384 

16.641 
16,900 

17.161 
17,424 
17,689 
17,956 
18,225 
18,496 
18,769 
19,044 
19,321 

19.600 
19,881 
20,164 
20,449 
20,736 

21.025 
21,316 
21,609 
21,904 
22,201 
22,500 
22,801 
23,104 
23,409 
23,716 

24.025 
24,336 
24,649 
24,964 
25,281 

25.600 
25,921 
26,244 
26,569 
26,896 
27,225 
27,556 
27,889 
28,224 
28,561 
28,900 
29,241 
28,584 
29,929 
30,276 
30,625 
30,976 
31,329 
31,684 
32,041 
32,400 
32,761 

1,685,159 

1.728.000 
1,771,561 
1,815,848 
1,860,867 

1.906.624 
1,953,125 
2,000,376 
2,048,383 
2,097,152 
2,146,689 

2.197.000 
2,248,091 
2,299,968 
2,352,637 
2,406,104 
2,460,375 
2,515,456 
2,571,353 
2,628,072 
2,685,619 

2.744.000 
2,803,221 
2,863,288 
2,924,207 
2,985,984 

3.048.625 
3,112,136 
3,176,523 
3,241,792 
3,307,949 

3.375.000 
3,442,951 
3,511,008 
3,581,577 
3,652,264 
3,723,875 
3,796,416 
3,869,893 
3,944,312 
4,019,679 

4.096.000 
4,173,281 
4,251,528 
4,330,747 
4,410,944 
4,492,125 
4,574,296 
4,657,463 
4,741,632 
4,826,809 

4.913.000 
5,000,211 
5,088,448 
5,177,717 
5,268,024 
5,359,375 
5,451,776 
5,545,233 
5,639,752 
5,735,339 

5.832.000 
5,929,741 

10.9087 

10.9545 

11.0000 

11.0454 

11.0905 

11.1355 

11.1803 

11.2250 

11.2694 

11.3137 

11.3578 

11.4018 

11.4455 

11.4891 

11.5326 

11.5758 

11.6190 

11.6619 

11.7047 

11.7473 

11.7898 

11.8322 

11.8743 

11.9164 

11.9583 

12.0000 

12.0416 

12.0830 

12.1244 

12.1655 

12.2066 

12.2474 

12.2882 

12.3288 

12.3693 

12.4097 

12.4499 

12.4900 

12.5300 

12.5698 

12.6095 

12.6491 

12.6886 

12.7279 

12.7671 

12.8062 

12.8452 

12.8841 

12.9228 

12.9615 

13.0000 

13.9384 

13.0767 

13.1149 

13.1529 

13.1909 

13.2288 

13.2665 

13.3041 

13.3417 

13.37&L 

13.4164 

13.4536 

4.9187 

4.9324 

4.9461 

4.9597 

4.9732 

4.9866 

5.0000 

5.0133 

5.0265 

5.0397 

5.0528 

5.0658 

5.0788 

5.0916 

5.1045 

5.1172 

5.1299 

5.1426 

5.1551 

51676 

5.1801 

5.1925 

5.2048 

5.2171 

5.2293 

5.2415 

5.2536 

5.2656 

5.2776 

5.2896 

5.3015 

5.3133 

5.3251 

5.3368 

5.3485 

5.3601 

5.3717 

5.3832 

5.3947 

5.4061 

5.4175 

5.4288 

5.4401 

5.4514 

5.4626 

5.4737 

5.4848 

5.4959 

5.5069 

5.5178 

5.5288 

5.5397 

5.5505 

5.5613 

5.5721 

5.5828 

5.5934 

5.6041 

5.6147 

5.6252 

5.6357 

5.6462 

5.6567 

.008403361 

.008333333 

.008264463 

.008196721 

.008130081 

.008064516 

.008000000 

.007936508 

.007874016 

.007812500 

.007751938 

.007692308 

.007633588 

.007575758 

.007518797 

.007462687 

.007407407 

.007352941 

.007299270 

.007246377 

.007194245 

.007142857 

.007092199 

.007042254 

.006993007 

.006944444 

.006896552 

.006849315 

.006802721 

.006756757 

.006711409 

.006666667 

.006622517 

.006578947 

.006535948 

.006493506 

.006451613 

.006410256 

.006369427 

.006329114 

.006289308 

.006250000 

.006211180 

.006172840 

.006134969 

.006097561 

.006060606 

.006024096 

.005988024 

.005952381 

.005917160 

.005882353 

.005847953 

.005813953 

.005780347 

.005747126 

.005714286 

.005681818 

.005649718 

.005617978 

.005586592 

.005555556 

.005524862 

373.85 

376.99 

380.13 

383.27 
386.42 
389.56 
392.70 
395.84 
398.98 

402.12 

405.27 
408.41 
411.55 
414.69 
417.83 
420.97 

424.12 
427.26 
430.40 
433.54 
436.68 
439.82 

442.96 
446.11 
449.25 
452.39 
455.53 
458.67 

461.81 

464.96 
468.10 
471.24 
474.38 
477.52 
480.66 

483.81 
486.95 
490.09 
493.23 
496.37 
499.51 

502.65 
505.80 
508.94 
512.08 
515.22 
518.36 

521.50 

524.65 
527.79 
530.93 
534.07 
537.21 

540.35 

543.50 
546.64 
549.78 
552.92 
556.06 
559.20 

562.35 
565.49 
568.63 

11,122.02 

11,309.73 

11.499.01 

11.689.87 
11,882.29 
12,076.28 

12.271.85 
12,468.98 
12,667.69 
12,867.96 
13,069.81 
13,273.23 
13,478.22 
13,684.78 
13,892.91 

14.102.61 

14.313.88 
14,526.72 
14,741.14 
14,957.12 
15,174.68 
15,393.80 

15.614.50 
15,836.77 

16.060.61 

16.286.02 

16.513.00 

16.741.55 

16.971.67 
17,203.36 
17,436.62 
17,671.46 

17.907.86 
18,145.84 
18,385.39 

18.626.50 

18.869.19 

19.113.45 
19,359.28 

19.606.68 
19,855.65 

20.106.19 
20,358.31 
20,611.99 
20,867.24 

21.124.07 

21.382.46 

21.642.43 
21,903.97 

22.167.08 
22,431.76 

22.698.01 
22,965.83 
23,235.22 
23,506.18 
23,778.71 
24,052.82 
24,328.49 
24,605.74 

24.884.56 
25,164.94 
25,446.90 

25.730.43 

548 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

182 

183 

184 

185 

186 

187 

188 

189 

190 

191 

192 

193 

194 

195 

196 

197 

198 

199 

200 
201 
202 

203 

204 

205 

206 

207 

208 

209 

210 
211 
212 

213 

214 

215 

216 

217 

218 

219 

220 
221 
222 

223 

224 

225 

226 

227 

228 

229 

230 

231 

232 

233 

234 

235 

236 

237 

238 

239 

240 

241 

242 

243 

244 

33,124 

33,489 

33,856 

34.225 
34,596 
34,969 
35,344 
35,721 

36.100 
36,481 
36,864 
37,249 
37,636 

38.025 
38,416 
38,809 
39,204 
39,601 
40,000 
40,401 
40,804 
41,209 
41,616 

42.025 
42,436 
42,849 
43,264 
43,681 

44.100 
44,521 
44,944 
45,369 
45,796 

46.225 
46,656 
47,089 
47,524 
47,961 
48,400 
48,841 
49,284 
49,729 
50,176 
50,625 
51,076 
51,529 
51,984 
52,441 
52,900 
53,361 
53,824 
54.289 
54,756 

55.225 
55,696 
56,169 
56,644 
57,121 
57,600 
58,081 
58,564 
59,049 
59,536 

6,028,568 

6,128,487 

6,229,504 

6.331.625 
6,434,856 
6,539,203 
6,644,672 
6,751,269 

6.859.000 
6,967,871 
7,077,888 
7,189,017 
7,301,384 

7.414.875 
7,529,536 
7,645,373 
7,762,392 
7,880,599 
8,000,000 
8,120,601 
8,242,408 
8,365,427 
8,489,664 
8,615,125 
8,741,836 
8,869,743 
8,998,912 
9,129,329 

9.261.000 
9,393,931 
9,528.128 
9,663,597 
9,800,344 
9,938,375 

10,077,696 

10,218,313 

10,360,232 

10,503,459 

10.648.000 
10,793,861 
10,941,048 
11,089,567 
11,239,424 

11.390.625 
11,543,176 
11,697,083 
11,852,352 
12,008,989 

12.167.000 
12,326,391 
12,487,168 
12,649,337 
12,812,904 

12.977.875 
13,144,256 
13,312,053 
13,481,272 
13,651,919 

13.824.000 
13,997,521 
14,172,488 
14,348,907 
14,526,784 

13.4907 

13.5277 

13.5647 

13.6015 

13.6382 

13.6748 

13.7113 

13.7477 

13.7840 

13.8203 

13.8564 

13.8924 

13.9284 

13.9642 

14.0000 
14.0357 
14.0712 
14.1067 
14.1421 
14.1774 
14.2127 
14.2478 
14.2829 
14.3178 
14.3527 
14.3875 
14.4222 
14.4568 
14.4914 
14.5258 
14.5602 
14.5945 
14.6287 
14.6629 
14.6969 
14.7309 
14.7648 
14.7986 
14.8324 
14.8661 
14.8997 
14.9332 
14.9666 

15.0000 
15.0333 
15.0665 
15.0997 
15.1327 
15.1658 
15.1987 
15.2315 
15.2643 
15.2971 
15.3297 
15.3623 
15.3948 
15.4272 
15.4596 
15.4919 
15.5242 
15.5563 
15.5885 
15.6205 

5.6671 

5.6774 

5.6877 

5.6980 

5.7083 

5.7185 

5.7287 

5.7388 

5.7489 

5.7590 

5.7690 

5.7790 

5.7890 

5.7989 

5.8088 

5.8186 

5.8285 

5.8383 

5.8480 

5.8578 

5.8675 

5.8771 

5.8868 

5.8964 

5.9059 

5.9155 

5.9250 

5.9345 

5.9439 

5.9533 

5.9627 

5.9721 

5.9814 

5.9907 

6.0000 

6.0092 

6.0185 

6.0277 

6.0368 

6.0459 

6.0550 

6.0641 

6.0732 

6.0822 

6.0912 

6.1002 

6.1091 

6.1180 

6.1269 

6.1358 

6.1446 

6.1534 

6.1622 

6.1710 

6.1797 

6.1885 

6.1672 

6.2058 

6.2145 

6.2231 

6.2317 

6.2403 

6.2488 

.005494505 

.005464481 

.005434783 

.005405405 

.005376344 

.005347594 

.005319149 

.005291005 

.005263158 

.005235602 

.005208333 

.005181347 

.005154639 

.005128205 

.005102041 

.005076142 

.005050505 

.005025126 

.005000000 

.004975124 

.004950495 

.004926108 

.004901961 

.004878049 

.004854369 

.004830918 

.004807692 

.004784689 

.004761905 

.004739336 

.004716981 

.004694836 

.004672897 

.004651163 

.004629630 

.004608295 

.004587156 

.004566210 

.004545455 

.004524887 

.004504505 

.004484305 

.004464286 

.004444444 

.004424779 

.004405286 

.004385965 

.004366812 

.004347826 

.004329004 

.004310345 

.004291845 

.004273504 

.004255319 

.004237288 

.004219409 

.004201681 

.004184100 

.004166667 

.004149378 

.004132231 

.004115226 

.004098361 

571.77 

574.91 

578.05 

581.19 
584.34 
587.48 
590.62 
593.76 
596.90 

600.04 

603.19 
606.33 
609.47 
612.61 
615.75 
618.89 

622.04 
625.18 
628.32 
631.46 
634.60 
637.74 

640.88 
644.03 
647.17 
650.31 
653.45 
656.59 

659.73 

662.88 
666.02 
669.16 
672.30 
675.44 

678.58 

681.73 
684.87 
688.01 
691.15 
694.29 
697.43 

700.58 
703.72 
706.86 
710.00 
713.14 
716.28 

719.42 
722.57 
725.71 
728.85 
731.99 
735.13 

738.27 

741.42 
744.56 
747.70 
750.84 
753.98 
757.12 

760.27 
763.41 
766.55 

26,015.53 

26.302.20 
26,590.44 

26.880.25 

27.171.63 
27,464.59 

27.759.11 

28.055.21 
28,352.87 

28.652.11 

28.952.92 
29,255.30 

29.559.25 

29.864.77 

30.171.86 

30.480.52 
30,790.75 

31.102.55 

31.415.93 

31.730.87 
32,047.39 

32.365.47 

32.685.13 
33.006.36 
33,329.16 

33.653.53 

33.979.47 

34.306.98 

34.636.06 

34.966.71 

35.298.94 

35.632.73 

35.968.09 

36.305.03 

36.643.54 

36.983.61 

37.325.26 

37.668.48 

38.013.27 

38.359.63 

38.707.56 

39.057.07 

39.408.14 

39.760.78 
40,115.00 

40.470.78 

40.828.14 

41.187.07 

41.547.56 
41*909.63 

42.273.27 

42.638.48 
43,005.26 

43.373.61 

43.743.54 

44.115.03 

44.488.09 

44.862.73 
45,238.93 

45.616.71 
45,996.06 

46.376.98 
46,759.47 

CIRCUMFERENCES , AND  AREAS. 


549 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

245 

246 

247 

248 

249 

250 

251 

252 
258 

254 

255 
256. 

257 

258 

259 

260 
261 
262 

263 

264 

265 

266 

267 

268 

269 

270 

271 

272 

273 

274 

275 

276 

277 

278 

279 

280 
281 
282 

283 

284 

285 

286 

287 

288 

289 

290 

291 

292 

293 

294 

295 

296 

297 

298 

299 

300 

301 

302 

303 

304 

305 

306 

307 

60.025 

60.516 

61.009 

61.504 
62,001 
62,500 
63,001 

63.504 

64.009 

64.516 

65.025 
65.536 
66,049 
66,564 
67,081 
67,600 
68,121 
68,644 
69,169 
69,696 

70.225 
70,756 
71,289 
71,824 
72,361 
72,900 
73,441 
73,984 
74,529 
75,076 
75,625 
76,176 
76,729 
77,284 
77,841 

78.400 
78,961 
79,524 
80,089 
80,656 

81.225 
81,796 
82,369 
82,944 
83,521 
84,100. 
84,681 
85.264 
85', 849 
86,436 

87.025 
87,616 
88,209 
88,804 

89.401 
90,000 
90,601 
91,204 
91,809 
92,416 

93.025 
93,636 
94,249 

14,706,125 

14,886,936 

15,069,223 

15,252,992 

15,438,249 

15.625.000 
15,813,251 
16,003,008 
16,194,277 
16,387,064 
16,581,375 
16,777,216 
16,974,593 
17,173,512 
17,373,979 

17.576.000 
17,779,581 
17,984,728 
18,191,447 
18,399,744 
18,609,625 
18,821,096 
19,034,163 
19,248,832 
19.465,109 
19^683,000 
19,902,511 
20,123,643 
20,346,417 
20,570,824 
20,796,875 
21,024,576 
21,253,933 
21,484,952 
21,717,639 

21.952.000 
22,188,041 
22,425,768 
22,665,187 
22,906,304 
23,149,125 
23,393,656 
23,639,903 
23,887,872 
24,137,569 

24.389.000 
24,642,171 
24,897,088 
25,153,757 
25,412,184 
25,672,375 
25,934,836 
26,198,073 
26,463,592 
26,730,899 
27,000,000 
27,270,901 
27,543,608 
27,818,127 
28,094,464 
28,372,625 
28,652,616 
28,934,443 

15.6525 

15.6844 

15.7162 

15.7480 

15.7797 

15.8114 

15.8430 

15.8745 

15.9060 

15.9374 

15.9687 

16.0000 

16.0312 

16.0624 

16.0935 

16.1245 

16.1555 

16.1864 

16.2173 

16.2481 

16.2788 

16.3095 

16.3401 

16.3707 

16.4012 

16.4317 

16.4621 

16.4924 

16.5227 

16.5529 

16.5831 

16.6182 

16.6433 

16.6783 

16.7033 

16.7332 

16.7631 

16.7929 

16.8226 

16.8523 

16.8819 

16.9115 

16.9411 

16.9706 

17.0000 

17.0294 

17.0587 

17.0880 

17.1172 

17.1464 

17.1756 

17.2047 

17.2337 

17.2627 

17.2916 

17.3205 

17.3494 

17.3781 

17.4069 

17.4356 

17.4642 

17.4929 

17.5214 

6.2573 

6.2658 

6.2743 

6.2828 

6.2912 

6.2996 

6.3080 

6.3164 

6.3247 

6.3330 

6.3413 

6.3496 

6.3579 

6.3661 

6.3743 

6.3825 

6.3907 

6.3988 

6.4070 

6.4151 

6.4232 

6.4312 

6.4393 

6.4473 

6.4553 

6.4633 

6.4713 

6.4792 

6.4872 

6.4951 

6.5030 

6.5108 

6.5187 

6.5265 

6.5343 

6.5421 

6.5499 

6.5577 

6.5654 

6.5731 

6.5808 

6.5885 

6.5962 

6.6039 

6.6115 

6.6191 

6.6267 

6.6343 

6.6419 

6.6494 

6.6569 

6.6644 

6.6719 

6.6794 

6.6869 

6.6943 

6.7018 

6.7092 

6.7166 

6.7240 

6.7313 

6.7387 

6.7460 

.004081633 

.004065041 

.004048583 

.004032258 

.004016064 

.004000000 

.003984064 

.003968254 

.003952569 

.003937008 

.003921569 

.003906250 

.003891051 

.003875969 

.003861004 

.003846154 

.003831418 

.003816794 

.003802281 

.003787879 

.003773585 

.003759398 

.003745318 

.003731343 

.003717472 

.003703704 

.003690037 

.003676471 

.003663004 

.003649635 

.003636364 

.003623188 

.003610108 

.003597122 

.003584229 

.003571429 

.003558719 

.003546099 

.003533569 

.003522127 

.003508772 

.003496503 

.003484321 

.003472222 

.003460208 

.003448276 

.003436426 

.003424658 

.003412969 

.003401361 

.003389831 

.003378378 

.003367003 

.003355705 

.003344482 

.003333333 

.003322259 

.003311258 

.003301330 

.003289474 

.003278689 

.003267974 

.003257329 

769.69 

772.83 

775.97 

779.11 
782.26 
785.40 
788.54 
791.68 
794.82 

797.96 

801.11 
804.25 
807.39 
810.53 
813.67 
816.81 

819.96 
823.10 
826.24 
829.38 
832.52 
835.66 
838.81 
841.95 
845.09 
848.23 
851.37 
854.51 

857.65 
860.80 
863.94 
867.08 
870.22 
873.36 

876.50 

879.65 
882.79 
885.93 
889.07 
892.21 

895.35 

898.50 
901.64 
904.78 
907.92 
911.06 
914.20 

917.35 
920.49 
923.63 
926.77 
929.91 
933.05 

936.19 
939.34 
942.48 
945.62 
948.76 
951.90 
955.04 

958.19 
961.33 
964.47 

47.143.52 
47,529.16 
47,916.36 
48,305.13 
48,695.47 
49,087.39 

49.480.87 

49.875.92 

50.272.55 

50.670.75 

51.070.52 
51,471.85 

51.874.76 

52.279.24 
52,685.29 

53.092.92 

53.502.11 

53.912.87 

54.325.21 

54.739.11 
55,154.59 
55,571.63 

55.990.25 
56,410.44 
56,832.20 

57.255.53 

57.680.43 
58,106.90 
58,534.94 

58.964.55 

59.395.74 

59.828.49 
60,262.82 
60,698.71 

61.136.18 

61.575.22 

62.015.82 
62,458.00 

62.901.75 

63.347.07 
63,793.97 

64.242.43 
64,692.46 

65.144.07 
65,597.24 

66.051.99 
66,508.30 

66.966.19 

67.425.65 
67,886.68 
68,349.28 

68.813.45 

69.279.19 

69.746.50 
70,215.38 

70.685.83 
71,157.86 

71.631.45 
72,106.62 
72,583.36 

73.061.66 
73,541.54 

74.022.99 

550 


SQUARES,  CUBES , SQUARE  AND  CUBE  ROOTS , 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

308 

309 

310 

311 

312 

313 

314 

315 

316 

317 

318 

319 

320 

321 

322 

323 

324 

325 

326 

327 

328 

329 

330 

331 

332 

333 

334 

335 

336 

337 

338 

339 

340 

341 

342 

343 

344 

345 

346 

347 

348 

349 

350 

351 

352 

353 

354 

355 

356 

357 

358 

359 

360 

361 

362 

363 

364 

365 

366 

367 

368 

369 

370 

94,864 

95,481 

96,100 

96,721 

97,344 

97,969 

98,596 

99,225 

99,856 

100,489 

101,124 

101,761 

102,400 

103,041 

103,684 

104,329 

104,976 

105,625 

106,276 

106,929 

107,584 

108,241 

108.900 
109,561 

110.224 
110,889 
111,556 

112.225 
112,896 
113,569 
114,244 
114,921 

115.600 
116,281 
116,964 
117,649 
118,336 

119.025 
119,716 
120,409 
121,104 
121,801 
122,500 
123,201 
123,904 
124,609 
125,316 

126.025 
126,736 
127,449 
128,164 
128,881 

129.600 
130,321 
131,044 
131,769 
132,496 

133.225 
133,956 
134,689 
135,424 
136,161 

136.900 

29,218,112 

29,503,629 

29.791.000 
30,080,231 
30,371,328 
30,664,297 
30,959,144 

31.255.875 
31,554,496 
31,855,013 
32,157,432 
32,461,759 

32.768.000 
33,076,161 
33,386,248 
33,698,267 
34,012,224 

34.328.125 

34.645.976 
34,965,783 
35,287,552 
35,611,289 

35.937.000 
36,264,691 
36,594,368 
36,926,037 
37,259,704 
37,595,375 
37,933,056 
38,272,753 
38,614,472 
38,958,219 

39.304.000 
39,651,821 
40,001,688 
40,353,607 
40,707,584 
41,063,625 
41,421,736 
41,781,923 
42,144,192 
42,508,549 

42.875.000 
43,243,551 
43,614,208 

43.986.977 
44,361,864 

44.738.875 
45,118,016 
45,499,293 
45,882,712 
46,268,279 

46.656.000 
47,045,881 
47,437,928 
47,832,147 
48,228,544 

48.627.125 
49,027,896 
49,430,863 
49,836,032 
50,243,409 

50.653.000 

17.5499 

17.5784 

17.6068 

17.6352 

17.6635 

17.6918 

17.7200 

17.7482 

17.7764 

17.8045 

17.8326 

17.8606 

17.8885 

17.9165 

17.9444 

17.9722 

18.0000 

18.0278 

18.0555 

18.0831 

18.1108 

18.1384 

18.1659 

18.1934 

18.2209 

18.2483 

18.2757 

18.3030 

18.3303 

18.3576 

18.3848 

18.4120 

18.4391 

18.4662 

18.4932 

18.5203 

18.5472 

18.5742 

18.6011 

18.6279 

18.6548 

18.6815 

18.7083 

18.7350 

18.7617 

18.7883 

18.8149 

18.8414 

18.8680 

18.8944 

18.9209 

18.9473 

18.9737 

19.0000 

19.0263 

19.0526 

19.0788 

19.1050 

19.1311 

19.1572 

19.1833 

19.2094 

19.2354 

6.7533 

6.7606 

6.7679 

6.7752 

6.7824 

6.7897 

6.7969 

6.8041 

6.8113 

6.8185 

6.8256 

6.8328 

6.8399 

6.8470 

6.8541 

6.8612 

6.8683 

6.8753 

6.8824 

6.8894 

6.8964 

6.9034 

6.9104 

6.9174 

6.9244 

6.9313 

6.9382 

6.9451 

6.9521 

6.9589 

6.9658 

6.9727 

6.9795 

6.9864 

6.9932 

7.0000 

7.0068 

7.0136 

7.0203 

7.0271 

7.0338 

7.0406 

7.0473 

7.0540 

7.0607 

7.0674 

7.0740 

7.0807 

7.0873 

7.0940 

7.1006 

7.1072 

7.1138 

7.1204 

7.1269 

7.1335 

7.1400 

7.1466 

7.1531 

7.1596 

7.1661 

7.1726 

7.1791 

.003246753 

.003236246 

.003225806 

.003215434 

.003205128 

.003194888 

.003184713 

.003174603 

.003164557 

.003154574 

.003144654 

.003134796 

.003125000 

.003115265 

.003105590 

.003095975 

.003086420 

.003076923 

.003067485 

.003058104 

.003048780 

.003039514 

.003030303 

.003021148 

.003012048 

.003003003 

.002994012 

.002985075 

.002976190 

.002967359 

.002958580 

.002949853 

.002941176 

.002932551 

.002923977 

.002915452 

.002906977 

.002898551 

.002890173 

.002881844 

.002873563 

.002865330 

.002857143 

.002849003 

.002840909 

.002832861 

.002824859 

.002816901 

.002808989 

.002801120 

.002793296 

.002785515 

.002777778 

.002770083 

.002762431 

.002754821 

.002747253 

.002739726 

.002732240 

.002724796 

.002717391 

.002710027 

.002702703 

967.61 

970.75 

973.89 

977.04 

980.18 

983.32 

986.46 

989.60 

992.74 

995.88 

999.03 

1,002.17 

1,005.31 

1,008.45 

1,011.59 

1.014.73 
1,017.88 
1,021.02 
1,024.16 
1,027.30 
1,030.44 

1.033.58 

1.036.73 
1,039.87 
1,043.01 
1,046.15 
1,049.29 
1,052.43 

1.055.58 
1,058.72 
1,061.86 
1,065.00 
1,068.14 
1,071.28 

1.074.42 
1,077.57 
1,080.71 
1,083.85 
1,086.99 
1,090.13 

1.093.27 

1.096.42 
1,099.56 
1,102.70 
1,105.84 
1,108.98 
1,112.12 

1.115.27 
1,118.41 
1,121.55 
1,124.69 
1,127.83 
1,130.97 

1.134.11 
1,137.26 
1,140.40 
1,143.54 
1,146.68 
1,149.82 
1,152.96 

1.156.11 
1,159.25 
1,162.39 

74.506.01 

74.990.60 

75.476.76 
75,964.50 

76.453.80 

76.944.67 

77.437.12 

77.931.13 

78.426.72 

78.923.88 

79.422.60 

79.922.90 

80.424.77 

80.928.21 

81.433.22 

81.939.80 

82.447.96 

82.957.68 
83,468.98 

83.981.84 

84.496.28 

85.012.28 

85.529.86 

86.049.01 

86.569.73 

87.092.02 

87.615.88 

88.141.31 

88.668.31 

89.196.88 

89.727.03 

90.258.74 

90.792.03 

91.326.88 

91.863.31 

92.401.31 

92.940.88 
93,482.02 
94,024.73 

94.569.01 

95.114.86 

95.662.28 

96.211.28 

96.761.84 

97.313.97 

97.867.68 
98,422.96 

98.979.80 

99.538.22 
100,098.21 

100.659.77 

101.222.90 

101.787.60 
102,353.87 
102,921.72 

103.491.13 
104,062.12 
104,634.67 
105,208.80 
105,784.49 
106,361.76 

106.940.60 

107.521.01 

CIR C UMEERENCES,  AND  AREAS. 


551 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

371 

372 

373 

374 

375 

376 

377 

378 

379 

380 

381 

382 

383 

384 

385 

386 

387 

388 

389 

390 

391 

392 

393 

394 

395 

396 

397 

398 

399 

400 

401 

402 

403 

404 

405 

406 

407 

408 

409 

410 

411 

412 
’413 

414 

415 

416 

417 

418 

419 

420 

421 

422 

423 

424 

425 

426 

427 

428 

429 

430 

431 

432 

433 

137.641 
138,384 

139.129 
139,876 
140,625 
141,376 

142.129 
142,884 

143.641 
144,400 
145,161 
145,924 
146,689 
147,456 

148.225 
148,996 
149,769 
150,544 
151,321 

152.100 
152,881 
153,664 
154,449 
155,236 

156.025 
156,816 
157,609 
158,404 
159,201 
160,000 
160,801 
161,604 
162,409 
163,216 

164.025 
164,836 
165,649 
166,464 
167,281 

168.100 
168,921 
169,744 
170,569 
171,396 

172.225 
173,056 
173,889 
174,724 
175,561 
176,400 
177,241 
178,084 
178,929 
179,776 
180,625 
181,476 
182,329 
183,184 
184,041 
184,900 
185,761 
186,624 
187,489 

51,064,811 

51,478,848 

51,895,117 

52.313.624 

52.734.375 

53.157.376 
53,582,633 
54,010,152 
54,439,939 

54.872.000 
55,306,341 
55,742,968 
56,181,887 
56,623,104 

57.066.625 
57,512,456 
57,960,603 
58,411,072 
58,863,869 

59.319.000 
59,776,471 
•60,236,288 

60,698,457- 

61,162,984 

61,629,875 

62,099,136 

62,570,773 

63,044,792 

63,521,199 

64,000,000 

64,481,201 

64,964,808 

65,450,827 

65,939,264 

66,430,125 

66,923,416 

67,419,143 

67,917,312 

68,417,929 

68.921.000 
69,426,531 
69,934,528 
70,444,997 
70,957,944 
71,473,375 
71,991,296 
72,511,713 
73,034,632 
73,560,059 

74.088.000 
74,618,461 
75,151,448 
75,686,967 
76,225,024 
76,765,625 
77,308,776 
77,854,483 
78,402,752 
78,953,589 

79.507.000 
80,062,991 
80,621,568 
81,182,737 

19.2614 

19.2873 

19.3132 

19.3391 

19.3649 

19.3907 

19.4165 

19.4422 

19.4679 

19.4936 

19.5192 

19.5448 

19.5704 

19.5959 

19.6214 

19.6469 

19.6723 

19.6977 

19.7231 

19.7484 

19.7737 

19.7990 

19.8242 

19.8494 

19.8746 

19.8997 

19.9249 

19.9499 

19.9750 

20.0000 

20.0250 

20.0499 

20.0749 

20.0998 

20.1246 

20.1494 

20.1742 

20.1990 

20.2237 

20.2485 

20.2731 

20.2978 

20.3224 

20.3470 

20.3715 

20.3961 

20.4206 

20.4450 

20.4695 

20.4939 

20.5183 

20.5426 

20.5670 

20.5913 

20.6155 

20.6398 

20.6640 

20.6882 

20.7123 

20.7364 

20.7605 

20.7846 

20.8087 

7.1855 

7.1920 

7.1984 

7.2048 

7.2112 

7.2177 

7.2240 

7.2304 

7.2368 

7.2432 

7.2495 

7.2558 

7.2622 

7.2685 

7.2748 

7.2811 

7.2874 

7.2936 

7.2999 

7.3061 

7.3124 

7.3186 

7.3248 

7.3310 

7.3372 

7.3434 

7.3496 

7.3558 

7.3619 

7.3681 

7.3742 

7.3803 

7.3864 

7.3925 

7.3986 

7.4047 

7.4108 

7.4169 

7.4229 

7.4290 

7.4350 

7.4410 

7.4470 

7.4530 

7.4590 

7.4650 

7.4710 

7.4770 

7.4829 

7.4889 

7.4948 

7.5007 

7.5067 

7.5126 

7.5185 

7.5244 

7.5302 

7.5361 

7.5420 

7.5478 

7.5537 

7.5595 

7.5654 

.002695418  : 

.002688172  : 

.002680965  : 

.002673797  : 

.002666667  : 

.002659574  : 

.002652520 

.002645503 

.002638521 

.002631579 

.002624672 

.002617801 

.002610966 

.002604167 

.002597403 

.002590674 

.002583979 

.002577320 

.002570694 

.002564103 

.002557545 

.002551020 

.002544529 

.002538071 

.002531646 

.002525253 

.002518892 

.002512563 

.002506266 

.002500000 

.002493766 

.002487562 

.002481390 

.002475248 

.002469136 

.002463054 

.002457002 

.002450980 

.002444988 

.002439024 

.002433090 

.002427184 

.002421308 

.002415459 

.002409639 

.002406846 

.002398082 

.002392344 

.002386635 

.002380952 

.002375297 

.002369668 

.002364066 

.002358491 

.002352941 

.002347418 

.002341920 

.002336449 

.002331002 

.002325581 

.002320186 

.002314815 

.002309469 

1,165.53  ! 
1,168.67  : 

1.171.81  : 
1,174.96  : 
1,178.10  : 
1,181.24  : 
1,184.38  : 
1,187.52  : 
1,190.66  : 

1.193.81  : 
1,196.95  : 
1,200.09 
1,203.23 
1,206.37 
1,209.51 

1.212.65 
1,215.80 
1,218.94 
1,222.08 
1.225.22 
1,228.36 

1.231.50 

1.234.65 
1,237.79 
1,240.93 
1,244.07 
1,247.21 

1.250.35 

1.253.50 
1,256.64 
1,259.78 
1,262.92 
1,266.06 
1,269.20 

1.272.35 
1,275.49 
1,278.63 
1,281.77 
1,284.91 
1,288.05 

1.291.19 
1,294.34 
1,297.48 
1,300.62 
1,303.76 
1,306.90 

1.310.04 

1.313.19 
1,316.33 
1,319.47 
1,322.61 
1,325.75 
1,328.89 

1.332.04 
1,335.18 
1,338.32 
1,341.46 
1,344.60 
1,347.74 
1,350.88 
1,354.03 
1,357.17 
1,360.31 

L08, 102.99 
L08, 686.54 

109.271.66 
109, 858.35 

110.446.62 

111.036.45 

111.627.86 
112,220.83 
112,815.38 
113,411.49 

114.009.18 
114,608.44 
115,209.27 

115.811.67 
116,415.64 

117.021.18 
117,628.30 
118,236.98 

118.847.24 

119.459.06 

120.072.46 

120.687.42 
121,303.96 

121.922.07 

122.541.75 
123,163.00 
123,785.82 
124,410.21 
125,036.17 
125,663.71 
126,292.81 
126,923.48 

127.555.73 
128,189.55 
128,824.93 
129,461.89 

130.100.42 
130,740.52 

131.382.19 

132.025.43 

132.670.24 

133.316.63 
133,964.58 

134.614.10 

135.265.20 

135.917.86 

136.572.10 

137.227.91 
137,885.29 

138.544.24 

139.204.76 

139.866.85 

140.530.51 

141.195.74 
141,862.54 

142.530.92 

143.200.86 
143,872.38 
144,545.46 
145,220.12 
145.896.35 
146,574.15 

147.253.52 

552 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS , 


| No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

- 

Area. 

4B4 

435 

436 

437 

438 

439 

440 

441 

442 

443 

444 

445 

446 

447 

448 

449 

450 

451 

452 

453 

454 

455 

456 

457 

458 

459 

460 

461 

462 

463 

464 

465 

466 

467  i 

468 

469 

470 

471 

472 

473 

474 

475 

476 

477 

478 

479 

480 

481 

482 

483 

484 

485 

486 

487 

488 

489 

490 

491 

492 

493 

494 

495 

496 

188,356 

189,225 

190,096 

190,969 

191,844 

192,721 

193.600 
194,481 
195,364 
196,249 
197,136 

198.025 
198,916 
199,809 
200,704 

201.601 
202,500 
203,401 
204,304 
205,209 
206,116 

207.025 
207,936 
208,849 
209,764 
210,681 

, 211,600 
212,521 
213,444 
214,369 
215,296 

216.225 
217,156 
218,089 

219.024 
219,961 
220,900 
221,841 
222,784 
223,729 
224,676 
225,625 
226,576 
227,529 
228,484 
229,441 
230,400 
231,361 
232,324 
233,289 
234,256 

235.225 
236,196 
237,169 
238,144 
239,121 
240,100 
241,081 
242,064 
243,049 
244,036 

245.025 
246,^016 

81,746,504 

82.312.875 
82,881,856 
83,453,453 
84,027,672 
84,604,519 

85.184.000 
85,766,121 
86,350,888 
86,938,307 
87,528,384 

88.121.125 
88,716,536 
89,314,623 
89,915,392 
90,518,849 

91.125.000 
91,733,851 
92,345,408 
92,959,677 
93,576,664 

94.196.375 
94,818,816 
95,443,993 
96.071,912 
96,702,579 

97.336.000 
97,972,181 
98,611,128 
99,252,847 
99,897,344 

100,544,625 

101,194,696 

101,847,563 

102,503,232 

103,161,709 

103.823.000 
104,487,111 
105,154,048 
105,823,817 
106.496,424 

107.171.875 
107,850,176 
108,531,333 
109,215,352 
109,902,239 

110.592.000 
111,284,641 

111.980.168 
112,678,587 
113,379,904 

114.084.125 
114,791,256 
115,501,303 
116,214,272 

116.930.169 

117.649.000 
118,370,771 
119,095,488 
119,823,157 
120,553,784 

121.287.375 
122,023,936 

20.8327 

20.8567 

20.8806 

20.9045 

20.9284 

20.9523 

20.9762 

21.0000 

21.0238 

21.0476 

21.0713 

21.0950 

21.1187 

21.1424 

21.1660 

21.1896 

21.2132 

21.2368 

21.2603 

21.2838 

21.3073 

21.3307 

21.3542 

21.3776 

21.4009 

21.4243 

21.4476 

21.4709 

21.4942 

21.5174 

21.5407 

21.5639 

21.5870 

21.6102 

21.6333 

21.6564 

21.6795 

21.7025 

21.7256 

21.7486 

21.7715 

21.7945 

21.8174 

21.8403 

21.8632 

21.8861 

21.9089 

21.9317 

21.9545 

21.9775 

22.0000 

22.0227 

22.0454 

22.0681 

22.0907 

22.1133 

22.1359 

22.1585 

22.1811 

22.2036 

22.2261 

22.2486 

22.2711 

7.5712 

7.5770 

7.5828 

7.5886 

7.5944 

7.6001 

7.6059 

7.6117 

7.6174 

7.6232 

7.6289 

7.6346 

7.6403 

7.6460 

7.6517 

7.6574 

7.6631 

7.6688 

7.6744 

7.6801 

7.6857 

7.6914 

7.6970 

7.7026 

7.7082 

7.7188 

7.7194 

7.7250 

7.7306 

7.7362 

7.7418 

7.7473 

7.7529 

7.7584 

7.7639 

7.7695 

7.7750 

7.7805 

7.7860 

7.7915 

7.7970 

7.8025 

7.8079 

7.8134 

7.8188 

7.8243 

7.8297 

7.8352 

7.8406 

7.8460 

7.8514 

7.8568 

7.8622 

7.8676 

7.8730 

7.8784 

7.8837 

7.8891 

7.8944 

7.8998 

7.9051 

7.9105 

7.9158 

.002304147  : 
.002298851  : 
.002293578  : 
.002288330  : 
.002283105  : 
.002277904  : 
.002272727  ! 
.002267574  : 
.002262443 
.002257336 
.002252252 
.002247191 
.002242152 
.002237136 
.002232143 
.002227171 
.002222222 
.002217295 
.002212389 
.002207506 
.002202643 
.002197802 
.002192982 
.002188184 
.002183406 
.002178649 
.002173913 
.002169197 
.002164502 
.002159827 
.002155172 
.002150538 
.002145923 
.002141328 
.002136752 
.002132196 
.002127660 
.002123142 
.002118644 
.002114165 
.002109705 
.002105263 
.002100840 
.002096486 
.002092050 
.002087683 
.002083333 
.002079002 
.002074689 
.002070393 
.002066116 
.002061856 
.002057613 
.002053388 
.002049180 
.002044990 
.002040816 
.002036660 
.002032520 
.002028398 
.002024291 
.002020292 
.002016129 

1,363.45  : 
1,366.59  : 

1.369.73  : 
1,372.88  : 
1,376.02  : 
1,379.16  : 
1,382.30  : 
1,385.44 

1.388.58  : 

1.391.73 
1,394.87 
1,398.01 
1,401.15 
1,404.29 
1,407.43 

1.410.58 
1,413.72 
1,416.86 
1,420.00 
1,423.14 
1,426.28 

1.429.42 
1,432.57 
1,435.71 
1,438.85 
1,441.99 
1,445.13 

1.448.27 

1.451.42 
1,454.56 
1,457.70 
1,460.84 
1,463.98 
1,467.12 

1.470.27 
1,473.41 
1,476.55 
1,479.69 
1,482.83 
1,485.97 

1.489.11 
1,492.26 
1,495.40 
1,498.54 
1,501.68 
1,504.82 

1.507.96 

1.511.11 
1,514.25 
1.517.39 
1,520.53 
1,523.67 

1.526.81 

1.529.96 
1,533.10 
1,536.24 
1,539.38 
1,542.52 
1,545.66 

1.548.81 
1,551.95 
1,555.09 
1,558.23 

L47, 934.46 
L48, 616.97 
L49, 301.05 

149.986.70 
150,673.93 

151.362.72 

152.053.08 

152.745.02 

153.438.53 

154.133.60 

154.830.25 

155.528.47 

156.228.26 

156.929.62 

157.632.55 
158,337.06 

159.043.13 

159.750.77 
160,459.99 

161.170.77 

161.883.13 

162.597.05 

163.312.55 

164.029.62 

164.748.26 

165.468.47 
166,190.25 

166.913.60 

167.638.53 

168.365.02 

169.093.08 

169.822.72 
170,553.92 

171.286.70 

172.021.05 
172,756.97 

173.494.45 
174,233.51 

174.974.14 
175,716.35 
176,460.12 

177.205.46 
177,952.37 

178.700.86 
179,450.91 

180.202.54 

180.955.74 

181.710.50 
182,466.84 

183.224.75 

183.984.23 
134,745.28 
185,507.90 

186.272.10 

187.037.86 
187,805.19 

188.574.10 
189, 344., 57 
190,116.62 

190.890.24 
191 ,665.43 
192,442.18 

193.220.51 

CIRCUMFERENCES,  AND  AREAS. 


553 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

497 

498 

499 

500 

501 

502 
508 

504 

505 

506 

507 

508 

509 

510 

511 

512 

513 

514 

515 

516 

517 

518 

519 

520 

521 

522 

523 

524 

525 

526 

527 

528 

529 

530 

531 

532 

533 

534 

535 

536 

537 

538 

539 

540 

541 

542 

543 

544 

545 

546 

547 

548 

549 

550 

551 

552 

553 

554 

555 

556 

557 

558 

559 

247.009 

248.004 
249,001 

250.000 

251.001 

252.004 

253.009 
254,016 
255,025 
256,036 
257,049 
258,064 
259,081 
260,100 
261,121 
262,144 
263,169 
264,196 

265.225 
266,256 
267,289 
268,324 
269,361 
270,400 
271,411 
272,484 
273,529 
274,576 
275,625 
276,676 
277,729 
278,784 
279,841 
280,900 
281,961 

283.024 
284,089 
285,156 

286.225 
287,296 
288,369 
289,444 
290,521 

291.600 
292,681 
293,764 
294,849 
295,936 

297.025 
298,116 
299,209 
300,304 
301,401 

' 302,500 

303.601 
304,704 
305,809 
306,916 

308.025 
309,136 
310,249 
311,364 
312,481 

122,763,473 

123,505,992 

124,251,499 

125,000,000 

125,751,501 

126,506,008 

127,263,527 

128,024,064 

128,787,625 

129,554,216 

130,323,843 

131,096,512 

131,872,229 

132.651.000 

133.432.831 
134,217,728 
135,005,697 
135,796,744 
136,590,875 
137,388,096 
138,188,413 

138.991.832 
139,798,359 

140.608.000 
141,420,761 
142,236,648 
143,055,667 
143,877,824 
144,703,125 
145,531,576 

146.363.183 
147,197,952 
148,035,889 

148.877.001 
149,721,291 
150,568,768 
151,419,437 
152,273,304 
153,130,375 
153,990,656 
154,854,153 
155,720,872 
156,590,819 

157.464.000 
158,340,421 
159,220,088 
160,103,007 

160.989.184 
161,878,625 
162,771,336 
163,667,323 
164,566,592 
165,469,149 

166.375.000 
167,284,151 
168,196,608 
169,112,377 
170,031,464 
170,953,875 
171,879,616 
172,808,693 
173,741.112 
174,676,879 

22.2935 

22.3159 

22.3383 

22.3607 

22.3830 

22.4054 

22.4277 

22.4499 

22.4722 

22.4944 

22.5167 

22.5389 

22.5610 

22.5832 

22.6053 

22.6274 

22.6495 

22.6716 

22.6936 

22.7156 

22.7376 

22.7596 

22.7816 

22.8035 

22.8254 

22.8473 

22.8692 

22.8910 

22.9129 

22.9347 

22.9565 

22.9783 

23.0000 

23.0217 

23.0434 

23.0651 

23.0868 

23.1084 

23.1301 

23.1517 

23.1733 

23.1948 

23.2164 

23.2379 

23.2594 

23.2809 

23.3024 

23.3238 

23.3452 

23.3666 

23.3880 

23.4094 

23.4307 

23.4521 

23.4734 

23.4947 

23.5160 

23.5372 

23.5584 

23.5797 

23.6008 

23.6220 

23.6432 

7.9211 

7.9264 

7.9317 

7.9370 

7.9423 

7.9476 

7.9528 

7.9581 

7.9634 

7.9686 

7.9739 

7.9791 

7.9843 

7.9895 

7.9948 

8.0000 

8.0052 

8.0104 

8.0156 

8.0208 

8.0260 

8.0311 

8.0363 

8.0415 

8.0466 

8.0517 

8.0569 

8.0620 

8.0671 

8.0723 

8.0774 

8.0825 

8.0876 

8.0927 

8.0978 

8.1028 

8.1079 

8.1130 

8.1180 

8.1231 

8.1281 

8.1332 

8.1382 

8.1433 

8.1483 

8.1533 

8.1583 

8.1633 

8.1683 

8.1733 

8.1783 

8.1833 

8.1882 

8.1932 

8.1982 

8.2031 

8.2081 

8.2130 

8.2180 

8.2229 

8.2278 

8.2327 

8.2377 

.002012072  • : 
.002008032  : 
.002004008  : 

.002000000  : 

.001996008  ; 
.001992032 
.001988072  : 
.001984127  : 
.001980198 
.001976285 
.001972387 
.001968504 
.001964637 
.001960785 
.00L956947 
.001953125 
.001949318 
.001945525 
.001941748 
.001937984 
.001934236 
.001930502 
.001926782 
.001923077 
.001919386 
.001915709 
.001912046 
.001908397 
.001904762 
.001901141 
.001897533 
.001893939 
.001890359 
.001886792 
.001883239 
.001879699 
.001876173 
.001872659 
.001869159 
.001865672 
.001862197 
.001858736 
.001855288 
.001851852 
.001848429 
.001845018 
.001841621 
.001838235 
.001834862 
.001831502 
.001828154 
.001824818 
.001821494 
.041818182 
.001814882 
.041811594 
.001808318 
.001805054 
.001801802 
.001798561 
.001795332 
.001792115 
.001788909 

L, 561.37  1 
L, 564.51  1 
L, 567.65  1 
1,570.80  : 
1,573.94  : 
1,577.08  : 
1,580.22  : 
1,583.36  : 

1.586.50  ! 
1,589.65  : 
1,592.79  ! 
1,595.93  : 
1,599.07  : 
1,602.21 
1,605.35 

1.608.50 
1,611.64 
1,614.78 
1,617.92 
1,621.06 
1,624.20 

1.627.34 
1,630.49 
1,633.63 
1,636.77 
1,639.91 
1,643.05 

1.646.19 

1.649.34 
1,652.48 
1,655.62 
1,658.76 
1,661.90 

1.665.04 

1.668.19 
1,671.33 
1,674.47 
1,677.61 
1,680.75 
1,683.89 

1.687.04 
1,690.18 
1,693.32 
1,696.46 
1,699.60 
1,702.74 

1.705.88 
1,709.03 
1,712.17 
1,715.31 
1,718.45 
1,721.59 

1.724.73 

1.727.88 
1,731.02 
1,734.16 
1,737.30 
1,740.44 
1,743.58 

1.746.73 
1,749.87 
1,753.01 
1,756.15 

L94, 000.41 
L94, 781.89 
L95, 564.93 
L96, 349.54 
L97, 135.72 
L97, 923.48 
L98, 712.80 
199,503.70 

200.296.17 
201,090.20 

201.885.81 
202,682.99 

203.481.74 
204,282.06 
205,083.95 

205.887.42 
206,692.45 
207,499.05 
208,307.23 

209.116.97 
209,928.29 

210.741.18 
211,555.63 
212,371.66 
213,189.26 

214.008.43 
214,829.17 
215,651.49 
216,475.37 

217.300.82 

218.127.85 

218.956.44 
219,786.61 
220,618.34 

221.451.65 
222,286.53 

223.122.98 

223.961.00 

224.800.59 

225.641.75 
226,484.48 

227.328.79 

228.174.66 
229,022.10 
229,871.12 

230.721.71 

231.573.86 

232.427.59 
233,282.89 

234.139.76 

234.998.20 

235.858.21 

236.719.79 
237,582.94 

238.447.67 
239,313.96 

240.181.83 

241.051.26 

241.922.27 
242,794.85 

243.668.99 

244.544.71 

245.422.00 

554  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

560 

561 

562 

563 

564 

565 

566 

567 

568 

569 

570 

571 

572 

573 

574 

575 

576 

577 

578 

579 

580 

581 

582 

583 

584 

585 

586 

587 

588 

589 

590 

591 

592 

593 

594 

595 

596 

597 

598 

599 

600 
601 
602 

603 

604 

605 

606 

607 

608 

609 

610 
611 
612 

613 

614 

615 

616 

617 

618 

619 

620 
621 
622 

313,600 

314,721 

315,844 

316,969 

318,096 

319.225 
320,356 
321,489 

322.624 
323,761 
324,900 
326,041 
327,184 
328,329 
329,476 

330.625 
331,776 
332,929 
334,084 
335,241 
336,400 
337,561 
338,724 
339,889 
341,056 

342.225 
343,396 
344,569 
345,744 
346,921 

348.100 
349,281 
350,464 
351,649 
352,836 

354.025 
355,216 
356,409 
357,604 
358,801 
360,000 
361,201 
362,404 
363,609 
364,816 

366.025 
367,236 
368,449 
369,664 
370,881 

372.100 
373,321 
374,544 
375.769 
376,996 

378.225 
379,456 
380,689 
381,924 
383,161 
384,400 
385,641 
386-884 

175.616.000 
176,558,481 
177,504,328 
178,453,547 
179,406,144 

180.362.125 
181,321,496 
182,284,263 
183,250,432 
184,220,009 

185.193.000 
186,169,411 
187,149,248 
188,132,517 
189,119,224 
190,109,375 
191,102,976 
192,100,033 
193,100,552 
194,104,539 

195.112.000 
196,122,941 
197,137,368 
198,155,287 
199,176,704 
200,201,625 
201,230,056 
202,262,003 
203,297,472 
204,336,469 

205.379.000 
206,425,071 
207,474,688 
208,527,857 
209,584,584 
210,644,875 
211,708,736 
212,776,173 
213,847,192 
214,921,799 
216,000,000 
217,081,801 
218,167,208 
219,256,227 
220,348,864 

221.445.125 
222,545,016 

223.648.543 
224,755,712 
225,866,529 

226.981.000 
228,099,131 
229,220,928 
230,346,397 

231.475.544 
232,608,375 
233,744,896 
234,885,113 
236,029,032 
237,176,659 

238.328.000 
239,483,061 
240,641,848 

23.6643 

23.6854 

23.7065 

23.7276 

23.7487 

23.7697 

23.7908 

23.8118 

23.8328 

23.8537 

23.8747 

23.8956 

23.9165 

23.^374 

23.9583 

23.9792 

24.0000 

24.0208 

24.0416 

24.0624 

24.0832 

24.1039 

24.1247 

24.1454 

24.1661 

24.1868 

24.2074 

24.2281 

24.2487 

24.2693 

24.2899 

24.3105 

24.3311 

24.3516 

24.3721 

24.3926 

24.4131 

24.4336 

24.4540 

24.4745 

24.4949 

24.5153 

24.5357 

24.5561 

24.5764 

24.5968 

24.6171 

24.6374 

24.6577 

24.6779 

24.6982 

24.7184 

24.7386 

24.7588 

24.7790 

24.7992 

24.8193 

24.8395 

24.8596 

24.8797 

24.8998 

24.9199 

24.9399 

8.2426 

8.2475 

8.2524 

8.2573 

8.2621 

8.2670 

8.2719 

8.2768 

8.2816 

8.2865 

8.2913 

8.2962 

8.3010 

8.3059 

8.3107 

8.3155 

8.3203 

8.3251 

8.3300 

8.3348 

8.3396 

8.3443 

8.3491 

8.3539 

8.3587 

8.3634 

8.3682 

8.3730 

8.3777 

8.3825 

8.3872 

8.3919 

8.3967 

8.4014 

8.4061 

8.4108 

8.4155 

8.4202 

8.4249 

8.4296 

8.4343 

8.4390 

8.4437 

8.4484 

8.4530 

8.4577 

8.4623 

8.4670 

8.4716 

8.4763 

8.4809 

8.4856 

8.4902 

8.4948 

8.4994 

8.5040 

8.5086 

8.5132 

8.5178 

8.5224 

8.5270 

8.5316 

8.5362 

.001785714 

.001782531 

.001779359 

.001776199 

.001773050 

.001769912 

.001766784 

.001763668 

.001760563 

.001757469 

.001754386 

.001751313 

.001748252 

.001745201 

.001742164 

.001739130 

.001736111 

.001733102 

.001730104 

.001727116 

.001724138 

.001721170 

.001718213 

.001715266 

.001712329 

.001709402 

.001706485 

.001703578 

.001700680 

.001697793 

.001694915 

.001692047 

.001689189 

.001686341 

.001683502 

.001680672 

.001677852 

.001675042 

.001672241 

.001669449 

.001666667 

.001663894 

.001661130 

.001658375 

.001655629 

.001652893 

.001650165 

.001647446 

.001644737 

.001642036 

.001639344 

.001636661 

.001633987 

.001631321 

.001628664 

.001626016 

.001623377 

.001620746 

.001618123 

.001615509 

.001612903 

.001610306 

.001607717 

1,759.29 

1,762.43 

1,765.58 

1,768.72 

1,771.86 

1,775.00 

1,778.14 

1,781.28 

1.784.42 
1,787.57 
1,790.71 
1,793.85 
1,796.99 
1,800.13 

1.803.27 

1.806.42 
1,809.56 
1,812.70 
1,815.84 
1,818.98 
1,822.12 

1.825.27 
1,828.41 
1,831.55 
1,834.69 
1.837.83 
1,840.97 

1.844.11 
1,847.26 
1,850.40 
1,853.54 
1,856.68 
1,859.82 

1.862.96 

1.866.11 
1,869.25 
1,872.39 
1,875.53 
1,878.67 
1,881.81 

1.884.96 
1,888.10 
1,891.24 
1,894.38 
1,897.52 
1,900.66 
1,903.81 
1,906.95 
1,910.09 
1,913.23 
1,916.37 
1,919.51 

1.922.65 
1,925.80 
1,928.94 
1,932.08 
1,935.22 
1,938.36 
1,941.50 

1.944.65 
1,947.79 
1,950.93 
1,954.07 

246.300.86 

247.181.30 

248.063.30 

248.946.87 

249.832.01 

250.718.73 

251.607.01 

252.496.87 

253.388.30 
254,281.29 
255,175.86 
256,072.00 
256,969.71 

257.868.99 

258.769.85 

259.672.27 

260.576.26 

261.481.83 

262.388.96 
263,297.67 

264.207.94 
265,119.79 

266.033.21 
266,948.20 
267,864.76 
268,782.89 

269.702.59 

270.623.86 
271,546.70 
272,471.12 
273,397.10 
274,324.66 
275,253.78 

276.184.48 
277,116.75 
278,050.58 

278.985.99 

279.922.97 
280,861.52 

281.801.65 
282,743.34 

283.686.60 
284,631.44 

285.577.84 
286,525.82 
287,475.36 

288.426.48 

289.379.17 

290.333.43 

291.289.26 

292.246.66 
293,205.63 

294.166.17 

295.128.28 

296.091.97 

297.057.22 

298.024.05 

298.992.44 
299,962.41 

300.933.95 

301.907.05 

302.881.73 

303.857.98 

CIRCUMFERENCES , AND  AREAS. 


555 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

623 

624 

625 

626 

627 

628 

629 

630 

631 

632 

633 

634 

635 

636 

637 

638 

639 

640 

641 

642 

643 

644 

645 

646 

647 

648 

649 

650 

651 

652 

653 

654 

655 

656 

657 

658 

659 

660 
661 
662 

663 

664 

665 

666 

667 

668 

669 

670 

671 

672 

673 

674 

675 

676 

677 

678 

679 

680 
681 
682 

683 

684 

685 

388.129 
389,376 
390,625 
391,876 

393.129 
394,384 
395,641 
396,900 
398,161 
399,424 
400,689 
401,956 
403,225 
404,496 
405,769 
407,044 
408,321 

409.600 
410,881 
412,164 
413,449 
414,736 
416,125 
417,316 
418,609 
419,904 
421,201 
422,500 
423,801 
425,104 
426,409 
427,716 
429,025 
430,336 
431,639 
432,964 
434,281 

435.600 
436,921 
438,244 
439,569 
440,896 
442,225 
443,556 

444.899 

446.224 
447,561 

448.900 
450,241 
451,584 
452,929 
454,276 
455,625 
456,976 
458,329 
459,684 
461,041 
462,400 
463,761 
465,124 
466,489 
467,856 

469.225 

241,804,367 

242.970.624 

244.140.625 
245,314,376 
246,491,883 
247,673,152 
248,858,189 

250.047.000 
251,239,591 
252,435,968 
253,636,137 
254,840,104 
256,047,875 
257,259,456 
258,474,853 
259,694,072 
260,917,119 

262.144.000 
263,374,721 
264,609,288 
265,847,707 
267,089,984 
268,336,125 
269,585,136 
270,840,023 
272,097,792 
273,359,449 

274.625.000 
275,894,451 
277,167,808 
278,445,077 
279,726,264 
281,011,375 
282,300,416 
283,593,393 
284,890,312 
286,191,179 

287.496.000 
288,804,781 
290,117,528 
291,434,247 
292,754,944 
294,079,625 
295,408,296 
296,740,963 
298,077,632 
299,418,309 

300.763.000 
302,111,711 
303,464,448 
304,821,217 
306,182,024 
307,546,875 
308,915,776 
310,288,733 
311,665,752 
313,046,839 

314.432.000 
315,821,241 
317,214,568 
318,611,987 
320,013,504 
321,419,125 

24.9600 

24.9800 

25.0000 

25.0200 

25.0400 

25.0599 

25.0799 

25.0998 

25.1197 

25.1396 

25.1595 

25.1794 

25.1992 

25.2190 

25.2389 

25.2587 

25.2784 

25.2982 

25.3180 

25.3377 

25.3574 

25.3772 

25.3969 

25.4165 

25.4362 

25.4558 

25.4755 

25.4951 

25.5147 

25.5343 

25.5539 

25.5734 

25.5930 

25.6125 

25.6320 

25.6515 

25.6710 

25.6905 

25.7099 

25.7294 

25.7488 

25.7682 

25.7876 

25.8070 

25.8263 

25.8457 

25.8650 

25.8844 

25.9037 

25.9230 

25.9422 

25.9615 

25.9808 

26.0000 

26.0192 

26.0384 

26.0576 

26.0768 

26.0960 

26.1151 

26.1343 

26.1534 

26.1725 

8.5408 

8.5453 

8.5499 

8.5544 

8.5589 

8.5635 

8.5681 

8.5726 

8.5772 

8.5817 

8.5862 

8.5907 

8.5952 

8.5997 

8.6043 

8.6088 

8.6132 

8.6177 

8.6222 

8.6267 

8.6312 

8.6357 

8.6401 

8.6446 

8.6490 

8.6535 

8.6579 

8.6624 

8.6668 

8.6713 

8.6757 

8.6801 

8.6845 

8.6890 

8.6934 

8.6978 

8.7022 

8.7066 

8.7110 

8.7154 

8.7198 

8.7241 

8.7285 

8.7329 

8.7373 

8.7416 

8.7460 

8.7503 

8.7547 

8.7590 

8.7634 

8.7677 

8.7721 

8.7764 

8.7807 

8.7850 

8.7893 

8.7937 

8.7980 

8.8023 

8.8066 

8.8109 

8.8152 

.001605136 

.001602564 

.001600000 

.001597444 

.001594896 

.001592357 

.001589825 

.001587302 

.001584786 

.001582278 

.001579779 

.001577287 

.001574803 

.001572327 

.001569859 

.001567398 

.001564945 

.001562500 

.001560062 

.001557632 

.001555210 

.001552795 

.001550388 

.001547988 

.001545595 

.001543210 

.001540832 

.001538462 

.001536098 

.001533742 

.001531394 

.001529052 

.001526718 

.001524390 

.001522070 

.001519751 

.001517451 

.001515152 

.001512859 

.001510574 

.001508296 

.001506024 

.001503759 

.001501502 

.001499250 

.001497006 

.001494768 

.001492537 

.001490313 

.001488095 

.001485884 

.001483680 

.001481481 

.001479290 

.001477105 

.001474926 

.001472754 

.001470588 

.001468429 

.001466276 

.001464129 

.001461988 

.001459854 

1,957.21 

1.960.35 
1,963.50 
1,966.64 
1,969.78 
1,972.92 
1,976.06 
1,979.20 

1.982.35 
1,985.49 
1,988.63 
1,991.77 
1,994.91 
1,998.05 

2.001.19 
2,004.34 
2,007.48 
2,010.62 
2,013.76 
2,016.90 

2.020.04 

2.023.19 
2,026.33 
2,029.47 
2,032.61 
2,035.75 
2,038.89 

2.042.04 
2,045.18 
2,048.32 
2,051.46 
2,054.60 
2,057.74 
2,060.88 
2,064.03 
2,067.17 
2,070.31 
2,073.45 
2,076.59 

2.079.73 
2,082.88 
2,086.02 
2,089.16 
2,092.30 
2,095.44 

2.098.58 

2.101.73 
2,104.87 
2,108.01 
2,111.15 
2,114.29 
2,117.43 

2.120.58 
2,123.72 
2,126.86 
2,130.00 
2,133.14 
2,136.28 
2,139.42 
2,142.57 
2,145.71 
2,148.85 
2,151.99 

304,835.80 

305,815.20 

306.796.16 

307.778.69 
308,762.79 
309,748.47 

310.735.71 

311.724.53 
312,714.92 

313.706.88 
314,700.40 
315,695.50 

316.692.17 
317,690.42 

318.690.23 
319,691.61 
320,694.56 

321.699.09 

322.705.18 

323.712.85 

324.722.09 

325.732.89 
326,745.27 
327,759.22 

328.774.74 
329,791.83 

330.810.49 

331.830.72 

332.852.53 

333.875.90 

334.900.85 
335,927.36 
336,955.45 

337.985.10 
339,016.33 
340,049.13 

341.083.50 

342.119.44 
343,156.95 

344.196.03 

345.236.69 

346.278.91 

347.322.70 
348,368.07 
349,415.00 

350.463.51 

351.513.59 

352.565.24 

353.618.45 

354.673.24 

355.729.60 

356.787.54 

357.847.04 

358.908.11 

359.970.75 
361,034.97 

362.100.75 

363.168.11 

364.237.04 

365.307.54 

366.379.60 

367.453.24 

368.528.45 

556  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

686 

687 

688 

689 

690 

691 

692 

693 

694 

695 

696 

697 

698 

699 

700 

701 

702 

703 

704 

705 

706 

707 

708 

709 

710 

711 

712 

713 

714 

715 

716 

717 

718 

719 

720 

721 

722 

723 

724 

725 

726 

727 

728 

729 

730 

731 

732 

733 

734 

735 

736 

737 

738 

739 

740 

741 

742 

743 

744 

745 

746 

747 

748 

470,596 

471,969 

473,344 

474,721 

476.100 
477,481 
478,864 
480,249 
481,636 

483.025 
484, 4l6 
485,809 
487,204 
488,601 
490,000 
491,401 
492,804 
494,209 
495,616 

497.025 
498,436 
499,849 
501,264 
502,681 

504.100 
505,521 
506,944 
508,369 
509,796 

511.225 
512,656 
514,089 
515,524 
516,961 
518,400 
519,841 
521,284 
522,729 
524,176 
525,625 
527.076 
528,529 
529,984 
531,441 
532,900 
534,361 
535,824 
537,289 
538,756 

540.225 
541,696 
543,169 
544,644 
546,121 
547,600 
549,801 
550,564 
552,049 
553,536 
555,025 
556,516 
558,009 
559,504 

322,828,856 

324,242,703 

325,660,672 

327,082,769 

328.509.000 
329,939,371 
331,373,888 
332,812,557 
334,255,384 
335,702,375 
337,153,536 
338,608,873 
340,068,392 
341,532,099 
343,000,000' 
344,472,101 
345,948,408 
347,428,927 
348,913,664 
350,402,625 
351,895,816 
353,393,243 
354,894,912 
356,400,829 

357.911.000 
359,425,431 
360,944,128 
362,467,097 
363,994,344 
365,525,875 
367,061,696 
368,601,813 
370,146,232 
371,694,959 

373.248.000 
374,805,361 
376,367,048 
377,933,067 
379,503,424 
381,078,125 
382,657,176 
384,240,583 
385,828,352 
387,420,489 

389.017.000 
390,617,891 
392,223,168 
393,832,837 
395,446,904 
397,065,375 
398,688,256 
400,315,553 
401,947,272 
403,583,419 

405.224.000 
406,869,021 
408,518,488 
410,172,407 
411,830,784 
413,493,625 
415,160,936 
416,832,723 
418,508,992 

26.1916 

26.2107 

26.2298 

26.2488 

26.2679 

26.2869 

26.3059 

26.3249 

26.3439 

26.3629 

26.3818 

26.4008 

26.4197 

26.4386 

26.4575 

26.4764 

26.4953 

26.5141 

26.5330 

26.5518 

26.5707 

26.5895 

26.6083 

26.6271 

26.6458 

26.6646 

26.6833 

26.7021 

26.7208 

26.7395 

26.7582 

.26.7769 

26.7955 

26.8142 

26.8328 

26.8514 

26.8701 

26.8887 

26.9072 

26.9258 

26.9444 

26.9629 

26.9815 

27.0000 

27.0185 

27.0370 

27.0555 

27.0740 

27.0924 

27.1109 

27.1293 

27.1477 

27.1662 

27.1846 

27.2029 

27.2213 

27.2397 

27.2580 

27.2764 

27.2947 

27.3130 

27.3313 

27.3496 

8.8194 

8.8237 

8.8280 

8.8323 

8.8366 

8.8408 

8.8451 

8.8493 

8.8536 

8.8578 

8.8621 

8.8663 

8.8706 

8.8748 

8.8790 

8.8833 

8.8875 

8.8917 

8.8959 

8.9001 

8.9043 

8.9085 

8.9127 

8.9169 

8.9211 

8.9253 

8.9295 

8.9337 

8.9378 

8.9420 

8.9462 

8.9503 

8.9545 

8.9587 

8.9628 

8.9670 

8.9711 

8.9752 

8.9794 

8.9835 

8.9876 

8.9918 

8.9959 

9.0000 

9.0041 

9.0082 

9.0123 

9.0164 

9.0205 

9.0246 

9.0287 

9.0328 

9.0369 

9.0410 

9.0450 

9.0491 

9.0532 

9.0572 

9.0613 

9.0654 

9.0694 

9.0735 

9.0775 

.001457726  ! 

.001455604  ! 

.001453488  ! 

.001451379  ! 

.001449275  ! 

.001447178  : 

.001445087  : 

.001443001  : 

.001440922  : 

.001438849  : 

.001436782 

.001434720 

.001432665 

.001430615 

.001428571 

.001426534 

.001424501 

.001422475 

.001420455 

.001418440 

.001416431 

.001414427 

.001412429 

.001410437 

.001408451 

.001406470 

.001404494 

.001402525 

.001400560 

.001398601 

.001396648 

.001394700 

.001392758 

.001390821 

.001388889 

.001386963 

.001385042 

.001383126 

.001381215 

.001379310 

.001377410 

.001375516 

.001373626 

.001371742 

.001369863 

.001367989 

.001366120 

.001364256 

.001362398 

.001360544 

.001358696 

.001356852 

.001355014 

.001353180 

.001351351 

.001349528 

.001347709 

.001345895 

.001344086 

.001342282 

.001340483 

.001338688 

.001336898 

2,155.13  ! 

2.158.27  : 
2,161.42  I 
2,164.56  : 
2,167.70  : 
2,170.84  : 
2,173.98  : 
2,177.12  : 

2.180.27  : 
2,183.41 
2,186.55 
2,189.69 
2,192.83 
2,195.97 

2.199.11 
2,202.26 
2,205.40 
2,208.54 
2,211.68 
2,214.82 

2.217.96 

2.221.11 
2,224.25 
2,227.39 
2,230.53 
2,233.67 

2.236.81 

2.239.96 
2,243.10 
2,246.24 
2,249.38 
2,252.52 
2,255.66 

2.258.81 
2,261.95 
2,265.09 
2,268.23 
2,271.37 
2,274.51 

2.277.65 
2,280.80 
2,283.94 
2,287.08 
2,290.22 
2,293.36 

2.296.50 

2.299.65 
2,302.79 
2,305.93 
2,309.07 
2,312.21 
2,315.35 

2.318.50 
2,321.64 
2,324.78 
2,327.92 
2,331.06 
2,334.20 
2,337.34 
2,340.49 
2,343.63 
2,346.77 
2,349.91 

369,605.23 

370.683.59 

371.763.51 
372,845.00 

373.928.07 

375.012.70 
376,098.91 
377,186.68 
378,276.03 
379,366.95 

380.459.44 
381,553.50 
382,649.13 
383,746.33 
384,845.10 

385.945.44 
387,047.36 

388.150.84 

389.255.90 

390.362.52 

391.470.72 

392.580.49 
393,691.82 

394.804.73 

395.919.21 

397.035.26 
398,152.89 

399.272.08 

400.392.84 

401.515.18 

402.639.08 
403,764.56 

404.891.60 

406.020.22 
407,150.41 
408,282.17 

409.415.50 

410.550.40 
411,686.87 

412.824.91 

413.964.52 

415.105.71 
416,248.46 

417.392.79 
418,538.68 

419.686.15 

420.835.19 

421.985.79 
423,137.97 

424.291.72 
425,447.04 

426.603.94 

427.762.40 
428,922.43 
430,084.03 
431,247.21 

432.411.95 

433.578.27 

434.746.16 
435,915.62 
437,086.64 
438,259.24 

439.433.41 

CIRCUMFERENCES , AND  AREAS. 


557 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

749 

750 

751 

752 

753 

754 

755 

756 

757 

758 

759 

760 

761 

762 

763 

764 

765 

766 

767 

768 

769 

770 

771 

772 

773 

774 

775 

776 

777 

778 

779 

780 

781 

782 

783 

784 

785 

786 

787 

788 

789 

790 

791 

792 

793 

794 

795 

796 

797 

798 

799 

800 
801 
802 

803 

804 

805 

806 

807 

808 

809 

810 
811 

561.001 
562,500 

564.001 
565,504 
567,009 
568,516 
570,025 
571,536 
573,049 
574,564 
576,081 
577,600 
579,121 
580,644 
582,169 
583,696 

585.225 
586,756 
588,289 
589,824 
591,361 
592,900 
594,441 
595,984 
597,529 
599,076 
600,625 
602,176 
603,729 
605,284 
606,841 

608.400 
609,961 
611,524 
613,089 
614,656 

616.225 
617,796 
619,369 
620,944 
622,521 

624.100 
625,681 
627,264 
628,849 
630,436 

632.025 
633,616 
635,209 
636.804 

638.401 
640,000 
641,601 
643,204 
644,809 
646,416 

648.025 
649,636 
651,249 
652,864 
654,481 

656.100 
657,721 

420,189,749 
. 421,875,000 
423,564,751 
425,259,008 
426,957,777 
428,661,064 
430,368,875 
432,081,216 
433,798,093 
435,519,512 
437,245,479 

438.976.000 
440,711,081 
442,450,728 
444,194,947 
445,943,744 
447,697,125 
449,455,096  1 
451,217,663 
452,984,832 
454,756,609 

456.533.000 
458,314,011 
460,099,648 
461,889,917 
463,684,824 
465,484,375 
467,288,576 
469,097,433 
470,910,952 
472,729,139 

474.552.000 
476,379,541 
478,211,768 
480,048,687 
481,890,304 
483,736,625 
485,587,656 
487,443,403 
489,303,872 
491,169.069 

493.039.000 
494,913,671 
496,793,088 
498,677,257 
500,566,184 
502,459,875 
504,358,336 
506,261,573 
508,169,592 
510,082,399 
512,000,000 
513,922,401 
515,849,608 
517,781,627 
519,718,464 
521,660,125 
523,606,616 
525,557,943 
527,514,112 
529,475,129 

531.441.000 
533,411,731 

27.3679 

27.3861 

27.4044 

27.4226 

27.4408 

27.4591 

27.4773 

27.4955 

27.5136 

27.5318 

27.5500 

27.5681 

27.5862 

27.6043 

27.6225 

27.6405 

27.6586 

27.6767 

27.6948 

27.7128 

27.7308 

27.7489 

27.7669 

27.7849 

27.8029 

27.8209 

27.8388 

27.8568 

27.8747 

27.8927 

27.9106 

27.9285 

27.9464 

27.9643 

27.9821 

28.0000 

28.0179 

28.0357 

28.0535 

28.0713 

28.0891 

28.1069 

28.1247 

28.1425 

28.1603 

28.1780 

28.1957 

28.2135 

28.2312 

28.2489 

28.2666 

28.2843 

28.3019 

28.3196 

28.3373 

28.3549 

28.3725 

28.3901 

28.4077 

28.4253 

28.4429 

28.4605 

28.4781 

9.0816 

9.0856 

9.0896 

9.0937 

9.0977 

9.1017 

9.1057 

9.1098 

9.1138 

9.1178 

9.1218 

9.1258 

9.1298 

9.1338 

9.1378 

9.1418 

9.1458 

9.1498 

9.1537 

9.1577 

9.1617 

9.1657 

9.1696 

9.1736 

9.1775 

9.1815 

9.1855 

9.1894 

9.1933 

9.1973 

9.2012 

9.2052 

9.2091 

9.2130 

9.2170 

9.2209 

9.2248 

9.2287 

9.2326 

9.2365 

9.2404 

9.2443 

9.2482 

9.2521 

9.2560 

9.2599 

9.2638 

9.2677 

9.2716 

9.2754 

9.2793 

9.2832 

9.2870 

9.2909 

9.2948 

9.2986 

9.3025 

9.3063 

9.3102 

9.3140 

9.3179 

9.3217 

9.3255 

.001335113  : 
.001333333  ! 
.001331558  ! 
.001329787  ! 
.001328021  ! 
.001326260  ! 
.001324503  : 
.001322751  : 
.001321004  : 
.001319261  : 
.001317523 
.001315789 
.001314060 
.001312336 
.001310616 
.001308901 
.001307190 
.001305483 
.001303781 
.001302083 
.001300390 
.001298701 
.001297017 
.001295337 
.001293661 
.001291990 
.001290323 
.001288660 
.001287001 
.001285347 
.001283697 
.001282051 
.001280410 
.001278772 
.001277139 
.001275510 
.001273885 
.001272265 
.001270648 
.001269036 
.001267427 
.001265823 
.001264223 
.001262626 
.001261034 
.001259446 
.001257862 
.001256281 
.001254705 
.001253133 
.001251364 
.001250000 
.001248439 
.001246883 
.001245330 
.001243781 
.001242236 
.001240695 
.001239157 
.001237624 
.001236094 
.001234568 
.001233046 

2,353.05  < 

2.356.19  < 
2,359.34  < 
2,362.48  < 
2,365.62  - 
2,368.76  < 
2,371.90  - 

2.375.04  • 

2.378.19  ■ 
2,381.33  • 
2,384.47  ■ 
2,387.61 
2,390.75 
2,393.89 

2.397.04 
2,400.18 
2,403.32 
2,406.46 
2,409.60 
2,412.74 

2.415.88 
2,419.03 
2,422.17 
2,425.31 
2,428.45 
2,431.59 

2.434.73 

2.437.88 
2,441.02 
2,444.16 
2,447.30 
2,450.44 

2.453.58 

2.456.73 
2,459.87 
2,463.01 
2,466.15 
2,469.29 
2,472.43 

2.475.58 
2,478.72 
2,481.86 
2,485.00 
2,488.14 
2,491.28 

2.494.42 
2,497.57 
2,500.71 
2,503.85 
2,506.99 
2,510.13 

2.513.27 

2.516.42 
2,519.56 
2,522.70 
2,525.84 
2,528.98 
2,532.12 

2.535.27 
2,538.41 
2,541.55 
2,544.69 
2,547.83 

140,609.16 

141,786.47 

142,965.35 

144.145.80 

445.327.83 
446,511.42 
447,696.59 
448,883.32 

450.071.63 
451,261.51 

452.452.96 
453,645.98 

454.840.57 

456.036.73 
457,234.46 

458.433.77 

459.634.64 
460,837.08 
462,041.10 

463.246.69 

464.453.84 

465.662.57 
466,872.87 

468.084.74 

469.298.18 

470.513.19 

471.729.77 
472,947.92 

474.167.65 

475.388.94 

476.611.81 

477.836.24 

479.062.25 

480.289.83 

481.518.97 

482.749.69 

483.981.98 

485.215.84 

486.451.28 

487.688.28 

488.926.85 

490.166.99 
491,408.71 

492.651.99 

493.896.85 

495.143.28 
496,391.27 
497,640.84 
498,891.98 

500.144.69 
501,398.97 

502.654.82 

503.912.25 
505,171.24 
506,431.80 

507.693.94 
508,957.64 
510,222.92 
511,489.77 
5^2,758.19 
514,028.18 
515,299.74 
516,572.87 

558  SQUARES , CUBES , SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

812 

813 

814 

815 

816 

817 

818 

819 

820 
821 
822 

823 

824 

825 

826 

827 

828 

829 

830 

831 

832 

833 

834 

835 

836 

837 

838 

839 

840 

841 

842 

843 

844 

845 

846 

847 

848 

849 

850 

851 

852 

853 

854 

855 

856 

857 

858 

859 

860 
861 
862 

863 

864 

865 

866 

867 

868 

869 

870 

871 

872 

873 

874 

659,344 

660,969 

662,596 

664.225 

665,856 

667,489 

669,124 

670,761 

672,400 

674,041 

675.584 
677,329 
678,976 
680,625 
682,276 
683,929 

685.584 
687,241 

688.900 
690.561 

692.224 
693,889 
695,556 

697.225 
698,896 
700,569 
702,244 
703,921 

705.600 
707,281 
708,964 
710,649 
712,336 

714.025 
715,716 
717,409 
719,104 
720,801 
722,500 
724,201 
725,904 
727,609 
729,316 

731.025 
732,736 
734,449 
736,164 
737,881 

739.600 
741,321  * 
743,044 
744,769 
746,496 
748/225 
749,956 
751,689 
753,424 
755,161 

756.900 
758,641 
760,384 
762,129 
763,876 

1 

535,387,328 

537,367,797 

539,353,144 

541.343.375 
543,338.496 
545,338,513 
547,343,432 
549,353,259 

551.368.000 
553,387,661 
555,412,248 
557,441,767 
559,476,224 

561.515.625 
563,559,976 
565,609,283 
567,663,552 
569,722,789 

571.787.000 

573.856.191 
575,930,368 
578,009,537 
580,093,704 
582,182,875 
584,277,056 
586,376,253 
588,480,472 
590,589,719 

592.704.000 
594,823,321 
596,947,688 
599,077,107 
601,211,584 
603,351,125 
605.495,736 
607,645,423 

609.800.192 
611,960,049 

614.125.000 
616,295,051 
618,470,208 
620,650,477 
622,835,864 

625.026.375 
627,222,016 
629,422,793 
631,628,712 
633,839,779 

636.056.000 
638,277,381 
640,503,928 
642,735,647 
644,972,544 

647.214.625 
649,461,896 
651,714,363 
653,972,032 
656,234,909 

658.503.000 
660,776,311 
663,054,848 
665,338,617 
667,627,624 

28.4956 

28.5132 

28.5307 

28.5482 

28.5657 

28.5832 

28.6007 

28.6182 

28.6356 

28.6531 

28.6705 

28.6880 

28.7054 

28.7228 

28.7402 

28.7576 

28.7750 

28.7924 

28.8097 

28.8271 

28.8444 

28.8617 

28.8791 

28.8964 

28.9137 

28.9310 

28.9482 

28.9655 

28.9828 

29.0000 

29.0172 

29.0345 

29.0517 

29.0689 

29.0861 

29.1033 

29.1204 

29.1376 

29.1548 

29.1719 

29.1890 

29.2062 

29.2233 

29.2404 

29.2575 

29.2746 

29.2916 

29.3087 

29.3258 

29.3428 

29.3598 

29.3769 

29.3939 

29.4109 

29.4279 

29.4449 

29.4618 

29.4788 

29.4958 

29.5127 

29.5296 

29.5466 

29.5635 

9.3294 
9.3332 
9.3370 
9.3408 
9.3447 
9.3485 
9.3523 
9.3561 
9.3599 
9.3637 
9.3675 
9.3713 
9.3751 
9.3789 
9.3827 
9.3865 
9 3902 
9.3940 
9.3978 
9.4016 
9.4053 
9.4091 
9.4129 
9.4166 
9.4204 
9.4241 
9.4279 
9.4316 
9.4354 
9.4391 
9.4429 
9.4466 
9.4503 
9.4541 
9.4578 
9.4615 
9.4652 
9.4690 
9.4727 
9.4764 
9.4801 
9.4838 
9.4875 
9.4912 
9.4949 
9.4986 
9.5023 
9.5060 
9.5097 
9.5135 
9.5171 
9.5207 
9.5244 
9.5281 
9.5317 
9.5354 
9.5391 
9.5427 
9.5464 
9.5501 
9.5537 
9.5574 
9.5610 

.001231527 

.001230012 

.001228501 

.001226994 

.001225490 

.001223990 

.001222494 

.001221001 

.001219512 

.001218027 

.001216545 

.001215067 

.001213592 

.001212121 

.001210654 

.001209190 

.001207729 

.001206273 

.001204819 

.001203369 

.001201923 

.001200480 

.001199041 

.001197605 

.001196172 

.001194743 

.001193317 

.001191895 

.001190476 

.001189061 

.001187648 

.001186240 

.001184834 

.001183432 

.001182033 

.001180638 

.001179245 

.001177856 

.001176471 

.001175088 

.001173709 

.001172333 

.001170960 

.001169591 

.001168224 

.001166861 

.001165501 

.001164144 

.001162791 

.001161440 

.001160093 

.001158749 

.001157407* 

.00115606SF 

.001154734 

.001153403 

.001152074 

.001150748 

.001149425 

.001148106 

.001146789 

.001145475 

.001144165 

2,550.97 

2.554.11 
2,557.26 
2,560.40 
2,563.54 
2,566.68 
2,569.82 

2.572.96 

2.576.11 
2,579.25 
2,582.39 
2,585.53 
2,588.67 

2.591.81 

2.594.96 
2,598.10 
2,601.24 
2,604.38 
2,607.52 
2,610.66 

2.613.81 
2,616.95 
2,620.09 
2,623.23 
2,626.37 
2,629.51 

2.632.65 
2,635.80 
2,638.94 
2,642.08 
2,615.22 
2,648.36 

2.651.50 

2.654.65 
2,657.79 
2,660.93 
2,664.07 
2,667.21 
2,670.35 

2.673.50 
2,676.64 
2.679.78 
2,682.92 
2,686.06 
2,689.20 

2.692.34 
2,695.49 
2,698.63 
2,701.77 
2,704.91 
2,708.05 

2.711.19 

2.714.34 
2,717.48 
2,720.62 
2,723.76 
2,726.90 
2,730.04 

2.733.19 
2,736.33 
2,739.47 
2,742.61 
2,745.75 

517.847.57 

519.123.84 

520.401.68 
521,681.10 
522,962.08 
524,244.63 

525.528.76 

526.814.46 
528,101.73 
529,390.56 
530,680.97 

531.972.95 

533.266.50 

534.561.62 
535,858.32 

537.156.58 

538.456.41 

539.757.82 
541,060.79 
542,365.34 

543.671.46 

544.979.15 
546,288.40 
547,599.23 

548.911.63 
550,225.61 

551.541.15 
552,858.26 
554,176.94 

555.497.20 

556.819.02 

558.142.42 
559,467.39 
560,793.92 

562.122.03 

563.451.71 

564.782.96 
566,115.78 
567,450.17 

568.786.14 
570,123.67 

571.462.77 
572,803.45 

574.145.69 

575.489.51 
576,834.90 

578.181.85 

579.530.38 
580,880.48 

582.232.15 

583.585.39 

584.940.20 

586.296.59 
587,654.54 
589,014.07 

590.375.16 

591.737.83 
593,102.06 
594.467.87 
595,835.25 

597.204.20 

598.574.72 
599,946.81 

CIRCUMFERENCES,  AND  AREAS. 


559 


No. 

Square. 

Cube. 

3q.  Root.  < 

Du.  Root. 

Reciprocal. 

Circum. 

Area. 

875 

876 

877 

878 

879 

880 
881 
882 

883 

884 

885 

886 

887 

888 

889 

890 

891 

892 

893 

894 

895 

896 

897 

898 

899 

900 

901 

902 

903 

904 

905 

906 

907 

908 

909 

910 

911 

912 

913 

914 

915 

916 

917 

918 

919 

920 

921 

922 

923 

924 

925 

926 

927 

928 

929 

930 

931 

932 

933 

934 

935 

936 

937 

765,625 

767,376 

769,129 

770,884 

772,641 

774,400 

776,161 

777,924 

779,689 

781,456 

783,225 

784,996 

786,769 

788,544 

790,321 

792.100 
793,881 
795,664 
797,449 
799,236 

801.025 
802,816 
804,609 
806,404 
808,201 
810,000 
811,801 
813,604 
815,409 
817,216 

819.025 
820,836 
822,649 
824,464 
826,281 

828.100 
829,921 
831,744 
833,569 
835,396 

837.225 
839,056 
840,889 
842,724 
844,561 
846,400 
848,241 
850,084 
851,929 
853,776 
855,625 
857,476 
859,329 
861,184 
863,041 
884,900 
866,761 
868,624 
870,489 
872,356 

874.225 
876,096 
877,969 

669,921,875 

672,221,376 

674,526,133 

676,836,152 

679,151,439 

681.472.000 
683,797.841 
686,128,968 
688,465,387 
690,807,104 
693,154,125 
695,506,456 
697,864,103 
700,227,072 
702,595,369 

704.969.000 
707,347,971 
707,932,288 
712,121,957 
714,516,984 
716,917,375 
719,323,136 
721,734,273 
724,150,792 
726,572,699 
729,000,000 
731,432,701 
733,870,808 
736,314,327 
738,763,264 
741,217,625 
743,677,416 
746,142,643 
748,613,312 
751,089,429 

753.571.000 
756,058,031 
758,550,825 
761,048,497 
763,551,944 
766,060,875 
768,575,296 
771,095,213 
773,620,632 
776,151,559 

778.688.000 
781,229,961 
783.777,448 
786^330,467 
788,889,024 
791,453,125 
794,022,776 
796,597,983 
799,178,752 
801,765,089 

804.357.000 
806,954,491 
809,557,568 
812,166,237 
814,780,504 
817,400,375 
820,025,856 
822,656,953 

29.5804 

29.5973 

29.6142 

29.6311 

29.6479 

29.6648 

29.6816 

29.6985 

29.7153 

29.7321 

29.7489 

29.7658 

29.7825 

29.7993 

29.8161 

29.8329 

29.8496 

29.8664 

29.8831 

29.8998 

29.9166 

29.9333 

29.9500 

29.9666 

29.9833 

30.0000 

30.0167 

30.0333 

30.0500 

30.0666 

30.0832 

30.0998 

30.1164 

30.1330 

30.1496 

30.1662 

30.1828 

30.1993 

30.2159 

30.2324 

30.2490 

30.2655 

30.2820 

30.2985 

30.3150 

30.3315 

30.3480 

30.3645 

30.3809 

30.3974 

30.4138 

30.4302 

30.4467 

30.4631 

30.4795 

30.4959 

30.5123 

30.5287 

30.5450 

30.5614 

30.5778 

30.5941 

30.6105 

9.5647 
9.5683 
9.5719 
9.5756 
9.5792 
9.5828 
9.5865 
9.5901 
9.5937 
9.5973 
9.6010 
9.6046 
9.6082 
9.6118 
9.6154 
9.6190 
9.6226 
9.6262 
9.6298 
9.6334 
9.6370 
9.6406 
9.6442 
9.6477 
9.6513 
9.6549 
9.6585 
9.6620 
9.6656 
9.6692 
9.6727 
9.6763 
9.6799 
9.6834 
9.6870 
9.6905 
9.6941 
9.6976 
9.7012 
9.7047 
9.7082 
9.7118 
9.7153 
9.7188 
9.7224 
9.7259 
9.7294 
9.7329 
9.7364 
9.7400 
9.7435 
9.7470 
9.7505 
■ 9.7540 
9.7575 
9.7610 
9.7645 
9.7680 
9.7715 
9.7750 
9.7785 
9.7829 
9.7854 

.001142857  S 
.001141553  5 
.001140251  5 
.001138952  5 
.001137656  5 
.001136364  i 
.001135074  5 
.001133787  5 
.001132503  i 
.001131222  ! 
.001129944  i 
.001128668  i 
.001127396  ! 
.001126126  : 
.001124859  ! 
.001123596  ! 
.001122334  : 
.001121076 
.001119821 
.001118568 
.001117818 
.001116071 
.001114827 
.001113586 
.001112347 
.001111111 
.001109878 
.001108647 
.001107420 
.001106195 
.001104972 
.001103753 
.001102536 
.001101322 
.001100110 
.001098901 
.001091695 
.001096491 
.001095290 
.001094092 
.001092896 
.001091703 
.001090513 
.001089325 
.001088139 
.001086957 
.001085776 
.001084599 
.001083423 
.001082251 
.001081081 
.001079914 
.001078749 
.001077586 
.001076426 
.001075269 
.001074114 
.001072961 
.001071811 
.001070664 
.001069519 
.001068376 
.001067236 

>,748.89  ( 
5,752.04  e 
5,755.18  ( 
5,758.32  ( 
5,761.46  ( 
5,764.60  ( 
5,767.74  ( 

5.770.88  ( 
5,774.03  ( 
5,777.17  < 
5,780.31  < 
5,783.45  < 
2,786.59  i 

2.789.73  i 

2.792.88  i 
2,796.02  1 
2,799.16  i 
2,802.30 
2,805.44 

2.808.58 

2.811.73 
2,814.87 
2,818.01 
2,821.15 
2,824.29 
2,827.43 

2.830.58 
2,833.72 
2,836.86 
2,840.00 
2,843.14 
2,846.28 

2.849.42 
2,852.57 
2,855.71 
2,858.85 
2,861.99 
2,865.13 

2.868.27 

2.871.42 
2,874.56 
2,877.70 
2,880.84 
2,883.98 
2.887.12 

2.890.27 
2,893.41 
2,896.55 
2,899.69 
2,902.83 
2,905.97 

2.909.11 
2,912.26 
2,915.40 
2,918.54 
2,921.68 
2,924.82 
2,927.96 

2.931.11 
2,934.25 
2,937.39 
2,940.53 
2,943.67 

>01,320.47 

>02,695.70 

>04,072.50 

>05,450.88 

>06,830.82 

>08,212.34 

>09,595.42 

>10,980.08 

312,366.31 

313,754.11 

515.143.48 

516.534.42 
517,926.93 

519.321.01 
620,716.66 
622,113.89 
623,512.68 
624,913.04 
626,314.98 

627.718.49 

629.123.56 

630.530.21 

631.938.43 

633.348.22 

634.759.58 

636.172.51 

637.587.01 

639.003.09 
640,420.73 
641,839.95 
*643,260.73 

644.683.09 

646.107.01 

647.532.51 

648.959.58 

650.388.22 

651.818.43 
653,250.21 

654.683.56 
656,118.48 
657,554.98 
658,993.04 

660.432.68 
661,873.88 
663,316.66 

664.761.01 
666,206.92 

667.654.41 
669,103.47 

670.554.10 
672,006.30 
673,460.08 

674.915.42 
676,372.33 
677,830.82 
679,290.87 
680,752.50 

682.215.69 
683,680.46 
685,146.80 
686,614.71 

, 688,084.19 
689,555.24 

560  SQUARES , CUBES,  SQUARE  AND  CUBE  ROOTS , 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

938 

939 

940 

941 

942 

943 

944 

945 

946 

947 

948 

949 

950 

951 

952 

953 

954 

955 

956 

957 

958 

959 

960 

961 

962 

963 

964 

965 

966 

967 

968 

969 

970 

971 

972 

973 

974 

975 

976 

977 

978 

979 

980 

981 

982 

983 

984 

985 

986 

987  . 

988 

989 

990 

991 

992 

993 

994 

995 

996 

997 

998 

999 
1000 

879,844 

881,721 

883.600 
885,481 
887,364 
889,249 
891,136 

893.025 
894,916 
896,808 
898,704 

900.601 
902,500 
904,401 
906,304 
908,209 
910,116 

912.025 
913,936 
915,849 
917,764 
919,681 
921,600 
923,521 
925,444 
927,369 
929,296 

931.225 
933,156 
935,089 

937.024 
938,961 
940,900 
942,841 
944,784 
946,729 
948,676 
950,625 
952,576 
954,529 
956,484 
958,441 
960,400 
962,361 
964,324 
966,289 
968,256 

970.225 
972,196 
974,169 
976,144 
978,121 
980,100 
982,081 
984,064 
986,049 
988,036 

990.025 
992,016 
994,009 
996,004 
998,001 

1,000,000 

825,293,672 

827,936,019 

830.584.000 
833,237,621 
835,896,888 
838,561,807 
841,232,384 

843.908.625 
846,590,536 
849,278,123 
851,971,392 
854,670,349 

857.375.000 

860.085.351 
862,801,408 
865,523,177 
868,250,664 

870.983.875 
873,722,816 
876,467,493 
879,217,912 
881,974,079 

884.736.000 
887,503,681 
890,277,128 
893,056,347 
895,841,344 
898,632,125 
901,428,696 
904,231,063 
907,039,232 
909,853,209 

912.673.000 
915,498,611 
918,330,048 
921,167,317 
924,010,424 
926,859,375 
929,714,176 
932,574,833 

935.441.352 
938,313,739 

941.192.000 
944,076,141 
946,966,168 
949,862,087 
952,763,904 

955.671.625 
958,585,256 
961,504,803 
964,430,272 
967,361,669 

970.299.000 
973,242,271 
976,191,488 
979,146,657 
982,107,784 

985.074.875 
988,047,936 
991,026,973 
994,011,992 
997,002,999 

1,000,000,000 

30.6268 

30.6431 

30.6594' 

30.6757 

30.6920 

30.7083 

30.7246 

30.7409 

30.7571 

30.7734 

30.7896 

30.8058 

30.8221 

30.8383 

30.8545 

30.8707 

30.8869 

30.9031 

30.9192 

30.9354 

30.9516 

30.9677 

30.9839 

31.0000 

31.0161 

31.0322 

31.0483 

31.0644 

31.0805 

31.0966 

31.1127 

31.1288 

31.1448 

31.1609 

31.1769 

31.1929 

31.2090 

31.2250 

31.2410 

31.2570 

31.2730 

31.2890 

31.3050 

31.3209 

31.3369 

31.3528 

31.3688 

31.3847 

31.4006 

31.4166 

31.4325 

31.4484 

31.4643 

31.4802 

31.4960 

31.5119 

31.5278 

31.5436 

31.5595 

31.5753 

31.5911 

31.6070 

31.6228 

9.7889 

9.7924 

9.7959 

9.7993 

9.8028 

9.8063 

9.8097 

9.8132 

9.8167 

9.8201 

9.8236 

9.8270 

9.8305 

9.8339 

9.8374 

9.8408 

9.8443 

9.8477 

9.8511 

9.8546 

9.8580 

9.8614 

9.8648 

9.8683 

9.8717 

9.8751 

9.8785 

9.8819 

9.8854 

9.8888 

9.8922 

9.8956 

9.8990 

9.9024 

9.9058 

9.9092 

9.9126 

9.9160 

9.9194 

9.9228' 

9.9261 

9.9295 

9.9329 

9.9363 

9.9396 

9.9430 

9.9464 

9.9497 

9.9531 

9.9565 

9.9598 

9.9632 

9.9666 

9.9699 

9.9733 

9.9766 

9.9800 

9.9833 

9.9866 

9.9900 

9.9933 

9.9967 

10.0000 

.001066098 

.001064963 

.001063830 

.001062699 

.001061571 

.001060445 

.001059322 

.001058201 

.001057082 

.001055966 

.001054852 

.001053741 

.001052632 

.001051525 

.001050420 

.001049318 

.001048218 

.001047120 

.001046025 

.001044932 

.001043841 

.001042753 

.001041667 

.001040583 

.001039501 

.001038422 

.001037344 

.001036269 

.001035197 

.001034126 

.001033058 

.001031992 

.001030928 

.001029866 

.001028807 

.001027749 

.001026694 

.001025641 

.001024590 

.001023541 

.001022495 

.001021450 

.001020408 

.001019168 

.001018330 

.001017294 

.001016260 

.001015228 

.001014199 

.001013171 

.001012146 

.001011122 

.001010101 

.001009082 

.001008065 

.001007049 

.001006036 

.001005025 

.001004016 

.001003009 

.001002004 

.001001001 

.001000000 

2.946.81 
2,949.96 
2,953.10 
2,956.24 
2,959.38 
2,962.52 
2,965.66 

2.968.81 
2,971.95 
2,975.09 
2,978.23 
2,981.37 
2,984.51 

2.987.65 
2,990.80 
2,993.94 
2,997.08 
3,000.22 
3,003.36 

3.006.50 

3.009.65 
3,012.79 
3,015.93 
3,019.07 
3,022.21 
3,025.35 

3.028.50 
3,031.64 
3,034.78 
3,037.92 
3,041.06 
3,044.20 

3.047.34 
3,050.49 
3,053.63 
3,056.77 
3,059.91 
3,063.05 

3.066.19 

3.069.34 
3,072.48 
3,075.62 
3,078.76 
3,081.90 

3.085.04 

3.088.19 
3,091.33 
3,094.47 
3,097.61 
3,100.75 
3,103.89 

3.107.04 
3,110.18 
3,113.32 
3,116.46 
3,119.60 
3,122.74 
3,125.88 
3,129.03 
3,132.17 
3,135.31 
3,138.45 
3,141.59 

691,027.86 

692.502.05 

693.977.82 

695.455.15 

696.934.06 

698.414.53 

699.896.58 
701,380.19 

702.865.38 

704.352.14 

705.840.47 

707.330.37 

708.821.84 
710,314.88 
711,809.50 
713,305.68 

714.803.43 

716.302.76 

717.803.66 

719.306.12 

720.810.16 

722.315.77 

723.822.95 

725.331.70 
726,842.02 
728,353.91 

729.867.37 
731,382.40 
732,899.01 
734,417.18 

735.936.93 
737,458.24 

738.981.13 

740.505.59 
742,031.62 
743,559.22 

745.088.39 

746.619.13 

748.151.44 
749,685.32 

751.220.78 
752,757.80 

754.296.40 
755,836.56 
757,378.30 

758.921.61 

760.466.48 

762.012.93 

763.560.95 

765.110.54 

766.661.70 

768.214.44 
769,768.74 

771.324.61 

772.882.06 

774.441.07 

776.001.66 

777.563.82 

779.127.54 

780.692.84 

782.259.71 

783.828.15 

785.398.16 

CIRCUMFERENCES 


AND  AREAS  OF  CIRCLES. 


561 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES 
FROM  1-64  TO  100. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam.  * 

Circum. 

Area. 

i 

0491 

0002 

6 

18.8496 

28.2744 

13} 

41.2335 

135.297 

6* 

1 

0982 

0008 

6? 

19.2423 

29.4648 

13} 

41.6262 

137.887 

3l 

1 

1963 

0031 

61 

19.6350 

30.6797 

13} 

42.0189 

140.501 

TS 

1 

3927 

0123 

6} 

20.0277 

31.9191 

13} 

42.4116 

143.139 

S 

3 

5890 

0276 

61 

20.4204 

33.1831 

13} 

42.8043 

145.802 

TS 

1 

7854 

]0491 

6} 

20.8131 

34.4717 

13} 

43.1970 

148.490 

¥ 

5 

9817 

0767 

6} 

21.2058 

35.7848 

13} 

43.5897 

151.202 

TS 

3 

1 1781 

.1104 

61 

21.5985 

37.1224 

14 

43.9824 

153.938 

l 

1 

1 3744 

1503 

7 

21.9912 

38.4846 

14} 

44.3751 

156.700 

1 5708 

1963 

7} 

22.3839 

39.8713 

14} 

44.7678 

159.485 

i 

TS 

6 

1 7671 

2485 

71 

22.7766 

41.2826 

14} 

45.1605 

162.296 

1 9635 

.3068 

7| 

23.1693 

42.7184 

14} 

45.5532 

165.130 

S 

n 

3 

2.1598 
2 3562 

.3712 

.4418 

71 

71 

23.5620 

23.9547 

44.1787 

45.6636 

14} 

14} 

45.9459 

46.3386 

167.990 

170.874 

?3 

2 5525 

.5185 

71 

24.3474 

47.1731 

14} 

46.7313 

173.782 

fr5 

2 7489 

6013 

71 

24.7401 

48.7071 

15 

47.1240 

176.715 

A 

2 9452 

6903 

8 

25.1328 

50.2656 

15} 

47.5167 

179.673 

l1 

3 1416 

.7854 

81 

25.5255 

51.8487 

15} 

47.9094 

182.655 

1 1 

3 5343 

.9940 

81 

25.9182 

53.4563 

15} 

48.3021 

185.661 

-*-8 

1 1 

3 9270 

1.2272 

81 

26.3109 

55.0884 

15} 

48.6948 

188.692 

X4 
1 3 

4 3197 

1.4849 

81 

26.7036 

56.7451 

15} 

49.0875 

191.748 

-•-8 

4.7124 

1.7671 

81 

27.0963 

58.4264 

15} 

49.4802 

194.828 

It 

5.1051 

2.0739 

81 

27.4890 

60.1322 

15} 

49.8729 

197.933 

8 

1 3 

5.4978 

2.4053 

81 

27.8817 

61.8625 

16 

50.2656 

201.062 

1- 

5.8905 

2.7612 

9 

28.2744 

63.6174 

16} 

50.6583 

204.216 

18 

2 

6.2832 

3.1416 

91 

28.6671 

65.3968 

16} 

51.0510 

207.395 

! 2^ 

6.6759 

3.5466 

91 

29.0598 

67.2008 

16} 

51.4437 

210.598 

21 

7.0686 

3.9761 

91 

29.4525 

69.0293 

16} 

51.8364 

213.825 

7.4613 

4.4301 

9a- 

29.8452 

70.8823 

16} 

52.2291 

217.077 

"8 

21 

7.8540 

4.9087 

91 

30.2379 

72.7599 

16} 

52.6218 

220.354 

"2 

21 

8.2467 

5.4119 

91 

30.6306 

74.6621 

16} 

53.0145 

223.655 

21 

8.6394 

5.9396 

91 

31.0233 

76.589 

17 

53.4072 

226.981 

21 

9.0321 

6.4918 

10 

31.4160 

78.540 

17} 

53.7999 

230.331 

"8 

3 

9.4248 

7.0686 

101 

31.8087 

80.516 

17} 

54.1926 

233.706 

3i 

9.8175 

7.6699 

101 

32.2014 

82.516 

17} 

54.5853 

237.105 

Br 

10.2102 

8.2958 

101 

32.5941 

84.541 

17} 

54.9780 

240.529 

31 

10.6029 

8.9462 

101 

32.9868 

86.590 

17} 

55.3707 

243.977 

31 

10.9956 

9.6211 

101 

33.3795 

88.664 

17} 

55.  / 634 

247.450 

'-'2 

31 

11.3883 

10.3206 

101 

33.7722 

90.763 

17} 

56.1561 

250.948 

u8 

31 

11.7810 

11.0447 

101' 

34.1649 

92.886 

18 

56.5488  . 

254.470 

°4 

31 

12.1737 

11.7933 

11 

34.5576 

95.033 

18} 

56.9415 

258.016 

4 

12.5664 

12.5664 

111 

34.9503 

97.205 

18} 

57.3342 

261.587 

41 

12.9591 

13.3641 

111 

35.3430 

99.402 

18} 

57.7269 

265.183 

41 

13.3518 

14.1863 

111 

35.7357 

101.623 

18} 

58.1196 

268.803 

A4 

41 

13.7445 

15.0330 

111 

36.1284 

103.869 

18} 

58.5123 

272.448 

^8 

41 

14.1372 

15.9043 

111 

36.5211 

106.139 

18} 

58.9050 

276.117 

41 

14.5299 

16.8002 

111 

36.9138 

108.434 

18} 

59.2977 

279.811 

A 8 
41 

14.9226 

17.7206 

111 

37.3065 

110.754 

19 

59.6904 

283.529 

A 4 

41 

15.3153 

18.6555 

12 

37.6992 

113.098 

19} 

60.0831 

287.272 

5 

15.7080 

19.6350 

121 

38.0919 

115.466 

19} 

60.4758 

291.040 

51 

16.1007 

20.6290 

121 

38.4846 

117.859 

19} 

60.8685 

294.832 

'"'8 

51 

16.4934 

21.6476 

12f 

38.8773 

120.277 

19} 

61.2612 

298.648 

u4 

51 

16.8861 

22.6907 

121 

39.2700 

122.719 

19} 

61.6539 

302.489 

“8 

51 

17.2788 

23.7583 

121 

39.6627 

125.185 

19} 

62.0466 

306.355 

51 

17.6715 

24.8505 

121 

40.0554 

127.677 

19} 

62.4393 

310.245 

w8 

51 

18.0642 

25.9673 

121 

40.4481 

130.192 

20 

62.8320 

314.160 

51 

18.4569 

27.1086 

13 

40.8408 

132.733 

20} 

63.2247 

318.099 

562 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


Diam. 

I 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

20} 

63.6174 

322.063 

28} 

88.3575 

621.264 

36 

113.098 

1,017.878 

20f 

64.0101 

326.051 

28} 

88.7502 

626.798 

36} 

113.490 

1,024.960 

20} 

64.4028 

330.064 

28} 

89.1429 

632.357 

36} 

113.8S3 

1,032.065 

20| 

64.7955 

334.102 

28} 

89.5356 

637.941 

36} 

114.276 

1,039.195 

m 

65.1882 

338.164 

28} 

89.9283 

643.549 

36} 

114.668 

1.046.349 

20} 

65.5809 

342.250 

28} 

90.3210 

649.182 

36} 

115.061 

1,053.528 

21 

65.9736 

346.361 

28} 

90.7137 

654.840 

36} 

115.454 

1.060.732 

21} 

66.3663 

350.497 

29 

91.1064 

660.521 

36} 

115.846 

1,067.960 

21} 

66.7590 

354.657 

29} 

91.4991 

666.228 

37 

116.239 

1,075.213 

21f 

67.1517 

358.842 

29} 

91.8918 

671.959 

37} 

116.632 

1.082.490 

21| 

67.5444 

363.051 

29} 

92.2845 

677.714 

37} 

117.025 

1,089.792 

21} 

67.9371 

367.285 

29} 

92.6772 

683.494 

37} 

117.417 

1.097.118 

21} 

68.3298 

371.543 

29} 

93.0699 

689.299 

37} 

117.810 

1,104.469 

21} 

68.7225 

375.826 

29} 

93.4626 

695.128 

37} 

118.203 

1,111.844 

22 

69.1152 

380.134 

29} 

93.8553 

700.982 

37} 

118.595 

1,119.244 

22} 

69.5079 

384.466 

30 

94.2480 

706.860 

37} 

118.988 

1.126.669 

22} 

69.9006 

388.822 

30} 

94.6407 

712.763 

38 

119.381 

1.134.118 

22} 

70.2933 

393.203 

30} 

95.0334 

718.690 

38} 

119.773 

1.141.591 

22} 

70.6860 

397.609 

30} 

95.4261 

724.642 

38} 

120.166 

1,149.089 

22f 

71.0787 

402.038 

30} 

95.8188 

730.618 

38} 

120.559 

1.156.612 

22} 

71.4714 

406.494 

30} 

96.2115 

736.619 

38} 

120.952 

1,164.159 

22} 

71.8641 

410.973 

30} 

96.6042 

742.645 

38} 

121.344 

1,171.731 

23 

72.2568 

415.477 

30} 

96.9969 

748.695 

38} 

121.737 

1,179.327 

23} 

72.6495 

420.004 

31 

97.3896 

754.769 

38} 

122.130 

1,186.948 

23} 

73.0422 

424.558 

31} 

97.7823 

760.869 

39 

122.522 

1,194.593 

23| 

73.4349 

429.135 

31} 

98.1750 

766.992 

39} 

122.915 

1.202.263 

23} 

73.8276 

433.737 

31} 

98.5677 

773.140 

39} 

123.308 

1.209.958 

23f 

74.2203 

438.364 

31} 

98.9604 

779.313 

39} 

123.700 

1.217.677 

23} 

74.6130 

443.015 

31} 

99.3531 

785.510 

39} 

124.093 

1,225.420 

23} 

75.0057 

447.690 

31} 

99.7458 

791.732 

39} 

124.486 

1.233.1S8 

24 

75.3984 

452.390 

31} 

100.1385 

797.979 

39} 

124. 879 

1.240.981 

24} 

75.7911 

457.115 

32 

100.5312 

804.250 

39} 

125.271 

1.248.798 

24} 

76.1838 

461.864 

32} 

100.9239 

810.545 

40 

125.664 

1,256.640 

24f 

76.5765 

466.638 

32} 

101.3166 

816.865 

40} 

126.057 

1.264.510 

24} 

76.9692 

471.436 

32}  1 

101.7093 

823.210 

40} 

126.449 

1,272.400 

24} 

77.3619 

476.259 

32} 

102.1020 

829.579 

40} 

126.842 

1,280.310 

24} 

77.7546 

481.107 

32} 

102.4947 

835.972 

40} 

127.235 

1.288.250 

24} 

78.1473 

485.979 

32}  : 

102.8874 

842.391 

40} 

127.627 

1.296.220 

25 

78.5400 

490.875 

32} 

103.280 

848.833 

40} 

128.020 

1.304.210 

25} 

78.9327 

495.796 

33 

103.673 

855.301 

40} 

128.413 

1.312.220 

25} 

79.3254 

500.742 

33} 

104.065 

861.792 

41 

128.806 

1.320.260 

25} 

79.7181 

505.712 

33} 

104.458 

868.309 

41} 

129.198 

1.328.320 

25} 

80.1108 

510.706 

33} 

104.851 

874.850 

41} 

129.591 

1.336.410 

25} 

80.5035 

515.726 

33} 

105.244 

881.415 

41} 

129.984 

1.344.520 

25} 

80.8962 

520.769 

33} 

105.636 

888.005 

41} 

130.376 

1.352.660 

25} 

81.2889 

525.838 

33} 

106.029 

894.620 

41} 

130.769 

1.360.820 

26 

81.6816 

530.930 

33} 

106.422 

901.259 

41} 

131.162 

1,369.000 

26} 

82.0743 

536.048 

34 

106.814 

907.922 

41} 

131.554 

1,377.210 

26} 

82.4670 

541.190 

34} 

107.207 

914.611 

42 

131.947 

1,385.450 

26} 

82.8597 

546.356 

34} 

107.600 

921.323 

42} 

132.340 

1,393.700 

26} 

83.2524 

551.547 

34} 

107.992 

928.061 

42} 

132.733 

1,401.990 

26} 

83.6451 

556.763 

84} 

108.385 

934.822 

42} 

133.125 

1,410.300 

26} 

84.0378 

562.003 

34} 

108.778 

941.609 

42} 

133.518 

1,418.630 

26} 

84.4305 

567.267 

34} 

109.171 

948.420 

42} 

133.911 

1.426.990 

27 

84.8232 

572.557 

34} 

109.563 

955.255 

42} 

134.303 

1,435.370 

27} 

85.2159 

577.870 

35 

109.956 

962.115 

42} 

134.696 

1.443.770 

27} 

85.6086 

583.209 

35} 

110.349 

969.000 

43 

135.089 

1.452.200 

27} 

86.0013 

588.571 

35} 

110.741 

975.909 

43}  -! 

135.481 

1,460.660 

27} 

86.3940 

593.959 

35} 

111.134 

982.842 

43} 

135.874 

1.469.140 

27} 

86.7867 

599.371 

35} 

111.527 

989.800 

43} 

136.267 

1,477.640 

27} 

87.1794 

604.807 

35} 

111.919 

996.783 

43} 

136.660 

1,486.170 

27} 

87.5721 

610.268 

35} 

112.312 

1,003.790 

43} 

137.052 

1,494.730 

28 

87.9648 

615.754 

35} 

112.705 

1,010.822 

43} 

137.445 

1,503.300 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


563 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

43! 

44 
44| 
44! 
44! 
44! 
44! 
44! 
44! 

45 
45! 
45! 
45f 
45! 
45| 
45! 
45! 

46 
46! 
46! 
46f 
46! 
46f 
46! 
46! 

47 
47! 
47! 
47! 
47! 
47! 
47! 
47! 

48 
48! 
48! 
48! 
48! 
48! 
48! 
48! 

49 
49! 
49! 
49! 
49! 
49! 
49! 
49! 

50 
50! 
50! 
50! 
50! 
50! 
50! 
50! 

51 
51! 
51! 
51! 
51! 
51| 

137.838 

138.230 

138.623 

139.016 

139.408 

139.801 

140.194 

140.587 

140.979 

141.372 

141.765 

142.157 

142.550 

142.943 

143.335 

143.728 

144.121 

144.514 

144.906 

145.299 

145.692 

146.084 

146.477 

146.870 

147.262 

147.655 

148.048 

148.441 

148.833 

149.226 

149.619 

150.011 

150.404 

150.797 

151.189 

151.582 

151.975 

152.368 

152.760 

153.153 

153.546 

153.938 

154.331 

154.724 

155.116 

155.509 

155.902 

156.295 

156.687 

157.080 

157.473 

157.865 

158.258 

158.651 

159.043 

159.436 

159.829 

160.222 

160.614 

161.007 

161.400 

161.792 

162.185 

1,511.910 

1,520.530 

1,529.190 

1,537.860  ' 

1,546.56 

1,555.29 

1.564.04 
1,572.81 
1,581.61 
1,590.43 
1,599.28 
1,608.16 

1.617.05 
1,625.97 
1,634.92 

1.643.89 

1.652.89 
1,661.91 

1.670.95 
1,680.02 
1,689.11 
1,698.23 

1.707.37 

1.716.54 

1.725.73 

1.734.95 
1,744.19 

1.753.45 

1.762.74 

1.772.06 
1,781.40 
1,790.76 

1.800.15 
1,809.56 
1,819.00 

1.828.46 

1.837.95 

1.847.46 
1,856.99 

1.866.55 
1,876.14 

1.885.75 

1.895.38 
1,905.04 
1,914.72 
1,924.43 

1.934.16 
1,943.91 
1,953.69 
1,963.50 
1,973.33 
1,983.18 
1,993.06 

2.002.97 

2.012.89 

2.022.85 

2.032.82 

2.042.83 

2.052.85 

2.062.90 

2.072.98 
2,083.08 
2,093.20 

51! 

51! 

52 
52! 

52! 

52! 

52! 

52! 

52! 

52! 

53 
53! 

53! 

53! 

53! 

53! 

53! 

53! 

54 
54! 

54! 

54! 

54! 

54! 

54! 

54! 

55 
55! 
55! 
55! 
55!  | 
55! 
55! 
55! 

56 
56! 
56! 
56! 
56! 
56! 
56! 
56! 

57 
57! 
57! 
57! 
57! 
57! 
57! 
57! 

58 
58! 
58! 
58! 
58! 
58! 
58! 
58! 

59 
59! 
59! 
59! 
59! 

162.578 

162.970 

163.363 

163.756 

164.149 

164.541 

164.934 

165.327 

165.719 

166.112 

166.505 

166.897 

167.290 

167.683 

168.076 

168.468 

168.861 

169.254 

169.646 

170.039 

170.432 

170.824 

171.217 

171.610 

172.003 

172.395 

172.788 

173.181 

173.573 

173.966 

174.359 

174.751 

175.144 

175.537 

175.930 

176.322 

176.715 

177.108 

177.500 

177.893 

178.286 

178.678 

179.071 

179.464 

179.857 

180.249 

180.642 

181.035 

181.427 

181.820 

182.213 

182.605 

182.998 

183.391 

183.784 

184.176 

184.569 

184.962 

185.354 

185.747 

186.140 

186.532 

186.925 

2,103.35 

2.113.52 
2,123.72 
2,133.94 

2.144.19 
2,154.46 
2,164.76 
2,175.08 
2,185.42 
2,195.79 

2.206.19 
2,216.61 

2.227.05 

2.237.52 

2.248.01 

2.258.53 

2.269.07 

2.279.64 

2.290.23 
2,300.84 

2.311.48 
2,322.15 

2.332.83 
2,343.55 

2.354.29 

2.365.05 

2.375.83 

2.386.65 

2.397.48 
2,408.34 

2.419.23 
2,430.14 

2.441.07 
2,452.03 

2.463.01 

2.474.02 

2.485.05 
2,496.11 

2.507.19 

2.518.30 
2,529.43 
2,540.58 
2,551.76 

2.562.97 

2.574.20 
2,585.45 
2,596.73 

2.608.03 

2.619.36 
2,630.71 
2,642.09 
2,653.49 
2,664.91 

2.676.36 

2.687.84 
2,699.33 
2,710.86 
2,722.41 

2.733.98 
2,745.57 

2.757.20 

2.768.84 
2,780.51 

59! 

59! 

59! 

60 

60! 

60! 

60! 

60! 

60! 

60! 

60! 

61 

61! 

61! 

61! 

61! 

61! 

61! 

61! 

62 

62! 

62! 

62! 

62! 

62! 

62! 

62! 

63 
63! 
63! 
63! 
63! 
63! 
63! 
63! 

64 
64! 
64! 
64! 
64! 
64! 
64! 
64! 

65 
65! 
65! 
65! 
65! 
65! 
65! 
65! 

66 
66! 
66! 
66! 
66! 
66! 
66! 
66! 
67 
67! 
67! 
67! 

187.318 

187.711 

188.103 

188.496 

188.889 

189.281 

189.674 

190.067 

190.459 

190.852 

191.245 

191.638 

192.030 

192.423 

192.816 

193.208 

193.601 

193.994 

194.386 

194.779 

195.172 

195.565 

195.957 

196.350 

196.743 

197.135 

197.528 

197.921 

198.313 

198.706 

199.099 

199.492 

199.884 

200.277 

200.670 

201.062 

201.455 

201.848 

202.240 

202.633 

203.026 

203.419 

203.811 

204.204 

204.597 

204.989 

205.382 

205.775 

206.167 

206.560 

206.953 

207.346 

207.738 

208.131 

208.524 

208.916 

209.309 

209.702 

210.094 

210.487 

210.880 

211.273 

211.665 

2,792.21 

2,803.93 

2.815.67 
2,827.44 
2,839.23 
2,851.05 

2.862.89 
2,874.76 
2,886.65 

2.898.57 

2.910.51 

2.922.47 

2.934.46 

2.946.48 

2.958.52 

2.970.58 

2.982.67 
2,994.78 

3.006.92 
3,019.08 
3,031.26 

3.043.47 
3,055.71 
3,067.97 

3.080.25 

3.092.56 

3.104.89 

3.117.25 
3,129.64 
3,142.04 

3.154.47 

3.166.93 
3,179.41 
3,191.91 

3.204.44 
3,217.00 

3.229.58 

3.242.18 
3,254.81' 
3,267.46 
3,280.14 
3,292.84 

3.305.56 
3,318.31 
3,331.09 

3.343.89 
3,356.71 

3.369.56 

3.382.44 
3,395.33 
3,408.26 
3,421.20 

3.434.17 

3.447.17 

3.460.19 

3.473.24 
3,486.30 
3,499.40 
3,512.52 
3,525.66 
3,538.83 
3,552.02 

3.565.24 

564 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area.  | 

Diam. 

Circum. 

Area. 

m 

1 

212.058 

3,578.48 

75# 

236.798 

4,462.16 

83# 

261.538 

5,443.26 

67# 

212.451 

3,591.74 

75# 

237.191 

4,476.98 

83# 

261.931 

5,459.62 

67# 

212.843 

3,605.04 

75# 

237.583 

4,491.81 

83# 

262.324 

5,476.01 

67# 

213.236 

3,618.35 

75# 

237.976 

4,506.67 

83# 

262.716 

5,492.41 

68 

213.629 

3,631.69 

75# 

238.369 

4,521.56 

83# 

263.109 

5,508.84 

68# 

214.021 

3,645.05 

76 

238.762 

4,536.47 

83# 

263.502 

5,525.30 

68# 

214.414 

3,658.44 

76# 

239.154 

4,551.41 

84 

263,894 

5,541.78 

68# 

214.807 

3,671.86 

76# 

239.547 

4,566.36 

84# 

264.287 

5,558.29 

68# 

215.200 

3,685.29 

76# 

239.940 

4,581.35 

84# 

264.680 

5,574.82 

68 1 

215.592 

3,698.76 

76# 

240.332 

4,596.36 

84# 

265.072 

5,591.37 

68# 

215.985 

3,712.24 

76# 

240.725 

4,611.39 

84# 

265.465 

5,607.95 

68# 

216.378 

3,725.75 

76# 

241.118 

4,626.45 

84# 

265.858 

5,624.56 

69 

216.770 

3,739.29 

76# 

241.510 

4,641.53 

84# 

266.251 

5,641.18 

69# 

217.163 

3,752.85 

77 

241.903 

4,656.64 

84# 

266.643 

5,657.84 

m 

217.556 

3,766.43 

771 

242.296 

4,671.77 

85 

267.036 

5,674.51 

69# 

217.948 

3,780.04 

77# 

242.689 

4,686.92 

85# 

267.429 

5,691.22 

69# 

218.341 

3,793.68 

77# 

243.081 

4,702.10 

85# 

267.821 

5,707.94 

69# 

218.734 

3,807.34 

77# 

243.474 

4,717.31 

85# 

268.214 

5,724.69 

69| 

219.127 

3,821.02 

77# 

243.867 

4,732.54 

85# 

268.607 

5,741.47 

69# 

219.519 

3,834.73 

77# 

244.259 

4,747.79 

85# 

268.999 

5,758.27 

70 

219.912 

3,848.46 

77# 

244.652 

4,763.07 

85# 

269.392 

5,775.10 

70# 

220.305 

3,862.22 

78 

245.045 

4,778.37 

85# 

269.785 

5,791.94 

70# 

220.697 

3,876.00 

78# 

245.437 

4,793.70 

86 

270.178 

5,808.82 

701 

221.090 

3,889.80 

78# 

245.830 

4,809.05 

86# 

270.570 

5,825.72 

70# 

221.483 

3,903.63 

78# 

246.223 

4,824.43 

86# 

270.963 

5,842.64 

70# 

221.875 

3,917.49 

78# 

246.616 

4,839.83 

86# 

271.356 

5,859.59 

70# 

222.268 

3,931.37 

78# 

247.008 

4,855.26 

86# 

271.748 

5,876.56 

70# 

222.661 

3,945.27 

78# 

247.401 

4,870.71 

86# 

272.141 

5,893.55 

71 

223.054 

3,959.20 

78# 

247.794 

4,886.18 

86# 

272.534 

5,910.58 

71# 

t 

223.446 

3,973.15 

79 

248.186 

4,901.68 

86# 

272.926 

5,927.62 

71# 

223.839 

3,987.13 

79# 

248.579 

4,917.21 

87 

273.319 

5,944.69 

71# 

t 

224.232 

4,001.13 

79# 

248.972 

4,932.75 

87# 

273.712 

5,961.79 

71# 

\ 

224.624 

4,015.16 

79# 

249.364 

4,948.33 

87# 

274.105 

5,978.91 

71# 

\ 

225.017 

4,029.21 

79# 

249.757 

4,963.92 

87# 

274.497 

5,996.05 

71# 

\ 

225.410 

4,043.29 

79# 

250.150 

4,979.55 

87# 

274.890 

6,013.22 

71# 

225.802 

4,057.39 

79# 

250.543 

4,995.19 

87# 

275.283 

6,030.41 

72 

226.195 

4,071.51 

79# 

250.935 

5,010.86 

87# 

275.675 

6,047.63 

72- 

■ 

226.588 

4,085.66 

80 

251.328 

5,026.56 

87# 

276.068 

6,064.87 

72, 

226.981 

4,099.84 

80# 

251.721 

5,042.28 

88 

276.461 

6,082.14 

72 

■ 

227.373 

4,114.04 

80# 

252.113 

5,058.03 

88# 

276.853 

6,099.43 

72- 

• 

227.766 

4,128.26 

80# 

252.506 

5,073.79 

88# 

277.246 

6,116.74 

72 

■ 

228.159 

4,142.51 

80# 

252.899 

5,089.59 

88# 

277.629 

6,134.08 

72; 

. 

228.551 

4,156.78 

80# 

253.291 

5,105.41 

88# 

278.032 

6,151.45 

72 

228.944 

4,171.08 

80# 

253.684 

5,121.25 

88# 

278.424 

6,168.84 

73 

229.337 

4,185.40 

80# 

254.077 

5,137.12 

88# 

278.817 

6,186.25 

73# 

229.729 

4,199.74 

81 

254.470 

5,153.01 

88# 

279.210 

6,203.69 

73# 

230.122 

4,214.11 

81# 

254.862 

5,168.93 

89 

279.602 

6,221.15 

73# 

230.515 

4,228.51 

81# 

255.255 

5,184.87 

89# 

279.995 

6,238.64 

73; 

230.908 

4,242.93 

81# 

255.648 

5,200.83 

89# 

280.388 

6,256.15 

73# 

231.300 

4,257.37 

81# 

256.040 

5,216.82 

89# 

280.780 

6,273.69 

73# 

231.693 

4,271.84 

81# 

256.433 

5,232.84 

89# 

281.173 

6,291.25 

73 

i 

232.086 

4,286.33 

81# 

256.826 

5,248.88 

89| 

281.566 

6,308.84 

74 

232.478 

4,300.85 

81# 

257.218 

5,264.94 

89# 

281.959 

6,326.45 

74 

L 

232.871 

4,315.39 

82 

257.611 

5,281.03 

89# 

282.351 

6,344.08 

74; 

233.264 

4,329.96 

82# 

258.004 

5,297.14 

90 

282.744 

6,361.74 

74# 

233.656 

4,344.55 

82# 

258.397 

5,313.28 

90# 

283.137 

6,379.42 

74 

234.049 

4,359.17 

82# 

258.789 

5,329.44 

90# 

283.529 

6,397.13 

74# 

234.442 

4,373.81 

82# 

259.182 

5,345.63 

90# 

283.922 

6,414.86 

74# 

234.835 

4,388.47 

82# 

259.575 

5,361.84 

90# 

284.315 

6,432.62 

74- 

i 

235.227 

4,403.16 

82# 

259.967 

5,378.08 

90# 

284.707 

6,450.40 

75 

235.620 

4,417.87 

82# 

260.360 

5,394.34 

90# 

285.100 

6,468.21 

• 75 

i 

236.013 

4,432.61 

83 

250.753 

5,410.62 

90# 

285.493 

6,486.04 

75# 

236.405 

4,447.38 

83# 

261.145 

5,426.93 

91 

285.886 

6,503.90 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


565 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area.  J 

91* 

91* 

91* 

91* 

91* 

91* 

91* 

92 
92* 
92* 
92* 
92* 
92* 
92* 
92* 

93 
93* 
93£ 
93* 
93* 
93* 
93* 
93* 

94 

286.278 

286.671 

287.064 

287.456 

287.849 

288.242 

288.634 

289.027 

289.420 

289.813 

290.205 

290.598 

290.991 

291.383 

291.776 

292.169 

292.562 

292.954 

293.347 

293.740 

294.132 

294.525 

294.918 

295.310 

6.521.78 

6.539.68 
6,557.61 

6.575.56 

6.593.54 

6.611.55 

6.629.57 
6,647.63 
6,665.70 
6,683.80 
6,701.93 
6,720.08 
6,738.25 
6,756.45 

6.774.68 

6.792.92 
6,811.20 
6,829.49 
6,847.82 
6,866.16 
6,884.53 

6.902.93 
6,921.35 

6.939.79 

94* 

94* 

94* 

94* 

94* 

94* 

94* 

95 
95* 
95* 
95* 
95* 
95* 
95* 
95* 

96 
96* 
96* 
96* 
96* 
96* 
96* 
96* 

97 

295.703 

296.096 

296.488 

296.881 

297.274 

297.667 

298.059 

298.452 

298.845 

299.237 

299.630 

300.023 

300.415 

300.808 

301.201 

301.594 

301.986 

302.379 

302.772 

303.164 

303.557 

303.950 

304.342 

304.735 

6,958.26 

6,976.76 

6,995.28 

7.013.82 
7,032.39 

7.050.98 

7.069.59 

7.088.24 

7.106.90 

7.125.59 
7,144.31 
7,163.04 
7,181.81 

7.200.60 
7,219.41 

7.238.25 
7,257.11 

7.275.99 

7.294.91 
7,313.84 
7,332.80 

7.351.79 

7.370.79 

7.389.83 

97* 

97* 

97* 

97* 

97* 

97* 

97* 

98 
98* 
98* 
98* 
98* 
98* 
98* 
98* 

99 
99* 
99* 
99* 
99* 
99* 

• 99* 
99* 
100 

305.128 

305.521 

305.913 

306.306 

306.699 

307.091 

307.484 

307.877 

308.270 

308.662 

309.055 

309.448 

309.840 

310.233 

310.626 

311.018 

311.411 

311.804 

312.196 

312.589 

312.982 

313.375 

313.767 

314.160 

7,408.89 

7.427.97 
7,447.08 

7.466.21 

7.485.37 
7,504.55 
7,523.75 

7.542.98 
7,562.24 
7,581.52 
7,600.82 

7.620.15 
7,639.50 
7,658.88 
7,678.28 
7,697.71 

7.717.16 
7,736.63 
7,756.13 
7,775.66 

7.795.21 
7,814.78 

7.834.38 
7,854.00 

The  preceding  table  may  be  used  to  determine  the  diameter  when 
the  circumference  or  area  is  known.  Thus,  the  diameter  of  a circle  haying 
an  area  of  7,200  sq.  in.  is  approximately  95*  in. 


A GLOSSARY  OF  MINING  TERMS. 

The  present  glossary  is  a combination  of  glossaries  of  mining  terms  con- 
tained in  the  following  works:  Coal  and  Metal  Miners’  Pocketbook,  Fifth 
Edition;  Raymond’s  Glossary  of  Mining  and  Metallurgical  Terms;  Powers 
Pocketbook  for  Miners  and  Metallurgists;  Locke’s  Miners  ? Pocketbook; 
Vol  AC,  Second  Pennsylvania  Geological  Survey;  Ilhseng  s Manual  ot 
Mining;  Chism’s  Encyclopedia  of  Mexican  Mining  Law;  a Glossary  of  Terms 
as  Used  in  Coal  Mining,  by  W.  S.  Gresley;  11th  Annual  Report  of  the  State 
Mine  Inspector  of  Missouri;  Bullman’s  Colliery  Working  and  Management 
Reynolds’  Handbook  of  Mining  Laws;  Report  of  the  Mine  Inspector  of 
Tennessee  for  1897;  Smithsonian  Report  for  1886;  together  with  a large  num- 
ber of  words  which  have  been  added  from  various  stray  sources  It  is 
impossible  to  quote  the  authority  for  each  definition,  as  many  of  the  defini- 
tions are  combinations  from  a number  of  authors.  Where  such  different 
definitions  have  given  distinctly  different  meanings  each  one  has  been 
included,  but  where  there  has  been  expressed  merely  a slight  shade  of 
difference,  the  definition  agreeing  most  closely  with  current  American 
practice  has  been  taken,  or  else  modified  to  suit  such  .practice.  The  foreign 
words  selected  are  those  with  which  an  American  is  most  likely,  to  come 
in  contact,  and  this  portion  of  the  glossary  is,  of  course,  not  exhaustive.  For 
the  large  number  of  purely  local  terms  used  m the  several  coal  fields  of  Great 
Britain,  the  reader  is  referred  to  Mr.  Gresley’s  glossary. 


566 


Aba 


GLOSSARY. 


Air 


GLOSSARY. 


Abattis  (Leicester).— Cross-packing  of  branches  or  rough  wood,  used  to  keep 
roads  open  for  ventilation. 

Abra  (Spanish).— Fissure  in  a lode,  unfilled  or  only  partially  filled. 

Abronziado  ( Spanish ) .—Copper  sulphides. 

Absolute  Pressure—  The  pressure  reckoned  from  a vacuum. 

Absolute  Temperature.—' The  temperature  reckoned  from  the  absolute  zero, 
—459.2°  F.  or  —273°  C. 

Accompt  (Cornish).— Settling  day  or  place. 

Achicar  (Mexican).— To  diminish  the  quantity  of  water  in  any  gallery  or 
working,  generally  by  carrying  it  out  in  buckets  or  in  leather  bags. 
Achicadores  — Laborers  employed  for  said  purpose.  Achichinques.— Same 
as  Achicadores.  Also  applied  to  hangers-on  about  police  courts,  etc. 
Such  people  as  are  generally  called  strikers  in  the  United  States. 

Acreage  Rent  (English).— Royalty  or  rent  for  working  minerals. 

Adarme  (Mexican).— A weight  for  gold,  about  1.8  grams. 

Addlings  (North  of  England).— Earnings. 

Ademador  ( Spanish)  .—Mine  carpenter,  or  timberman. 

Ademar  (Spanish). — To  timber.  . 

Adit— A nearly  horizontal  passage  from  the  surface,  by  which  a mine  is 
entered  and  unwatered  with  just  sufficient  slope  to  insure  drainage. 
In  the  United  States,  an  adit  driven  across  the  measures  is  usually  called 
a tunnel,  though  the  latter,  strictly  speaking,  passes  entirely  through  a 
hill,  and  is  open  at  both  ends. 

Adobe.— Sun-dried  brick. 

Adventurers—  Original  prospectors. 

Adverse— To  oppose  the  granting  of  a patent  to  mining  claim. 

Adze. — A curved  cutting  instrument  for  dressing  timber. 

Aerage  (French).— Ventilation. 

Aerometers.— The  air  pistons  of  a Struve  ventilator. 

Aerophore—  The  name  given  to  an  apparatus  that  will  enable  a man  to  enter 
places  in  mines  filled  with  explosive  or  other  deadly  gases,  with  safety. 

Afinar  (Mexican).— Refining  gold  and  silver. 

Afterdamp—  The  gaseous  mixture  resulting  from  an  explosion  of  firedamp. 

Agent—  The  manager  of  a mining  property. 

Agitator— A mechanical  stirrer  used  in  pan  amalgamation. 

Ahondar  (Spanish).— To  sink. 

Air  —The  current  of  atmospheric  air  circulating  through  and  ventilating  the 
workings  of  a mine. 

Air  Box. — Wooden  tubes  used  to  convey  air  for  ventilating  headings  or 
sinkings  or  other  local  ventilation. 

Air  Compartment— An  air-tight  portion  of  any  shaft,  winze,  rise,  or  level, 
used  for  improving  ventilation. 

Air-Course—  See  Airway. 

Air  Crossing— A bridge  that  carries  one  air-course  over  another. 

Air  Cushion— A spring  caused  by  confined  air. 

Air  Door.— A door  for  the  regulation  of  currents  of  air  through  the  workings 
of  a mine.  „ , . , . , 

Air-End  Way  (Locke).— Ventilation  levels  run  parallel  with  mam  level. 

Air  Furnace. — A reverberatory  furnace  in  which  to  smelt  lead. 

Air  Gates  (Locke).— (l)  Underground  roadways,  used  principally  for  venti- 
lating purposes.  (2)  An  air  regulator. 

Air  Head  (Staff).— Ventilation  ways. 

Air  Heading— An  airway.  . 

Air  Hole  (Powers). — A hole  drilled  in  advance  to  improve  ventilation  by 
communication  with  other  workings  or  the  surface. 

Airless  End.— The  extremity  of  a stall  in  longwall  workings  in  which  there 
is  no  current  of  air,  or  circulation  of  ventilation,  but  which  is  kept  pure 
by  diffusion  and  by  the  ingress  and  egress  of  cars,  men,  etc. 


AIR 


GLOSS  AR  Y. 


Aqu 


567 


Air  Level— A.  level  or  airway  of  former  workings  made  use  of  in  subsequent 
deeper  mining  operations  for  ventilating  purposes. 

Air  Oven  —A  heated  chamber  for  drying  samples  of  ore,  etc. 

Air  Five  —A  pipe  made  of  canvas  or  metal,  or  a wooden  box  used  in  con- 
A veying  airPto  the  workmen,  or  for  rock  drills  or  air  locomotives. 
Air-Shaft.— A shaft  or  pit  used  expressly  for  ventilation. 

Air  Slit  (Yorks). — A short  head  between  other  air  heads.  . , 

Air  Sollar .-A  brattice  carried  beneath  the  tram  rails  or  road  bed  in  a head- 

Air  ^Stnclf.—A  Sack  or  chimney  built  over  a shaft  for  ventilation. 

Airway— Any  passage  through  which  air  is  carried. 

Aitch  Piece—  Parts  of  a pump  in  which  the  valves  are  fixed. 

Albanil  (Spanish).— Mason. 

AWerU^rnac^— ^continuous  reverberatory  for  mercury  ores. 

Alcam  (Wales).— Tin. 

jllloy  homogeneous  mixture  of  two  or  more  metals  by  fusion. 

Alluvial  Gold—  Gold  found  associated  with  water- worn  material. 

Alluvium. — Gravel,  sand,  and  mud  deposited  by  streams. 

Almadeneta  (Spanish).— Stamp  head. 

AUern^m^^^nl—Y^^  down,  or  backward  and  forward  motion. 

Alto  ( Mexican)  —The  hanging  wall  of  a vein.  See  Respaldos. 

Aludel  (Spanish).— Earthen  condenser  for  mercury 
Amalgam.- An  alloy  of  quicksilver  with  some  other  metal. 

Amalgamation. — Absorption  of  gold  and  silver  by  mercury. 

Amalgamator.— One  that  amalgamates  gold  and  silver  ores. 

Ana^is?— The  dttSminatio^of  the  original  elements  and  the  proportions 

Anemometer^—  An  instrument  used  for  measuring  the  velocity  of  a ventilating 

An^Beam  — A two-limbed  beam  used  for  turning  angles  in  shafts,  etc. 

heating  and  then  cooling 

Anth^iU- Coal  containing  a small  percentage  of  volatile  matter 
Anticline.- A flexure  or  fold  in  which  the  rock s on  the  °fPff)sl{|tf 

fold  dip  awav  from  each  other,  like  the  two  legs  ot  tne  letter  a.  ±iie 
inclination  on  one  side  may  be  much  greater  than  on n&e n^PwSh  sides 
An  anticlinal  is  said  to  be  overturned  when  the  rocks  on  both  sides 

a saddle  in  a mineral  vein,  or  the  line  along 
the  summit  of  a vein,  from  which  the  vein  dips  in  opposite  directions. 
Anticlinal  Flexure:  Anticlinal  Fold. — An  anticline.  < . . 

Antiauos  Los  (Mexican).— The  Spanish  or  Indian  miners  of  colonial  times. 
Antimony  Star.— The  metal  antimony  when  crystallized,  showing  fern-like 

that  rewash  or  rework  tailings  from  silver 

^pcros^exican)8-^!' kinds^miningiupplies  in  general.  Aperador.-A 

Apex™ TheeePlinding  point  at  the  top  of  a slope  or  incHned  plane  the 
knuckle;  also,  the  top  of  an  anticlinal.  In  the  U.  S.  Revised  statutes, 
the  end  or  edge  of  a vein  nearest  the  surface. 

A pique  (Mexican).— Perpendicular. 

Apolvillados  (Spanish). — Superior  ores.  a «nir- 

Anrnn  (English)  — (1)  A covering  of  timber,  stone,  or  metal,  .to  protect  a sur 
^Pr?ace  a^ainst  the  actionof  water  flowing’over  it.  (2)  A hinged  extension 
to  a loading  chute. 

Aprons . — Stamp-battery  copper  plates. 

Aqua  Fortis. — Nitric  acid.  * . _ ..  . . . 

Aqua  Regia— A mixture  of  hydrochloric  acid  and  nitric  acid. 

Aqueduct—  An  artificial  elevated  way  for  carrying  water. 


568 


Ara 


GLOSSARY. 


AZO 


Arajo  (Mexican).— See  Hatajo. 

Arch  (Cornish).— Portion  of  lode  left  standing  to  support  hanging  wall,  or 
because  too  poor. 

Archean.— An  early  period  of  geological  time. 

Arching—  Brickwork  or  stonework  forming  the  roof  of  any  underground 
roadway. 

Arenaceous. — Sandy;  rocks  are  arenaceous  when  they  contain  a considerable 
percentage  of  sand. 

Arends  Tap—  An  inverted  siphon  for  drawing  molten  lead  from  a crucible 
or  furnace.  ) 

Arenillas  (Spanish). — Refuse  earth. 

Argentiferous. — Silver-bearing. 

Argillaceous. — Clayey;  rocks  are  argillaceous  when  they  contain  a consid- 
erable percentage  of  clay,  or  have  some  of  the  characteristics  of  clay. 

Argol. — Crude  tartar  deposited  from  wine. 

Arian  (Wales).— Silver. 

Arm. — The  inclined  leg  of  a set  of  timber. 

Arrage  (North  England).— Sharp  corner. 

Arrastre. — A circular  trough  in  which  drags  are  pulled  round  by  being  con- 
nected with  a central  revolving  shaft  by  an  arm  and  chain.  Used  for 
grinding  and  amalgamating  ores.  Arrastre  de  cuchara , spoon  arrastre; 
de  marca,  large  arrastre;  de  mula,  mule-power  arrastre. 

Arvastrar  (Mexican).— To  drag  along  the  ground.  Arrastrar  el  Agua.— To 
almost  completely  exhaust  the  water  in  a sump  or  working. 

Arroba  (Mexican). — 25  lb. 

Artesian  Well. — An  artificial  channel  of  escape,  made  by  a bore  hole,  for  a 
subterranean  stream,  subject  to  hydrostatic  pressure. 

Ascensional  Ventilation. — The  arrangement  of  the  ventilating  currents  in 
such  a manner  that  the  air  shall  continuously  rise  until  reaching  the 
bottom  of  the  upcast  shaft.  Particularly  applicable  to  steep  seams. 

Ashlar.— A facing  of  cut  stone  applied  to  a backing  of  rubble  or  rough 
masonry  or  brickwork. 

Aspirail  (French).— Opening  for  ventilation. 

Assay.— The  determination  of  the  quality  and  quantity  of  any  particular 
substance  in  a mineral.  Assayer. — One  who  performs  assays. 

Assessment  Work. — The  annual  work  necessary  to  hold  a mining  claim. 

Astel. — Overhead  boarding  in  a gallery. 

Astyllen  (Cornish).— Small  dam  in  an  adit;  partition  between  ore  and  deads 
on  grass. 

.itacador  (Mexican).— A tamping  bar  or  tamping  stick. 

Atecas  (Mexican).— Same  as  Achicadores , etc. 

Atierres  (Spanish).— Refuse  rock  or  dirt  inside  a mine. 

Attle  (Cornish). — Refuse  rock. 

Attle  {Addle). — The  waste  of  a mine. 

Attrition. — The  act  of  wearing  away  by  friction. 

Auger  Stem.— The  iron  rod  or  bar  to  which  the  bit  is  attached  in  rope  drilling. 

Auget. — Priming  tube. 

Aur  (Wales).— Gold. 

Auriferous. — Gold-bearing. 

Ausscharen  (German).— Junction  of  lodes. 

Auszimmern  ( German) . — Timbering. 

Average  Produce  (Cornish). — Percentage  of  fine  copper  in  ore. 

Average  Standard  (Cornish). — Price  of  pure  copper  in  ore. 

Aviador  (Spanish). — One  who  provides  the  capital  to  work  a mine. 
Avio. — Money  furnished  to  the  proprietors  of  a mine  to  work  the  mine, 
by  another  person,  the  Aviador.  Avio  Contract. — A contract  between 
two  parties  for  working  a mine  by  which  one  of  the  parties,  the  aviador , 
furnishes  the  money  to  the  proprietors  for  working  the  mine. 

Axis. — An  imaginary  line  passing  through  a body  that  may  be  supposed  to 
revolve  around  it. 

Azimuth—  The  azimuth  of  a body  is  that  arc  of  the  horizon  that  is  included 
between  the  meridian  circle  at  the  given  place  and  a vertical  plane 
passing  through  the  body.  It  is  always  measured  from  due  north  around 
to  the  right. 

Azogue  (Spanish). — Mercury.  Azogueria. — Amalgamating  works.  Azoguero. 
Amalgamator.  The  person  in  charge  of  a patio  works.  Azogues—  Free 
milling  ores. 

Azoic.— The  age  of  rocks  that  were  formed  before  animal  life  existed. 


Bac 


GLOSSARY. 


Ban 


569 


Back. — (1)  A plane  or  cleavage  in  coal,  etc.,  having  frequently  a smooth 
parting  and  some  sooty  coal  included  in  it.  (2)  The  inner  end  of  a 
heading  or  gangway.  (3)  To  throw  back  into  the  gob  or  waste  the  small 
slack,  dirt,  etc. g (4)  To  roll  large  coals  out  of  a waste  for  loading  into  cars. 
Back  Balance.— A self-acting  incline  m the  mnie^wherea  glance  caranda 
carriage  in  which  the  mine  car  is  placed  are  used.  The  loaded  car  upoA. 
the  carriage  will  hoist  the  balance  car,  and  the  balance  car  will  hoist  the 

Backbye^WorL— Wor^done  between  the  shaft  and  the  working  face,  in 
contradistinction  to  face  work,  or  work  done  at  the  face.  .f 

Back  Casing.— A wall  or  lining  of  dry  bricks  used  m ®^1?ftthr^fhQ£1 
deposits,  the  permanent  walling  being  built  up  within  it.  The  use  oi 
timber  cribs  and  planking  serves  the  same  purpose. 

Back  End  (England). -The  last  portion  of  a jud. 

Backina.—(  1)  The  rough  masonry  of  a wall  faced  with  finer  work.  (2)  Eartn 
deposited  behind  a retaining  wall,  etc.  (3)  Timbers  let  into  notches  m 
the  rock  across  the  top  of  a level.  , . , - Plirh„  fnr 

Backing  Deals—  Deal  boards  or  planking  placed  at  the  back  of  curbs  tor 
supporting  the  sides  of  a shaft  that  is  liable  to  run. 

Back  Joint. — Joint  plane  more  or  less  parallel  to  the  strike  of  the  cleavage, 

BaddasA— {!)  Backward  suction  of  air-currents  produced  after  an  explosion 
of  firedamp.  (2)  Reentry  of  air  into  a fan.  , . 

Back  of  Ore.— The  ore  between  two  levels  which  has  to  be  worked  from  the 

Back  Pressured—  The  loss,  expressed  in  pounds  per  square  inch,  due  to  getting 
the  steam  out  of  the  cylinder  after  it  has  done  its  work. 

Back  Shift—  Afternoon  shift.  , . . . 

Back  Skin  (North  of  England). -A  leather  jacket  for  wet  workings. 
Backstay.— A wrought-iron  forked  bar  attached  to  the  back  of  pars  when 
ascending  an  inclined  plane,  which  throws  them  off  the  rails  if  the  rope 

BaffEnds^— Long  wooden  edges  for  adjusting  linings  in  sinking  shafts  dur- 
ing the  operation  of  fixing  the  lining. 

Baffle— To  brush  out  firedamp. 

Bait.—  Provisions.  _ , _ 

Bajo  (Mexican).— The  footwall  of  a vein.  See  Respaldo. 

B alance.— 0*)  The  counterpoise  or  weights  attached  to  the 

engine,  to  assist  the  engine  m lifting  the  load  out  of  a shaft  bottom  and 
in  helping  it  to  slacken  speed  when  the  cage  reaches  the  surface,  it 
consists  often  of  a bunch  of  heavy  chains  suspended  in  a shallow  shaft, 
the  chains  resting  on  the  shaft  bottom  as  unwound  off  the  balance  drum 
attached  to  the  main  shaft  of  the  engine.  (2)  Scales  used  in  chemical 

, Balance  ^Bob .^A  farge  beam  or  lever  attached  to  the  main  rods  of  a Cornisb 
pumping  engine,  carrying  on  its  outer  end  a counterpoise. 

Balance  Box.— A large  box  placed  on  one  end  of  a balance  bob  and  fillea 
with  old  iron,  rock,  etc.  to  counterbalance  the  weight  of  pump  rods 
Balance  Brow.— An  inclined  plane  in  steep  seams  on  which  a platform  on 
wheels  travels  and  carries  the  cars  of  coal. 

Balance  Car.— A small  weighted  truck  mounted  upon  a short  inchnM  track, 
and  carrying  a sheave  around  which  the  rope  of  an  endless  haulage 
system  passes  as  it  winds  off  the  drum. 

Balance  Pit.— A pit  or  shaft  in  which  a balance  rises  or  falls. 

Balanzon  (Mexican). -The  balance  bob  of  a Cornish  pump 
Balk  _(i)  a more  or  less  sudden  thinning  out  of  a seam  of  coal.  (2)  irregu- 
lar-shaped masses  of  stone  intruding  into  a coal  seam,  or  bulgings  out 
of  the  stone  roof  into  the  seam.  (3)  A bar  of  timber  supporting  the  roof 
of  a mine,  or  for  carrying  any  heavy  load. 

Balland  (Derbyshire). — Pulverulent  lead  ore.  . ,D 

Ballast.— Broken  stone,  gravel,  sand,  etc.  used  for  keeping  railroad  ties  stead, . 
Bancos  (Spanish) .—Horses  in  a vein  or  cross-courses.  # 

Band.— A seam  or  thin  stratum  of  stone  or  other  refuse  in  a seam  of  coal. 
Bank.—(  1)  The  top  of  the  shaft,  or  out  of  the  shaft.  (2)  The  surface  around 
the  mouth  of  a shaft.  (3)  To  manipulate  coals,  etc.  on  the  bant. 
(4)  The  whole  or  sometimes  only  one  side  or  one  end  of  a worxm& 
place  underground.  (5)  A large  heap  of  mineral  on  the  surface. 


570 


Ban 


GLOSSARY. 


Bas 


Bank  Chain— A chain  that  includes  the  bank  of  a river  or  creek. 

Bank  Claim  (Australian).— Mining  right  on  bank  of  stream. 

Banket. — Auriferous  conglomerate  of  South  Africa. 

Bank  Head. — The  upper  end  of  an  inclined  plane,  next  to  the  engine  or  drum, 
made  nearly  level. 

Bank  Right  (Australian). — Right  to  divert  water  to  bank  claim. 

Banksman.— The  man  in  attendance  at  the  top  of  the  shaft,  superintending 
the  work  of  banking. 

Bankwork.—A  system  of  working  coal  in  South  Yorkshire. 

Bank  to  Bank. — A shift. 

Bannocking. — See  Kirving. 

Bano  (Spanish).— Excess  of  mercury  used  in  torta. 

Bar— A length  of  timber  placed  horizontally  for  supporting  the  roof.  In 
some  cases,  bars  of  wrought  iron,  about  3 in.  X 1 in.  X 5 ft.  are  used. 

Bar  Diggings. — (1)  River  placers  subject  to  overflow.  (2)  Auriferous  claims 
on  shallow  streams. 

Bargain.— Portion  of  mine  worked  by  a gang  on  contract. 

Barilla  (Spanish).— Grains  of  native  copper  disseminated  through  ores. 

Baring.— See  Stripping. 

Barmaster  (Derbyshire) — Mine  manager,  agent,  and  engineer. 

Bar  Mining.— The  mining  of  river  bars,  usually  between  low  and  high  water, 
although  the  stream  is  sometimes  deflected  and  the  bar  worked  below 
water  level. 

Barney.— A small  car,  used  on  inclined  planes  and  slopes  to  push  the  mine 
car  up  the  slope.  Barney  Pit.— A pit  at  the  bottom  of  a slope  or  plane 
into  which  the  barney  runs  to  allow  the  mine  car  to  pass  over  it. 

Barra  (Mexican).— (1)  A bar,  as  of  gold,  silver,  iron,  steel,  etc.  (2)  A cer- 
tain share  in  a mine.  The  ancient  Spanish  laws,  from  time  immemorial, 
considered  a mine  as  divided  into  24  parts,  and  each  part  was  called  a 
“ barra.” 

Barra  Viuda,  or  Aviada  (Mexican).— These  are  “ barras  ” or  shares  that  par- 
ticipate in  the  profits,  but  not  in  the  expenses,  of  mining  concerns. 
Their  share  of  the  expenses  is  paid  by  the  other  shares.  Non-assessable 
shares. 

Barranca  (Mexican).— A ravine,  a gulch.  What  is  improperly  called  in  the 
United  States  a canyon  or  canon. 

Barrel  Amalgamation. — Amalgamating  ores  in  revolving  barrels. 

Barrel  Work. — (1)  Native  copper  that  can  be  hand-sorted  ready  for  smelt- 
ing. (2)  Barrel  amalgamation. 

Barrena  (Mexican).— A hand  drill  for  opening  holes  in  rocks  for  blasting 
purposes. 

Barrenarse  (Mexican).— When  two  mines  or  two  workings  (as  a shaft  or 
winze,  or  a gallery)  communicate  with  each  other. 

Barren  Ground—  Strata  unproductive  of  seams  of  coal,  etc.  of  a workable 
thickness. 

Barreno  (Mexican)  .—(1)  A drill  hole  for  blasting  purposes.  In  mechanics,  any 
bored  hole.  (21  A communication  between  two  mines  or  two  workings. 

Barretero  (Mexican).— A miner  of  the  first  class;  one  that  knows  how  to 
point  his  holes,  drill,  and  blast,  or  work  with  a gad. 

Barrier  Pillar— A solid  block  or  rib  of  coal,  etc.,  left  unworked  between  two 
collieries  or  mines  for  security  against  accidents  arising  from  influx  of 
water. 

Barrier  System. — The  method  of  working  a colliery  by  pillar  and  stall,  where 
solid  ribs  or  barriers  of  coal  are  left  in  between  a set  or  series  of  working 
places. 

Barrow—  (1)  A box  with  two  handles  at  one  end  and  a wheel  at  the  other. 
(2)  Heap  of  waste  stuff  raised  from  a mine;  a dump. 

Bar  Timbering. — A system  of  supporting  a tunnel  roof  by  long  top  bars, 
while  the  whole  lower  tunnel  core  is  taken  out,  leaving  an  open  space 
for  the  masons  to  run  up  the  arching.  Under  certain  conditions,  the 
bars  are  withdrawn  after  the  masonry  is  completed,  otherwise  they  are 
bricked  in  and  not  drawn. 

Base  Bullion. — Lead  combined  with  precious  metals. 

Base  Metal.— Metal  not  classed  with  the  precious  metals,  gold,  silver,  plat- 
inum, etc.,  that  are  not  easily  oxidized. 

Basin. — (1)  A coal  field  having  some  resemblance  in  form  to  a basin.  (2) 
The  synclinal  axis  of  a seam  of  coal  or  stratum  of  rock 

Basket.— A measure  of  weight  = 2 cwt. 


Bas 


GLOSSARY. 


Ben 


571 


Basque.— Crucible  or  furnace  lining. 

Bass  (Derbyshire).— Indurated  clay. 

Basset— Outcrop  of  a lode  or  stratum. 

Rastard A particularly  hard  massive  rock  or  boulder. 

Batch.— An  assorted  parcel  of  ore,  sometimes  called  doles,  when  divided 
into  equal  quantities.  , , 

rtnfpn A shallow  wooden  bowl  used  for  washing  out  gold,  etc. 

Batt  (English).— (1)  A highly  bituminous  shale  found  in  the  coal  measures. 
(2)  Hardened  clay,  but  not  fireclay.  Same  as  Bend  and  Bind. 

Ratten A niece  of  thin  board  less  than  12  in.  m width.  . 

Batter. — The  inclination  of  a face  of  masonry  or  of  any  inclined  portion  of 

BaUeriL—O- )° ^structure  built  to  keep  coal  from  sliding  down  a chute  or 
breast.  (2)  An  embankment  or  platform  on  which  miners  work.  (3) 

i^a^An^pen^pace  for  waste  between  two  packs  in  a longwall  working. 

I «£•  °r  phiatirT- 

Beans  (Nortl?  of  England)  .—All  coal  that  will  pass  through  about  9 
screen 

Bean  Shot.— Copper  granulated  by  pouring  into  hot  water. 

jipar A denosit  of  iron  at  the  bottom  of  a furnace.  ^ . , , , 

Bear;  to  Bear  In— Underholding  or  undermining;  driving  m at  the  top  or  at 

BeJern  -Pieces  of’ttaber  3 or  4 ft.  longer  than  the  breadth  of  a shaft, 
which  are  fixed  into  the  solid  rock  at  the  sides  at  certain  intervals  apart, 

BeaZg-d The  span  or  length  in  the  clear 
between  the  points  of  support  of  a beam,  etc.  (3)  The  points  of  support 

Bernina  JoT-AdoOT  placid  for  the  purpose  of  directing  and  regulating  the 
amount  If  ventilation  passing  through  an  entire  district  of  a mine. 
Bearing  In.— The  depth  or  distance  under  of  the  undercut  or  holing. 
BmHng-up Pulley.-k  pulley  wheel  fixed  in  a frame  and  arranged  to  tighten 
ud  or  take  up  the  slack  rope  in  endless-rope  haulage.  . 

Bearmg-up  Stop.— A partition  of  brattice  or  plank  that  serves  to  conduct  air 

to  a face. 

means  of  wedges  and  sledge  hammers 
Bed  — (i)  The  level  surface  of  a rock  upon  which  a curb  or  crib  is  laid.  (2)  A 

Bed^^^S^Austraii^)!— Ilciaim^th^includes  the  bed  of  a river  or  creek. 

Bednlate  —A  large  plate  of  iron  used  as  a foundation  for  an  engine. 

Bed-Rock. — The  f olid  rock  underlying  the  soil,  drift,  or  alluvial  deposits. 

of  “ the 

form,  disconnected  from  the 

5eid^-A°form  of  lead  poisoning  to  which  lead  miners  are  subject. 
rpJIv  — a swelling  mass  of  ore  in  a lode.  „ , . _ 

Ben,'  Benhayl  (Cornish).— Productive.  The  productive  portion  of 

Bench^—i 1)  A natural  terrace  marking  the  outcrop  of  any  stratum. 

stratum  of  coal  forming  a portion  of  the  vein. 

Bench  Diaaings.—  River  placers  not  subject  to  overnow.  , ,.  . 

Benching'.— Yo  break  up  with  wedges  the  bottom  coals  when  the  holing  is 

done  in  the  middle  of  the  seam.  * , 

Benching  Up  (North  of  England). -Working  on  top  of  coal. 

Bench  Mark.— A mark  cut  in  a tree  or  rock  whose  elevation  is  known.  Used 
bv  surveyors  for  reference  in  determining  elevations.  , ■»  . 

Bench  Working.—1 The  system  of  working  one  or  more  seams  or  beds  ot 
mineral  bv  open  working  or  stripping,  m stages  or  steps. 

Bend  (Derbyshire).— Indurated  clay.  _ +i,0 

Beneficiar  (Mexican).— To  treat  ores  for  the  purpose  of  extracting  the 

metallic  contents. 


a tin 
(2)  A 


572 


Ben 


GLOSSARY. 


Blo 


Beneficio  (Mexican).— Any  metallurgical  process. 

Benheyl  (Cornish).— Flowing  tin  stream. 

Bessemer  Steel—  Steel  made  by  the  Bessemer  process. 

Beton  (English).— Concrete  of  hydraulic  cement  with  broken  stone,  bricks, 
gravel,  etc. 

Bevel.— The  slope  formed  by  trimming  away  on  edge. 

Bevel  Gear.— A gear-wheel  whose  teeth  are  inclined  to  the  axis  of  the  wheel. 

Biche  — A hollow-ended  tool  for  recovering  boring  rods. 

Billy  Boy. — A boy  who  attends  a Billy  Playfair. 

Billy  Playfair.— A mechanical  contrivance  for  weighing  coal,  consisting  of 
an  iron  trough  with  a sort  of  hopper  bottom,  into  which  all  the  small 
coal  passing  through  the  screen  is  conducted  and  weighed  off  and 
emptied  from  time  to  time. 

Bin.— A box  with  cover,  used  for  tools,  stones,  ore,  etc. 

Bind,  or  Binder—  Indurated  argillaceous  shales  or  clay,  very  commonly 
forming  the  roof  of  a coal  seam  and  frequently  containing  clay  iron- 
stone. See  Batt. 

Binding.— Hiring  men. 

Bing  (North  of  England).— 8 cwt.  of  ore. 

Bing  Hole  (Derbyshire). — An  ore  shoot. 

Bing  Ore  (Derbyshire).— Lead  ore  in  lumps. 

Bing  Tale  (North  of  England).— Ore  given  to  the  miner  for  his  labor. 

Bit— A piece  of  steel  placed  in  the  cutting  edge  of  a drill  or  point  of  a pick. 

Blackband  — Carbonaceous  ironstone  in  beds,  mingled  with  coaly  matter 
sufficient  for  its  own  calcination. 

Black  Batt,  or  Black  Stone—  Black  carbonaceous  shale. 

Black  Copper. — Impure  smelted  copper. 

Blackdamp.— Carbonic-acid  gas. 

Black  Diamonds. — Coal. 

Black  Ends.— Refuse  coke. 

Black  Flux. — Charcoal  and  potassium  carbonate. 

Black  Jack.—(  1)  Properly  speaking,  dark  varieties  of  zinc  blende,  but  many 
miners  apply  it  to  any  black  mineral.  (2)  Crude  black  oil  used  to  oil 
mine  cars. 

Black  Lead—  Graphite. 

Black  Ore  (English).— Partly  decomposed  pyrites  containing  copper. 

Black  Sand. — Dark  minerals  found  with  alluvial  gold. 

Black  Stone.— A carbonaceous  shale. 

Black  Tin.— Dressed  cassiterite;  oxide  of  tin. 

Blanch.— (1)  A piece  of  ore  found  isolated  in  the  hard  rock.  (2)  Lead  ore 
mixed  with  other  minerals. 

Blanched  Copper.— Copper  alloyed  with  arsenic. 

Blanket  Stroke  (Australian).— Sloping  tables  or  sluices  lined  with  baize,  for 
catching  gold.  , , , 

Blanket  Tables.— Inclined  planes  covered  with  blankets,  to  catch  the  heavier 
minerals  passing  over  them.  / 

Blast— (1)  The  sudden  rush  of  fire,  gas,  and  dust  of  an  explosion  through  the 
workings  and  roadways  of  a mine.  (2)  To  cut  or  bring  down  coal, 
rocks,  etc.  by  the  explosion  of  gunpowder,  dynamite,  etc. 

Blasting  Barrel— A small  pipe  used  for  blasting  in  wet  or  gaseous  places. 

Blast  Pipe— A pipe  for  supplying  air  to  furnaces. 

Blende—  Sulphide  of  zinc;  sphalerite. 

Bliclz  (Germany).— Iridescence  on  gold  and  silver  at  end  of  cupeling. 

Blind  Coal— Coal  altered  by  the  heat  of  a trap  dike. 

Blind  Creek.— { 1)  A creek  in  which  water  flows  only  in  very  wet  weather. 
(2)  (Australasian)  Dry  watercourse. 

Blind  Drift.— A horizontal  passage  in  the  mine  not  yet  connected  with  the 
other  workings. 

Blind  Joint.— Obscure  bedding  plane. 

Blind  Lead,  or  Blind  Lode.— A vein  having  no  visible  outcrop. 

Blind  Level. — (1)  An  incomplete  level.  (2)  A drainage  level. 

Blind  Shaft,  or  Blind  Pit— A shaft  not  coming  to  the  surface. 

Bloat— A hammer  swelled  at  the  eye. 

Block  Claim  (Australian).— A square  mining  claim. 

Block  Coal—  Coal  that  breaks  in  large  rectangular  lumps. 

Blocking  0ut.—(l)  Working  deep  leads  in  blocks;  somewhat  like  horizontal 
stoping.  (2)  (Australian!  Washing  gold  gravel  in  sections. 

Block  Reefs—  Reefs  showing  frequent  contractions  longitudinally. 


Blo 


GLOSSARY. 


Bon 


573 


Block  Tin. — Cast  tin. 

J iWn,  or  any  indicating 
traces  of  a coal  bed  or  mineral  deposit.  Blossom  Rock.— (1)  Colored 
veln?toneadetached  from  an  outcrop.  (2)  The  rock  detached  from 
a vein  but  which  has  not  been  transported. 

Blow. — (1) * To  blast  with  gunpowder,  etc.  (2)  A dam  or  stopping  is  said  to 
blow  when  gas  escapes  through  it.  . . /r)>.  A 

Blower  — (1)  A sudden  emission  or  outburst  of  gas  m a mine.  (2)  Any 
emission  of  gas  from  a coal  seam  similar  to  that  from  an  ordinary  gas 
burner.  (3)  A 'type  of  centrifugal  fan  used  largely  to  force  air  into 
furnaces  (4)  A blowdown  ventilating  fan.  . , 

Blow  Fan.— A.  small  centrifugal  fan  used  to  force  air  through  canvas  pipes 
or  wooden  boxes  to  the  workmen. 

Blowdown  Fan.— A force  fan. 

Blow  In. — To  commence  a smelting  process.  . 

Blown- Out  Shot— A shot  that  has  blown  out  the  tamping,  but  not  broken  the 

coal  or  rock.  „ x _ ... 

Blow  Off — To  let  off  excess  of  steam  from  a boiler.  . 

Blow  Out  — (1)  To  finish  a smelting  campaign.  (2)  A blown-out  shot. 

(3)  The  decomposed  mineral  exposure  of  a vein.  . „ o 

Blowpipe—  An  instrument  for  creating  a blast  whereby  the  heat  of  a flame 

or  lamp  can  be  better  utilized. 

Blue  Billv. — Residue  of  copper  pyrites  after  roasting  with  salt. 

Blue  Cap!—1 The  blue  halo  of  ignited  gas  (firedamp  and  air)  on  the  top  of  the 
flame  in  a safety  lamp,  in  an  explosive  mixture. 

Blue  Elvan  (Cornish).— Greenstone. 

Blue  JJLeak  —A  blue^Sained  stratum  of  gravel  of  great  extent  and  richness. 
Blue  Metal.— A local  term  for  shale  possessing  a bluish  color. 

Blue  Peach  (Cornish). — A slate-blue  fine-grained  schorl. 

Milestone  —(1)  Sulphate  of  copper.  (2)  Lapis  lazuli.  (S)  Basalt.  (4)  Maryland, 
3 a gray  gneiss;  in  Ohio,  a gray  sandstone;  in  the  District  of  Columbia, 
a mica  schist;  in  New  York,  a blue-gray  sandstone;  in  Pennsylvania,  a 
blue-gray  sandstone.  (5)  A popular  term  among  stone  men  not  suf- 
ficiently definite  to  be  of  value. 

'Board.— A wide  heading  usually  from  3 to  5 yd.  wide. 

Board-and-Pillar .—  A system  of  working  coal  where  the  first  stage  of  exca- 
vation is  accomplished  with  the  roof  sustained  by  pillars  of  coal  left 
between  the  breasts;  often  called  Breast-and-Pillar. 

Bob  —An  oscillating  bell-crank,  or  lever,  tnrough  which  the  motion  of  an 
engine  is  transmitted  to  the  pump  rods  in  an  engine  or  pumping  pit. 
There  are  x bobs,  L bobs,  and  V bobs.  . , 

Boca  or  Boca  Mina  (Mexican).— Mouth  or  mine  mouth.  This  is  the  name 
applied  to  the  principal  or  first  opening  of  a mine,  or  to  the  one  where 

the  miners  are  accustomed  to  descend.  ... 

Bochorno  (Mexican).— Excessive  heat,  with  want  of  ventilation,  so  that  the 

Bodm—\lf°A^  ore  body,  or  pocket  of  mineral  deposit.  (2)  The  thickness  of 
a lubricating  oil  or  other  liquid;  also  the  measure  of  that  thickness 
exnressed  in  the  number  of  seconds  in  which  a given  quantity  of  the 
oil  at  a given  temperature  flows  through  a given  aperture. 

Bog  Iron  Ore.— Loose  earthy  brown  hematite  recently  formed  in  swampy 

Boleo  (Mexican) .—A  dump  pile  for  waste  rock. 

Boliche  (Spanish.).— Concentrating  bowl. 

Bollos  (Spanish).— Triangular  blocks  of  amalgam. 

Bolsa  (Spanish).— Small  bunch  of  ore.. 

Bonanza. — An  aggregation  of  rich  ore  m a mine.  , , » « 

Bond.—{  1)  The  arrangement  of  blocks  of  stone  or  brickwork  to  form  a firm 
structure  by  a judicious  overlapping  of  each  other  so  as  to  break  joint. 
(2)  An  agreement  for  hiring  men. 

Bone.— Slatv  coal  or  carbonaceous  shale  found  m coal  seams. 

Bone  Ash  —Burnt  bones  pulverized  and  sifted.  „ . 

Bonnet— (1)  The  overhead  cover  of  a cage.  .(2)  A cover  for  the  gauze  of 
a safety  lamp.  (3)  A cap  piece  for  an  upright  timber. 

Bonney  (Cornish)  .—An  isolated  body  of  ore. 


574 


Bon 


GLOSSARY. 


Bre 


Bonze. — U ndressed  lead  ore. 

Booming.— Ground  sluicing  on  a large  scale  by  emptying  the  contents  of  a 
reservoir  at  once  on  material  collected  below,  thus  removing  boulders. 

Bord  (English).— A narrow  breast. 

Bord-and-Pillar  (English).— See  Pillar-and- Breast. 

Bord  Room. — The  space  excavated  in  driving  a bord.  The  term  is  used  in 
connection  with  the  “ridding”  of  the  fallen  stone  in  old  bords  when 
driving  roads  across  them  in  pillar  working;  thus,  “ ridding  across  the 
old  bord  room.” 

Bord  Ways  Course.— The  direction  at  right  angles  to  the  mam  cleavage 
planes.  In  some  mining  districts,  it  is  termed  “on  face.” 

Bore.— To  drill. 

Bore  Hole. — A hole  made  with  a drill,  auger,  or  other  tools,  m coal,  rock,  or 
other  material. 

Borrasca  (Mexican). — The  reverse  of  bonanza.  When  the  mine  has  a vein, 
but  no  ore,  it  is  said  to  be  “ en  borrasca.” 

Bort.— Amorphous  dark  diamond. 

Bosh.— The  plane  in  a blast  furnace  where  the  greatest  diameter  is  reached. 

Boss  (English).— (1)  An  increase  of  the  diameter  at  any  part  of  the  shaft. 
(2)  A person  in  charge  of  a piece  of  work. 

Botas  (Mexican). — Buckets  made  of  an  entire  ox  skin,  to  take  out  water. 

Botryoidal.— Grape-like  in  appearance. 

Bottle  Jack  (English).— An  appliance  for  lifting  heavy  weights. 

Bottom.— (1)  The  landing  at  the  bottom  of  the  shaft  or  slope.  (2)  The  lowest 
point  of  mining  operations.  (3)  The  floor,  bottom  rock,  or  stratum 
underlying  a coal  bed.  (4)  In  alluvial,  the  bed  rock  or  reef. 

Bottomer,  Bottomman. — The  person  that  loads  the  cages  at  the  pit  bottom 
and  gives  the  signal  to  bank. 

Bottom  Joint.— Joint  or  bedding  plane,  horizontal  or  nearly  so. 

Bottom  Lift.—(  1)  The  deepest  column  of  a pump.  (2)  The  lowest  or  deepest 
lift  or  level  of  a mine. 

Bottom  Pillars.— Large  pillars  left  around  the  bottom  of  a shaft. 

Bottoms. — Impure  copper  alloy  below  the  matte  in  smelting. 

Boulders. — Loose  rounded  masses  of  stone  detached  from  the  parent  rock. 

Bounds  (Cornish).— A tract  of  tin  ground. 

Bout  (Derbyshire).— Twenty-four  dishes  of  lead  ore. 

.Bow.— The  handle  of  a kibble.  „ , _ , 

Bowk. — An  iron  barrel  or  tub  used  for  hoisting  rock  and  other  debris  when 
sinking  a shaft.  , , , 

Bowke  (Staffordshire).— A small  wooden  box  for  hauling  ironstone  under- 
ground. 

Bowl  Metal.— The  impure  antimony  obtained  from  doubling. 

Bowse  (Derbyshire).— Lead  ore  as  cut  from  the  lode. 

Box.— (1)  A 12'  to  14'  section  of  a sluice.  (2)  A mine  car. 

Box  Bill.— Tool  for  recovering  boring  rods. 

Boxing.— A.  method  of  securing  shafts  solely  by  slabs  and  w<3oden  pegs. 

Brace. — (1)  An  inclined  beam,  bar,  or  strut  for  sustaining  compression 
or  tension.  See  Tie-Brace , Sway-Brace.  (2)  A platform  at  the  top  of  a 
shaft  on  which  miners  stand  to  work  the  tackle.  (3)  (Cornish)  Building 
at  pit  mouth.  . _ , , . ,,  , 

Brace  Heads—  Wooden  handles  or  bars  for  raising  and  rotating  the  rods 


when  boring  a deep  hole. 

Braize.— Charcoal  dust. 

Brake  Seive—  Hand  jigger. 

Brances.— Iron  pyrites  in  coal. 

Branch.— Small  vein  shooting  off  from  main  lode. 

Brashy—  Short  and  tender.  _ . - , .. 

Brasque. — A mixture  of  clay  and  coke  or  charcoal  used  for  furnace  bottoms. 
Brass. — (1)  Iron  pyrites  in  coal.  (2)  An  alloy  of  copper  and  zinc. 

Brasses  (English).— Fitting  of  brass  in  plummer  blocks,  etc.,  for  diminishing 
the  friction  of  revolving  journals  that  rest  upon  them. 

Brat.— A thin  bed  of  coal  mixed  with  pyrites  or  limestone. 

Brattice— A lining  or  partition.  . , . 

Brattice  Cloth.— Ducking  or  canvas  used  for  making  a brattice. 

Brazzil  (North  of  England). — Iron  pyrites  in  coal.  _ . , , „ 

Breaker. — In  anthracite  mining,  the  structure  in  which  the  coal  is  broken, 
sized,  and  cleaned  for  market.  Known  also  as  Coal  Breaker. 

Breaker  Bov.— A boy  who  works  in  a coal  breaker. 


Bre 


GLOSSARY. 


BUL 


575 


Breakstaff.—  The  lever  for  blowing  a Dlacksmiths’  bellows,  or  for  working 

Breakthrough^- A^arrow  passage  cut  factor 

Breast— ( l)  A stall,  board,  or  room  m which  coal  is  mined.  (2)  I he  lace  or 

wall  of  a auarrv  is  sometimes  called  by  this  name. 

Breastand-Pttlar.—A  system  of  working  coal  by  boards  or  rooms  with  pillars 

Breattinfor f-The  orlTaken  from  the  face  or  end  of  the  tunnel. 

breast  Wall  (English) —A  wall  built  to  prevent  the  falling  of  a \ertical  face 

Brecc?a.— A rock^omposed  of  angular  fragments  cemented  together. 

Breeding  Fire. — See  Gob  L?ire. 

Breese.—  Fine  slack.  _ , . 

Breeze—  Small  coke,  probably  same  as  braize  or  braise. 

Brettis  fDerbvshire) .— A timber  crib  filled  with  slacR.  . 

Bridge.— {1)  A platform  on  wheels  running  on  rails  for  covering 

of  a shaft  or  slope.  (2)  A track  or  platform  passing  over  an  inclined 
haulage  way  and  which  can  be  raised  out  of  the  way  of  ascending  and 

BridtecTcdnt— Short  chains  by  which  a cage, . car,  or  attached  to 

a winding  rope;  of  use  in  case  the  rope  pulls  out  of  socket. 

Briquets. — Fuel  made  of  slack  or  culm  and  pressed  ^otaick  mrtiallv 

Broaching  Bit— A tool  for  reopening  a bore  hole  that  has  been  partially 
closed  by  swelling  of  the  walls. 

Brob.—A  spike  to  prevent  timber  slipping. 

Broil  (Cornish). — Traces  of  a vein  in  loose  matter.  ir,  nrmtrfl- 

Ttmken A district  of  coal  pillars  m process  of  removal,  so  called  m contra 

distinction^  to  the  tot  working  of  a seam  by  bord-and-wall,  or  working 
in  the  “whole.”  See  Whole  Working.  Q1  . 

Broken  Coal.— Anthracite  coal  that  will  pass  through  a mesh  or  bars  34  to 
44-  in. , and  over  a mesh  2f  in.  square.  ( See  page  434. ) 

Bronce  (Mexican).— In  mining,  copper  or  iron  pyrites. 

Brooch  (Cornish).— Mixed  ores. 

Broochinq. — Smoothing. 

Brood  (Cornish).— Heavy  waste  from  tin  and  copper  ores.  pithpr 

Brow.— An  underground  roadway  leading  to  a working  place  driven  either 

Brown^Coal— Lignite.6  A fuel  classed  between  peat  and  bituminous  coal. 
Brown  Spar.— Dolomite  containing  carbonate  of  iron. 

Brownstone.-iff)  Decomposed  iron  pyrites.  (2)  Brown ^sandstone. 

Browse. — Imperfectly  smelted  ore  mixed  with  cinder  and  clay. 

Brujula  (Mexican).— A surveyors’  (or  marine)  magnetic 1 ^P^s. 

Brush. — (1)  To  mix  air  with  the  gas  m a mine  working  swinging  a 
iacket  etc.  which  creates  a current.  (2)  To  brush  the  roof  oi  an 
airway,  is  to  take  down  some  of  the  roof  slate,  to  increase  the  height 

or  headroom.  . . , 

Brule  (Cornish). — Traces  of  a vein  in  loose  matter. 

Bucket.— (1)  An  iron  or  wooden  receptacle  for  hoisting  ore,  or  for  raising 
rock  in  shaft  sinking.  (2)  The  top  valve  or  clack  of  a pump. 

Bucket  Pump— A lifting  pump,  consisting  of  buckets  fastened  to  an  endless 

Bii^etVword^—A  wrought-iron  rod  to  which  the  PumP^c^i\^teached* 
Bucket  Tree  —The  pipe  between  the  working  barrel  and  the  wind  bore. 
Bucking. — Breaking  down  ore  with  a very  broad  banmeii * : brelkfng 

Bucking  Hammer.— An  iron  disk,  provided  with  a handle,  used  tor  breaking 

up  minerals  by  hand. 

Buck  Quartz. — Hard  non-auriferous  quartz.  o. 

Buck  Staff.— Uprights  for  bracing  reverberatory  furnaces  together . 
Buckwheat- Anthracite  coal  that  will  pass  through  a mesh  * in.  and  over  a 

Buddie^- Aifinclined  table,  circular  or  oblong,  on  which  ore  is  concentrated. 
Buddling.— Washing. 

Buggy.— A small  mine  car.  „ ■ ...  . , 

Bug  Hole.— A small  cavity  usually  lined  with  crystals.  f 

Building.— A built-up  block  or  pillar  of  stone  or  coal  to  support  the  roof. 
Buitron  (Spanish). — A silver  furnace  of  peculiar  form. 

Bulkhead.— (1)  A tight  partition  or  stopping.  (2)  The  end  of  a flume  carry 
ing  water  for  hydraulicking. 


576 


Bul 


GLOSSARY. 


Cal 


Bulldog.— A.  refractory  furnace  lining  of  calcined  mill  cinder,  containing 
iron  and  silica. 

Bull  Engine.— A single,  direct-acting  pumping  engine,  the  pump  rods  form- 
ing a continuation  of  the  piston  rod. 

Buller  Shot.— A second  shot  put  in  close  to,  and  to  do  the  work  not  done  by, 
a blown-out  shot,  loose  powder  being  used. 

Bud.— An  iron  rod  used  in  ramming  clay  to  line  a shot  hole. 

Bulling. — Lining  a shot  hole  with  clay. 

Bullion.— Uncoined  gold  and  silver. 

Bull  Pump. — A single-acting  pumping  engine  in  which  the  steam  cylinder  is 
placed  over  the  shaft  or  slope  and  the  pump  rods  are  attached  directly  to 
the  piston  rod.  The  steam  enters  below  the  piston  and  raises  the  pump 
rods;  the  water  is  pumped  on  the  down  stroke  by  the  weight  of  the  rode. 

Bull  Pup.— A worthless  claim. 

Bull  Wheel. — A wheel  on  which  the  rope  carrying  the  boring  rod  is  coiled 
when  boring  by  steam  machinery. 

Bully. — A miners’  hammer. 

Bumping  Table. — A concentrating  table  with  a jolting  motion. 

Bunch.— A small  rich  deposit  of  ore. 

Bunding— A staging  in  a level  for  carrying  debris. 

Bunkers—  Steam  coal  consumed  on  board  ship. 

Bunney.—A  nest  of  ore  not  lying  in  a regular  vein. 

Buntons. — Timbers  placed  horizontally  across  a shaft  or  slope  to  carry  the 
cage  guides,  pump  rods,  column  pipe,  etc.;  also,  to  strengthen  the  shaft 
timbering. 

Burden. — (1)  Earth  overlying  a bed  of  useful  mineral.  (2)  The  proportion 
of  ore  and  flux  to  fuel  in  the  charge  of  a blast  furnace. 

Burr. — Solid  rock. 

Burrow. — Refuse  heap. 

Buscones  (Spanish).— Prospectors,  fossickers,  tribute  workers. 

Bush.— To  line  a circular  hole  with  a ring  of  metal,  to  prevent  the  hole  from 
wearing  out. 

Butt—  (1)  Coal  surface  exposed  at  right  angles  to  the  face;  the  “ends”  of 
the  coal.  (2)  The  butt  of  a slate  quarry  is  where  the  overlying  rock 
comes  in  contact  with  an  inclined  stratum  of  slate  rock. 

Butt  Entry.— A gallery  driven  at  right  angles  with  the  butt  joint  (see  page  285). 

Butterfly  Valve.— A circular  valve  that  revolves  on  an  axis  passing  through 
its  center. 

Butt  Heading. — See  Butt  Entry. 

Button.— The  globule  of  metal,  the  result  of  an  assay. 

Button  Balance.— A small  very  delicate  balance  used  for  weighing  assay 
buttons. 

Butty'— A partner  in  a contract  for  driving  or  mining;  a comrade,  crony. 
Sometimes  called  “ Buddy.” 

By  Level. — A side  level  driven  for  some  unusual  but  necessary  purpose. 

Cab. — The  side  parts  of  a lode,  nearest  the  walls,  which  are  generally  hard 
and  deficient  of  ore. 

Caballo  (Mexican).— A “ horse  ” or  mass  of  barren  rock  in  a vein. 

Cabezuela  (Spanish).— Rich  gold  and  silver  concentrates.. 

Cabin. — (1)  A miner’s  house.  (2)  A small  room  in  the  mine  for  the  use  of  the 
officials. 

Cable  Drilling. — Rope  drilling. 

Cage. — A platform  on  which  mine  cars  are  raised  to  the  surface. 

Cage  Guides.— Vertical  rods  of  pine,  iron,  or  steel,  or  wire  rope,  fixed  in  a 
shaft,  between  which  cages  run,  and  whereby  they  are  prevented  from 
striking  one  another,  or  against  any  portion  of  the  shaft. 

Cager. — The  person  that  puts  the  cars  on  the  cage  at  the  bottom  of  the  shaft. 

Cage  Seat. — Scaffolding,  sometimes  fitted  v/ith  strong  springs,  to  take  off  the 
shock,  and  on  which  the  cage  drops  when  reaching  the  pit  bottom. 

Cage  Sheets. — Short  props  or  catches  on  which  cages  stand  during  caging  or 
changing  cars. 

Caking  Coal—  Coal  that  agglomerates  on  the  grate. 

Cal— Wolfram. 

Cala  (Spanish).— Prospecting  pit. 

Calcareous. — Containing  lime.  # . 

Calcine. — To  heat  a substance;  not  sufficiently  to  melt  it,  but  enough  to  drive 
off  the  volatile  contents. 


Cal 


GLOSSARY. 


Cau 


577 


Calcining  Furnace— A furnace  used  for  roasting  ore  in  order  to  drive  off 
certain  impurities. 

Wmnta^mp^-Itndevnmp  made  of  a wooden  box  th/ou,fh  which  an 
endless  belfwith  floats  circulates;  used  for  pumping  water  from  shallow 

CaKra°(€ornish). — Stratified  rocks  traversed  by  lodes.  . . t 

Cam.—(  1)  A curved  arm  attached  to  a revolving  shaft  for  raising  stamps. 

(2)  Carbonate  of  lime  and  fluorspar,  found  on  the  joints  of  lodes 
Camino  (Mexican).— Any  gallery,  winze,  or  shaft,  inside  of  a mine  used  tor 

general  transit.  „ . n.Woct 

Campaign.— The  length  of  time  a furnace  remains  m blast. 

' required  to .be ^removed l to  make 

sloping  sides  and  very  narrow  bottom. 

Cancha  (Spanish).— Space  for  drying  slimes. 

Cand  ( Cornish ) —Fluorspar. 

Cank  (Derbyshire).— Whinstone. . 

Canker. — The  ocherous  sediment  m coal-pit  waters. 

a mine-  " 

Cante^Enghsh)!— Tlm'pieces^ornnng  the  ends  of  ^ckete  of  a waterwheel. 

Capdlma{ Mexican).— An  old-style  retort  for  retorting  silver  amalgam. 

Caple  (Cornish).— Hard  rock  lining  tin  lodes. 

worked  by  horizontal 

arms  or  bars.  . ~ 

Captain. — Cornish  name  for  manager  or  boss  of  a mine.  o.aT1o-xVflVS  Qr 

Car.— Any  car  used  for  the  conveyance  of  coal  along  the  gangways  or 
haulage  roads  of  a mine. 

Carat.— A weight  nearly  equal  to  4 grains.  . . thp  comno- 

Carbon.— A combustible  elementary  substance  forming  the  largest  compo 

carh^-m  Arichbunch  of  ore  in  the  country  rock  connected  with  the 
lodeby  a mere  thr" ad  of  mineral.  (2)  (Cornish)  An  irregullr  deposit 
of  tin  ore.  . . . , 

Carbonaceous.— Coaly,  containing  carbon  or  coal. 

Carbonate.— Carbonic  acid  combined  with  a base.  , f i d. 

Carbonates. — Lead  ore.  The  oxide  and  carbonic-acid  compounds  ot  lead, 
also  applied  to  lead  sulphate. 

generally  of  300  pounds,  but 

variable  in  different  parts  of  Mexico. 

case  filled  with  gunpowder, 

forming  the  charge  for  blasting. 

Cascajo  (Mexican).— Gravel. 

Case—  A fissure  admitting  water  into  a mine.  . . steel  bv 

Case-Harden— To  convert  the  outer  surface  of  wrought  iron  into  steei  Dy 

Tubing1 in  serf  ed  h?  a?  ^^"keep  out  water  or  to  protect  the 

Casfn^n™. Sg^iro^thal  contains  carbon  (up  to  5$),  silicon,  sulphur,  phos- 

Cata  (Spanish ).— A mine  denounced  but  not  worked. 

Catches— {1)  Iron  levers  or  props  at  the  top  and  bottom  of  a shaft.  ( ) P 
fitted  on  a cage  to  prevent  cars  from  running  ofl. 

Catch  Pit— A reservoir  for  saving  tailings  from  reduction  works. 

Cauf  (North  of  England).— A coal  bucket  or  basket.  , trunks  of  sieil- 

Cauldron  Bottoms.- The  fossil  remains  or  the  casts  of  the  trunks  ot  s g 
laria  that  have  remained  vertical  above  or  belowtheseam. 

Caulk.— To  fill  seams  or  joints  with  something  to  prevent  leaking. 


GLOSSARY. 


Cho 


\78  Cau 


Cannier , or  Cannier  Lode  (Cornish).— A vein  running  obliquely  across  the 
regular  veins  of  the  district. 

Cave , or  Cave  In— A caving-in  of  the  roof  strata  of  a mine,  sometimes  extend- 
ing to  the  surface. 

Cavils—  Lots  drawn  by  the  hewers  each  quarter  year  to  determine  their 
working  places. 

Cawk  — Baryta  sulphate. 

Cazeador  (Spanish) . — Amalgamator. 

Cazo  (Mexican).— A vessel  for  hot  amalgamation.  Any  large  copper  or  iron 
vessel. 

Cebar  (Mexican).— (1)  To  melt  rich  ores,  or  lead  bullion,  etc.  in  a smelting 
furnace.  (2)  To  add  small  quantities  of  material,  from  time  to  time,  to 
the  melted  mass  within  a furnace.  (3)  Generally,  to  feed  any  kind  or 
metallurgical  machinery  or  process. 

Cement—  (1)  Auriferous  gravel  consolidated  together.  (2)  A finely  divided 
metal  obtained  by  precipitation.  (3)  A binding  material. 

Cementation— The  process  of  converting  wrought  iron  into  steel  by  heating 
it  in  contact  with  charcoal,  or  of  treating  cast  iron  in  a bed  of  hema- 
tite ore. 

Cendrada  (Mexican).— The  cupel  bottom  of  a furnace. 

CendradUla  (Mexican).— A small  reverberatory  furnace  for  smelting  rich 
silver  ores  in  a rough  way.  Also  called  Galeme. 

Center —A  temporary  support,  serving  at  the  same  time  as  a guide  to  the 
masons,  placed  under  an  arch  during  the  progress  of  its  construction. 

Centrifugal  Force.— A force  drawing  away  from  the  center. 

Centripetal  Force.— A force  drawing  toward  the  center. 

CHa—  Marsh  gas  (see  page  348). 

Chain.— A measure  66  or  100  ft.  long,  divided  into  100  links. 

Chain-Brow  Way— An  underground  inclined  plane  worked  on  the  endless- 
chain  svstem  of  haulage. 

Chain  Pillar.— A pillar  left  to  protect  the  gangway  and  air-course,  and  run- 
ning parallel  to  these  passages. 

Chain  Road—  An  underground  wagomvay  worked  on  the  endless-chain 
system  of  haulage. 

Chair. — Sometimes  applied  to  keeps. 

Chamber. — See  Breast. 

Charco  (Mexican).— A pool  of  water. 

Charge. — (1)  The  amount  of  powder  or  other  explosive  used  in  one  blast  or 
shot.  (2)  The  amount  of  flux  used  in  assaying.  (3)  The  material  fed 
into  a furnace  at  one  time. 

Charqnear  (Mexican).— To  dip  out  water  from  pools  within  the  mine, 
throwing  it  into  gutters  or  pipes  that  will  conduct  it  to  the  shaft. 

Chats—  (1)  The  gravel-like  tailings  derived  from  the  concentration  of  ores. 
(2)  A low-grade  ore,  often  too  poor  to  handle;  the  refuse  from  concen- 
tration works.  (3)  (North  of  England)  Small  pieces  of  stone  with  ore. 

Check- Battei'y—  A battery  to  close  the  lower  part  of  a chute,  acting  as  a 
check  to  the  flow  of  coal  and  as  an  air  stopping. 

Checker  Coal—  Anthracite  coal  that  seems  to  be  made  up  of  rectangular 
grains. 

Check-  Weighman.—A  man  appointed  and  paid  by  the  miners  to  check  the 
weighing  of  the  coal  at  the  surface. 

Cheek. — Wall. 

Chert.— A silicious  rock,  often  the  gangue  of  lead  and  zinc. 

Chestnut  Coa l.— Anthracite  coal  that  will  pass  through  a mesh  If  in.  square 
and  over  a mesh  f in.  square  (see  page  434). 

Chifion  (Mexican).— A narrow  drift  directed  obliquely  downwards.  Any 
pipe  from  which  issues  water  or  air  under  pressure,  or  at  high  velocity. 

Chile  Bars.— Bars  of  impure  copper,  weighing  about  200  lb.,  imported  from 
Chile,  corresponding  to  the  Welsh  blister  copper,  containing  98#  Cu. 

Chilian  Mill.— A roller  mill  for  crushing  ore. 

Chill  Hardening. — Giving  a greater  hardness  to  the  outside  of  cast  iron  by 
pouring  it  into  iron  molds,  which  causes  the  skin  of  the  casting  to  cool 
rapidly. 

Chimney.— (1)  An  ore  shoot.  (2)  A furnace  or  air  stack. 

Chinese  Pump.— Like  a California  pump,  but  made  entirely  of  wood. 

Chock.— A square  pillar  for  supporting  the  roof,  constructed  of  prop  timber 
laid  up  in  alternate  cross-layers,  in  log-cabin  style,  the  center  being  filled 
with  waste.  \ * 


Cho 


GLOSS  AR  Y. 


Cof  579 


Chun^rlli  -A  long  iron  bar  with  a cutting  end  of  steel,  used  in  quarrying, 
andworked  by  faising  and  letting  it  fall.  When  worked  by  blows  of  a 

CAMt^^l^^pelle^bVmfe)^— fl)6A  narrow'lnclined  passage  in  a mine,  down 
which  coal  or  ore  is  either  pushed  or  slides  by  gravity.  (2)  The  load- 
ing chute  of  a tipple.  . 

CT^f^^n?)-AcS^^r<*^e^U&---<>irerheadstoping. 

cS-A^vrS  i“opTned  and  closed  by  the  force  of  the  water.  . 

Clack  Door  — The  opening  into  the  valve  chamber  to  facilitate  repairs  and 
renewals  without  unseating  the  pump  or  breaking  the  connections. 

Clack  Piece.— The  casting  forming  the  valve  chamber. 

Clack  Seal. — The  receptacle  for  the  valve  to  rest  on.  . , f 

Clanav  (North  of  England).— When  coal  is  tightly  joined  to  the  roof. 
C^m.—A portion  of'  ground  staked  out  and  held  by  virtue  of  a miner’s 

ciminu^—A  tvne  of  safety  lamp  invented  by  Dr.  Clanny.  . 

Clastic—  Constituted  of  rocks  or  minerals  that  are  fragments  derived  from 

Cla^ Coursed— A clay  seam  or  gouge  found  at  the  sides  of  some  veins. 

Claying  Bar.— For  molding  clay  in  a wet  bore  hole.  mooonr,0fi 

Clay  Band. — Argillaceous  iron  ore;  common  m many  coal  measures. 

Clean-Up  —Collecting  the  product  of  a period  of  work  with  battery  or  sluice. 
Clearance— ( 1)  The  distance  between  the  piston  at  the  end  of  its  stroke  and 
the  end  of  the  cylinder.  (2)  The  volume  or  entire  space  filled  with 
steam  at  end  of  a stroke  including  the  space  between  piston  and 
cylinder  head,  and  the  steam  ducts  to  the  valve  seat.  . . . 

Cleat  — ( 1)  Vertical  cleavage  of  coal  seams,  irrespective  of  dip  or  strike.  (2) 
A small  piece  of  wood  nailed  to  two  planks  to  keep  them  together,  or 
nailed  to  any  structure  to  make  a support  for  something  else. 

Cleavage. — The  property  of  splitting  more  readily  in  some  directions  than  in 

Clinometer  — An  instrument  used  to  measure  the  angle  of  dip. 

CY^-Soft  and  tough  shale  or  slate  forming  the  roof  or  floor  of  a coal  seam. 
Closed  Season— When  placers  cannot  be  worked. 

separate  shafts  by  means  of  which 
they  catch  into  each  other,  so  that  both  can  revolve  together. 

Coal  Breaker.— See  Breaker. 

Coni  Cutter  — A machine  for  holing  or  undercutting  coal. 

Coal  Dust.— Very  finely  powdered  coal  suspended  in  the  airways  of  a mine. 
Coal  Measures.— Strata  of  coal  with  the  attendant  rocks. 

Coal  Pipes  (North  of  England). -Very  thin  irregular  coal  beds. 

Coal  Road— An  underground  roadway  or  heading  in  coai. 

Co^ly^Rashings—  Soft  dark  shale,  in  small  pieces,  containing  much  carbona- 

CoarseTc  “se)1- When  lode  stuff  is  not  rich,  the  ore  being  only  thinly  dis- 

CoaS^l^ol^f  salting,  the  compound  — the^  copper 
concentrated  in  it  after  the  first  smelting  to  get  rid  of  the  bulk  ot  tne 
gangue  in  the  ore. 

Coaster.— One  that  picks  ore  from  the  dump. 

Cob  (Cornish).—1 To  break  up  ore  for  sorting. 

Cobbing  Hammer.— A short  double-ended  hammer  for  breaking  minerals  to 
sizes. 

CocSrme^or1  CoXers.— Timber  used  to  hold  coal  face  while  it  is  being 

undGrcut  • 

Cockle  (Cornish).— Black  tourmaline,  often  mistaken  for  tin. 

Cod  (North  of  England).— The  bearing  of  an  axle.  ... 

Cofer  (Derbyshire).— To  calk  a shaft  by  ramming  clay  behind  the  lining. 
Cofer.— Mortar  box  of  a battery.  . . 

' Coffer  Dam.— An  enclosure  built  in  the  water,  and  then  pumped  dry,  so  as  to 
permit  masonry  or  other  work  to  be  carried  on  inside  of  it. 

Coffin  (Cornish).— An  old  pit. 


580 


Cog 


GLOSSARY. 


Cor 


Cog.  A chock. 

Coiiete  (Mexican).— A rocket;  applied  to  a blast  within  a mine  or  outside. 

Co# Drag— A tool  for  picking  pebbles,  etc.  from  drill  holes. 

Coke. — The  fixed  carbon  and  ash  of  coal  sintered  together. 

Colas  (Spanish).— Tailings  from  a stamp  mill  or  any  wet  process. 

Collar.— (1)  A flat  ring  surrounding  anything  closely.  (2)  Collar  of  a shaft 
is  the  first  wood  frame  of  a shaft.  (3)  The  bar  or  crosspiece  of  a framing 
in  entry  timbering. 

Colliery—  The  whole  plant,  including  the  mine  and  all  adjuncts. 

Colliery  Warnings  (English).— Telegraphic  messages  sent  from  signal-service 
stations  to  the  principal  colliery  centers  to  warn  managers  of  mines 
when  sudden  falls  of  the  barometer  occur. 

Color  ados  (Spanish).— Decomposed  ores  stained  with  iron. 

Colores  (Mexican).— Metal-stained  ground  or  rocks. 

Colrake  — A shovel  for  stirring  lead  ores  while  washing. 

Color—  Minute  traces  or  individual  specks  of  gold. 

Column , or  Column  Pipe.— The  pipe  conveying  the  drainage  water  from  the 
mine  to  the  surface. 

Comer  (Mexican).— To  eat.  Comerse  los  Pilares.— To  take  out  the  last  vestiges 
of  mineral  from  the  sides  and  rock  pillars  of  a mine. 

Conchoidal. — Shell-like,  such  as  the  curved  fracture  of  flint. 

Concrete.— Artificial  stone,  formed  by  mixing  broken  stone,  gravel,  etc.  with 
lime,  cement,  tar,  or  other  binder.  When  hydraulic  cement  is  used 
instead  of  lime,  the  mixture  is  called  beton  (English). 

Concretion.— A cemented  aggregation  of  one  or  more  kinds  of  minerals 
around  a nucleus. 

Conduit.— (1)  A covered  waterway.  (2)  An  airway. 

Conduit  Hole— A flat  hole  drilled  for  blasting  up  a thin  piece  in  the  bottom 
of  a level. 

Conductors  (English).— See  Guides. 

Conformable. — Strata  are  conformable  when  they  lie  one  over  the  other  with 
the  same  dip. 

Conglomerate.— The  rock  formation  underlying  the  Coal  Measures;  a rock 
containing  or  consisting  of  pebbles,  or  of  fragments  of  other  rocks 
cemented  together;  English  Pudding  Rock  or  millstone  grit. 

Conical  Drum.— The  rope  roll  or  drum  of  a winding  engine,  constructed  in 
the  form  of  two  truncated  cones  placed  back  to  back,  the  outer  ends 
being  usually  the  smaller  in  diameter. 

Consumido  (Mexican).— The  amount  of  mercury  that  disappears  by  chem- 
ical combination  during  the  treatment  of  ore  by  any  amalgamation 
process. 

Contact.— Union  of  different  formations. 

Contact  Load  or  Vein— A vein  lying  between  two  differently  constituted 
rocks. 

Contour.— (1)  The  line  that  bounds  the  figure  of  an  object.  (2)  In  survey- 
ing, a contour  line  is  a line  eveiy  point  of  which  is  at  an  equal  elevation. 

Contramina  (Mexican).— Countermine.  Any  communication  between  two 
or  more  mines.  Also,  a tunnel  communicating  with  a shaft. 

Cope  (Derbyshire)  .—Lead  mining  on  contract. 

Cope , or  Coup.— An  exchange  of  working  places  between  hewers. 

Copelilla  ( Spanish ) .-Zinc-blende. 

Copella  (Spanish).— Dry  amalgam. 

Copper  Plate.— A sheet  of  copper  that,  when  coated  with  mercury,  is  used  in 
amalgamation. 

Corbond. — An  irregular  mass  from  a lode. 

Cord. — A cord  weighs  about  8 tons. 

Cores. — Cylinder-shaped  pieces  of  rock  produced  by  the  diamond-drill  system 
of  boring. 

Corf. — A mine  wagon  or  tub. 

Cornish  Pumps.— A single-acting  pump,  in  which  the  motion  is  transmitted 
through  a walking  beam;  in  other  respects  similar  to  a Bull  Pump. 

Coro-Coro  (South  American).— Grains  of  native  copper  mixed  with  pyrite, 
chalcopyrite,  mispickel,  etc. 

Cortar  Pillar  (Mexican).— To  form  a rock  support  or  pillar  within  a mine, 
at  the  opening  of  a cross-cut  or  elsewhere.  ' 

Cortar  Sogas  (Mexican).— Literally,  to  cut  the  ropes.  To  abandon  the  mine, 
taking  away  everything  useful  or  movable. 

Corve.—A  mining  wagon  or  tub. 


Cos 


GLOSSARY. 


Cro 


581 


Costean  (Cornish).— To  prospect  a lode  by  sinking  pits  on  its  supposed 
course. 

Costeaning. — Trenching  for  a lode. 

Cost  Book  (Cornish). — Mining  accounts.  . ^ 

Cotton  Rock.—(  1)  Decomposed  chert.  (2)  A variety  of  earthy  limestone. 

Coulee .— (1)  A solified  stream  or  sheet  of  lava  extending  down  a volcano, 
often  forming  a ridge  or  spur.  (2)  A deep  gulch  or  water  channel. 

Count™— [if1!*  cross-vein.  (2)  (English)  An  apparatus  for  recording  the 
number  of  strokes  made  by  the  Cornish  pumping  engine.  (3)  A second- 
ary haulageway  in  a coal  mine.  . , x , 

Counterchute.— A chute  down  which  coal  is  dumped  to  a lower  level  or 
ffftnfifw&v. 

Counter  gangway A level  or  gangway  driven  at  a higher  level  than  the 
main  one. 

Country— The  formation  traversed  by  a lode. 

Country  Rock—  The  main  rock  of  the  region  through  which  the  veins  cut, 
or  that  surrounding  the  veins. 

Course— The  direction  of  a line  in  regard  to  the  points  of  compass. 

Coursing  or  Coursing  the  Air.— Conducting  it  through  the  different  portions 
of  a mine  by  means  of  doors,  stoppings,  and  brattices. 

Cow—  A self-acting  brake. 

Coyoting. — Irregular  mining  by  small  pits.  A . 

Crab  —A  variety  of  windlass  or  capstan  consisting  of  a short  shaft  or  axle, 
either  horizontal  or  vertical,  which  serves  as  a rope  drum  for  raising 
weights;  it  may  be  worked  by  a winch  or  handspikes. 

Crab  Holes—  Holes  often  met  with  in  the  bed  rock  of  alluvial.  Also  depres- 
sions on  the  surface  owing  to  unequal  disintegration  of  the  underlying 
rock. 

Cradle.— A box  with  a sieve  mounted  on  rockers  for  washing  auriferous 
alluvial.  „ _ _ 

Cradle  Dump. — A rocking  tipple  for  dumping  cars.  See  Dump. 

Cramp  (English).— (1)  A short  bar  of  metal  having  its  two  ends  bent  down- 
wards at  right  angles  for  insertion  into  two  adjoining  pieces  of  stone, 
wood,  etc.  to  hold  them  together.  (2)  A pillar  left  for  support  in  a mine. 

Cranch—  Part  of  a vein  left  by  previous  workers. 

Crane  (English).— A hoisting  machine  consisting  of  a revolving  vertical 
post  or  stalk,  a projecting  jib,  and  a stay  for  sustaining  the  outer  end  of 
the  jib;  these  do  not  change  their  relative  positions  as  they  do  in  a 
derrick.  There  is  also  a rope  drum  with  winding  rope,  etc.  v ^ 

Creaze  (Cornish).— (1)  Tin  ore  collected  in  the  middle  of  the  huddle.  (2)  The 
middle  of  a huddle.  „ . _ . . 

Creep  .—The  gradual  upheaval  of  the  floor  or  sagging  of  the  roof  of  mine 
workings  due  to  the  weighting  action  of  the  roof  and  a tender  floor. 

Creston  (Mexican).— The  outcrop  or  apex  of  a vein  or  mineral  deposit. 

Crevice.— A fissure.  . 

C revicing. — Picking  out  the  gold  caught  in  cracks  and  crevices  m the  rocks 
over  which  it  has  been  washed.  ' x . ... 

Criadero  (Mexican).— (1)  A mineral  deposit  of  irregular  form,  not  vem-like. 
(2)  A chamber  in  a vein  filled  with  ore  of  more  or  less  richness.  (3)  Any 
mineral  deposit.  This  latter  is  the  more  modern  sense,  and  the  word  is 
so  used  in  the  mining  laws  at  present  in  force  in  Mexico. 

Crib  —(1)  A structure  composed  of  horizontal  timbers  laid  on  one  another, 
or  a framework  built  like  a log  cabin.  See  Chock.  (2)  A miner’s  lunch- 
eon. (3)  See  Curb.  x . 

Cribbing. — Close  timbering,  as  the  lining  of  a shaft,  or  the  construction  ot 
cribs  of  timber,  or  timber  and  earth  or  rock  to  support  a roof. 

Cribble A sieve. 

Crisol  (Mexican).— A crucible  of  any  kind. 

Crop. — See  Outcrop.  , x 

Crop  Fall.— A caving  in  of  the  surface  at  or  near  the  outcrop  of  a bed  of  coal. 

Cropping  Coal. — The  leaving  of  a small  thickness  of  coal  at  the  bottom  of  the 
seam  in  a working  place,  usually  in  order  to  keep  back  water.  The  coal 
so  left  is  termed  “ Cropper  Coal.” 

Croppings.— Portions  of  a vein  as  seen  exposed  at  the  surface. 

Cropping  Out.— Appearing  at  the  surface;  outcropping.  . 

Cross-Course. — A vein  lying  more  or  less  at  right  angles  to  the  regular  vein  of 
the  district. 


582 


Cro 


GLOSSARY. 


Deb 


Crosscut.— (1)  A tunnel  driven  through  or  across  the  measures  from  one 
seam  to  another.  (2)  A small  passageway  driven  at  right  angles  to  the 
main  gangway  to  connect  it  with  a parallel  gangway  or  air-course. 

Crosses  and  Holes  (Derbyshire).— Made  in  the  ground  by  the  discoverer  of  a 
lode  to  tempoiarily  secure  possession. 

Cross-Heading. — A passage  driven  for  ventilation  from  the  airway  to  the  gang- 
way, or  from  one  breast  through  the  pillar  to  the  adjoining  working. 

Cross-Heading , or  Cross-Gateway  .—A  road  kept  through  goaf  and  cutting  off 
the  gateways  at  right  angles  or  diagonally. 

Cross-Hole. — See  Crosscut  (2). 

Cross- Latches. — See  Latches. 

Cross-Spur. — A vein  of  quartz  that  crosses  the  reef. 

Cross-  Vein. — An  intersecting  vein. 

Crouan  (Cornish).— Granite. 

Crowbar. — A strong  iron  bar  with  a slightly  curved  and  flattened  end. 

Crowfoot— A tool  for  drawing  broken  boring  rods. 

Crown  Tree.— A piece  of  timber  set  on  props  to  support  the  roof. 

Crucero  (Mexican). — A crosscut  for  ventilation  to  get  around  a horse,  or  to 
prospect  for  the  vein. 

Crucible.— ( 1)  The  bottom  of  a cupola  furnace  in  which  the  molten  materials 
collect.  (2)  Pots  for  smelting  assays  in. 

Crush. — See  Squeeze , Thrust. 

Crusher— A machine  used  for  crushing  ores  and  rock. 

Crushing—  Reduction  of  mineral  in  size  by  machinery. 

Crystal. — A solid  of  definite  geometrical  form,  which  mineral  (or  sometimes 
organic)  matter  has  assumed. 

Culm.— Anthracite-coal  dirt. 

Culm  Bank , or  Culm  Dump—  Heaps  of  culm  now  generally  kept  separate 
from  the  rock  and  slate  dumps. 

Cuna  (Mexican). — Literally,  a wedge.  A short  drill  or  picker  generally 
known  in  the  United  States  as  a “gad.” 

Cupel— A cup  made  of  bone  ash  for  absorbing  litharge. 

Curb.— (1)  A timber  frame  intended  as  a support  or  foundation  for  the  lining 
of  a shaft.  (2)  The  heavy  frame  or  sill  at  the  top  of  a shaft. 

Curbing.— The  wooden  lining*  of  a shaft. 

Cut. — (1)  To  strike  or  reach  a vein.  (2)  To  excavate  in  the  side  of  a hill. 

Cutter. — A term  employed  in  speaking  of  any  coal-cutting  or  rock-cutting 
machines;  the  men  operating  them,  or  the  men  engaged  in  underholing 
by  pick  or  drill. 

Cutting  Down.— To  cut  down  a shaft  is  to  increase  its  sectional  area. 

Dam.— A timber  bulkhead,  or  a masonry  or  brick  stopping  built  to  prevent 
the  water  in  old  workings  from  flooding  other  workings,  or  to  confine 
the  water  in  a mine  flooded  to  drown  out  a mine  fire. 

Damp.— Mine  gases  and  gaseous  mixtures  are  called  damps.  See  also  After- 
damp, Blackdamp , Firedamp , Stinkdamp. 

Dan  (North  of  England).— A truck  without  wheels. 

Danger  Board. — See  Fireboard. 

Dant  (North  of  England). — Soft  inferior  coal. 

Datum  Water  Level.— The  level  at  which  water  is  first  struck  in  a shaft 
sunk  on  a reef  or  gutter. 

Davy.— A safety  lamp  invented  by  Sir  Humphrey  Davy. 

Day. — Light  seen  at  the  top  of  a shaft. 

Day  Fall. — See  Crop  Fall. 

Day  Shift.— The  relay  of  men  working  in  the  daytime. 

Dead. — The  air  of  a mine  is  said  to  be  dead  or  heavy  when  it  contains  car- 
bonic-acid gas,  or  when  the  ventilation  is  sluggish. 

Dead. — (1)  Unproductive.  (2)  Unventilated. 

Dead  Men’s  Gi'aves  (Australian). — Grave-like  mounds  in  the  basalt  under- 
lying auriferous  gravels. 

Dead  Quartz.— Quartz  carrying  no  mineral. 

Dead  Riches.— Lead  carrying  much  bullion. 

Dead  Roast. — To  completely  drive  off  all  volatile  substances. 

Deads. — Waste  or  rubbish  from  a mine. 

Dead  Work. — Exploratory  or  prospecting  work  that  is  not  directly  productive. 
Brushing  roof,  lifting  bottom,  cleaning  up  falls,  blowing  rock,  etc. 

Dean  (Cornish).— The  end  of  a level. 

Debris—  Fragments  from  any  kind  of  disintegration. 


GLOSSARY. 


Dip 


583 


Dee 


Beep  (English).— “ To  the  deep,”  toward  the  lower  portion  of  a mine;  hence, 

Bella. — A triangularly  shaped  piece  of  alluvial  land  at  the  mouth  of  the 

Yiver  • 

Bemasia  (Mexican). — A piece  of  unoccupied  ground  between  two  mining 

concessions. 

Denudation The  laving  bare  by  water  or  other  agency. 

Benuncio  (Mexican).— Denouncement.  The  act  of  applying  for  a mining 
concession  under  the  old  mining  laws. 

Deposit.— { 1)  Irregular  ore  bodies  not  veins.  (2)  A bed  or  any  sedimentary 

DenSvTEnglish).— (1)  A man  who  fixes  and  withdraws  %etimker  sup- 
porting^!^ roof  of  a mine,  and  attends  to  the  safety  of  the  roof  and 
sides,  builds  stoppings,  puts  up  bratticing,  and  looks  after  t^  safety  of 
the  hewers,  etc.  (2)  An  underground  othcial  who  sees  to  the  general 
safety  of  a certain  number  of  stalls  or  of  a district,  but  does  not  set 
the  timber  himself,  although  he  has  to  see  that  it  is  properly  and  suffi- 
ciently done.  (3)  (American)  A deputy  sheriff.  . 

Berrick. — (1)  A crane  in  which  the  rope  or  chain  forming 

let  out  or  hauled  in  at  pleasure,  thus  altering  the  inclination  of  Ihe  jib 
(2)  The  structure  erected  to  sink  a drill  hole  and  the  framework  above 
shafts  are  sometimes  called  by  this  name.  . . - 0 

Derrumbe , or  Derrumbamineto  (Mexican). — The  caving  m of  the  whole  or  a 
portion  of  a mine.  . . 

Desaguador  (Spanish). — A water  pipe  or  dram. 

Besague  ( Mexican ) . — Drainage  of  a mine  by  any  means.  - 

Bescargar  (Mexican).— Literally,  “to  unload.  Bescargar  un  Homo.  To 

Descubridoral Mexican^— The  first  mine  opened  in  a new  district  or  on  a 
new  mineral  deposit. 

Besecho  (Spanish).— Foul  red  mercury. 

Besfrute  (Mexican).— Taking  out  ore.  Obras  de  Desfrute  — Stopes,  etc. 

Besmontar  (Mexican).— Literally,  to  clear  away  underbrush.  In  mining,  to 
take  away  useless  and  barren  rocks;  to  remove  rubbisn. 

Besmontes  (Spanish).— Poor  ores. 

Bespensa  (Mexican)  .—(1)  A pantry  or  storeroom.  (2) 
up  rich  ore. 

Bespoblado  (Spanish).— Ore  with  much  gangue.  , 

Bespoblar  ( Mexican ) . — To  suspend  work  m a mine. 

Bessue  (Cornish) —To  cut  away  the  ground  beside 

remove  the  latter  whole.  , . _ _ . . _ , „ 

Bestajo  (Mexican).— (1)  A contract  to  do  any  kind  of  work  in  or  ab9ut  a 
mine  or  elsewhere  for  a fixed  price.  (2)  Piece  work,  as  distinguished 
from  time  work.  Bestajero.— A contractor  for  piece  work. 

Detaching  Hook.— A self-acting  mechanical  contrivance  for  setting  free  J 
winding  rope  from  a cage  when  the  latter  is  raised  beyond  a certain 
point  in  the  head-gear;  the  rope  being  released,  the  cage  remains 
suspended  in  the  frame. 

Devil's  Dice. — Cubes  of  limomte,  pseudomorphs  after  pyrites. 

Diagonal  Joints.- Joints  diagonal  to  the  strike  of  the  cleavage. 

Dial  (English). — An  instrument  similar  to  a surveyors  compass,  witfi 
vernier  attached. 

Die.— The  bottom  iron  block  of  a battery,  or  grinding  pan  on  which  the 
sllOG  9/Ct)S 

Digging. — Mining  operations  in  coal  or  other  minerals. 

Diggings— Where  gold  and  other  minerals  are  dug  out  from  shallow 
alluvials. 

Lillies,  oT  M^Short  self-acting  inclines  where  one  or  two  tubs  at  a 
time  are  run.  . 

Dillueing  (Cornish). — Dressing  tin  slimes  in  a fine  sieve. 

Dip  —(l)  To  slope  downwards.  (2)  The  inclination  of  strata  with  a hon 
zontal  plane.  (3)  The  lower  workings  of  a mine. 

Dip  Joint. — V ertical  joints  about  parallel  to  the  direction  of  the  cleavage  dip. 

Dippa  (Cornish). — A small  catch-water  pit. 

Dipping  'Needle. — A magnetic  needle  suspended  in  a vertical  plane,  tor 
locating  iron  deposits. 


A secure  room  to  lock 


thin  vein  so  as  to 


584 


Dir 


GLOSSARY. 


Dre 


Dirt  Fault  —A  confusion  in  a seam  of  coal,  the  top  and  bottom  of  the  seam 
being  well  defined,  but  the  body  of  the  vein  being  soft  and  dirty. 

Dish  (Cornish) —An  ore  measure;  in  lead  mines,  a trough  28  in.  long,  4 in. 

deep  and  6 in.  broad;  sometimes  1 gallon,  sometimes  14  to  16  pints. 
Disintegration. — Separation  by  mechanical  means,  not  by  decomposition. 
Ditch — (1)  The  drainage  gutter  in  a mine.  (2)  A drainage  gutter  on  the 
surface.  (3)  An  open  conveyor  of  water  for  hydraulic  or  irrigation 
purposes.  , 

Divide. — The  top  of  a ridge,  hill,  or  mountain. 

Dividing  Slate— A stratum  of  slate  separating  two  benches  of  coal.  See 
PVLVtVflQ 

Divining , or  Dowsing , Rod— A small  forked  hazel  twig  that,  when  held 
loosely  in  the  hands,  is  supposed  to  dip  downwards  when  passing  over 
water  or  metallic  minerals. 

Dizzue  (Cornish).— See  Dessue.  . , , 

Doa—(l)  An  iron  bar,  spiked  at  the  ends,  with  which  timbers  are  held 
together  or  steadied.  (2)  A short  heavy  iron  bar,  used  as  a drag  behind 
a car  or  trip  of  cars  when  ascending  a slope  to  prevent  their  running 
back  down  the  slope  in  case  of  accident.  See  Drag. 

Dog  Hole.— A little  opening  from  one  place  in  a mine  to  another,  smaller 
than  a breakthrough.  , „ . , , _ . . , 

Doa  Iron.— A short  bar  of  iron  with  both  ends  pointed  and  bent  down  so  as 
to  hoid  together  two  pieces  of  wood  into  which  the  points  are  driven. 
Or  one  end  may  be  bent  down  and  pointed,  while  the  other  is  formed 
into  an  eye,  so  that  if  the  point  be  driven  into  a log,  the  other  end  may 
be  usedvto  haul  on.  ^ _ 

Doles. — Small  piles  of  assorted  or  concentrated  ore.  . , 

Dollv  — (1)  A machine  for  breaking  up  minerals,  being  a rough  pestle  and 
mortar,  the  former  being  attached  to  a spring  pole  by  a rope.  (2)  A 
tool  used  to  sharpen  drills.  . . , , . ^ „ 

Dolly  Tub  (Cornish).— A tub  in  which  ore  is  washed,  being  agitated  by  a 
dollv  or  perforated  boards. 

Donk  (North  of  Ehgland).— Soft  mineral  found  m cross-veins. 

Donkey  Engine  (English).— (1)  A small  steam  engine  attached  to  a large  one, 
and  fed  from  the  same  boiler;  used  for  pumping  water  into  the  boiler. 
(2)  A small  steam  engine.  „ . , . , , , 

Door  Piece  (English).— The  portion  of  a lift  of  pumps  in  which  the  clack  or 

valve  is  situated.  „ , . . , « . . 

j)00rs  —Wooden  doors  in  underground  roads  or  airways  to  deflect  the  air- 

current.  . , 

Door  Tender— A boy  whose  duty  it  is  to  open  and  close  a mine  door  before 
and  after  the  passage  of  a train  of  mine  cars.  , 

Dope. — An  absorbent  for  holding  a thick  liquid.  The  material  that  absorbs 
the  nitroglycerine  in  explosives.  ...... 

Double  Shift.— When  there  are  two  sets  of  men  at  work,  one  set  relieving  the 

Double *Tape  Fuse—  Fuse  of  superior  quality,  or  having  a heavier  and  stronger 

Double  timber. —Two  props  with  a bar  placed  across  the  tops  of  them  to  sup- 
port the  roof  and  sides.  „ , . . , „ , . . 

Downcast. — The  opening  through  which  the  fresh  air  is  drawn  or  forced  into 

Dradge  fCornish)6^ {if  Inferior  ore  separated  from  the  prill.  (2)  Pulverized 

refuse  ^ 

Draftage.—A  deduction  made  from  the  gross  weight  of  ore  when  transported, 

1) ' t he  frictional  resistance  offered  to  a current  of  air  in  a mine. 

Dra^-il)  To^‘  draw  ” the  pillars;  robbing  the  pillars  after  the  breasts  are 
exhausted.  (2)  An  effect  of  creep  upon  the  pillars  of  a mine. 

Draw  a Charge.— To  take  a charge  from  a furnace. 

Drawlift.—A  pump  that  receives  its  water  by  suction  and  will  not  iorce  it 

Dr(m-Hrte*—  Anaperture  in  a battery  through  which  the  coal  is  drawn. 
Drawing  an  Entry. — Removing  the  last  of  the  coal  from  an  entry 
Drawn.— The  condition  in  which  an  entry  or  room  is  left  after  all  the  coal 
has  been  removed.  See  Robbed. 

Dresser  (Staffordshire).— A large  coal  pick. 


L)RE 


GLOSSARY. 


Egg 


585 


Pressing— Preparing  poor  or  mixed  ores  mechanically  for  metallurgical 

nresSZa^Floors  —The  floors  or  places  where  ores  are  dressed. 

Drift (1)  A horizontal  passage  underground.  A drift  follows  the  vein,  as 
distinguished  from  a Crosscut,  which  intersects  it,  or  a level  or  gahery, 
which  may  do  either.  (2)  In  coal  mining,  a gangway  above  water 
level  driven  from  the  surface  in  the  seam.  (3)  Unstratified  diluvium. 

Drifting.— Winning  pay  dirt  from  the  ground  by  means  of  drives. 

Drill—  An  instrument  used  in  boring  holes. 

Drive  ( Drift).  A horizontal  passage  in  a lode. 

Drive  —To  cut  an  opening  through  strata.  . 

Driving. — Excavating  horizontal  passages,  in  contradistinction  to  sinking  or 

Driving  on' iine.-Keeping  a heading  or  breast  accurately  on  a given  course 

bv  means  of  a compass  or  transit.  . . n , 

Dronper  — (1)  A spur  dropping  into  the  lode.  (2)  A feeder.  (3)  A branch 
leaving  the  vein  on  the  footwall  side.  (4)  Water  dropping  from  the  roof 

Drop  Shaft— A monkey  shaft  down  which  earth  and  other  matter  are  lowered 
by  means  of  a drop  (i.  e.,  a kind  of  pulley  with  break  attached),  the 
empty  bucket  is  brought  up  as  the  full  one  is  lowered. 

Druqqon  (Staffordshire).— A vessel  for  carrying  fresh  water  into  a mine. 

Drum.— The  cylinder  or  pulley  on  which  the  winding  ropes  are  coiled  or 

Drmn  Rings.— Cast-iron  rings  with  projections  to  which  are  bolted  the 
laggings  forming  the  surface  for  the  ropes  to  lap  on.  _ 

Drummy.— Sounding  loose,  open,  shaky,  or  dangerous  when  tested. 

Druse.— A hollow  cavity  lined  with  small  crystals. 

Dry  Amalgamation.— Treating  ores  with  hot,  dry  mercury. 

Dry  Diggings—  Placers  never  subject  to  overflow. 

Dry  Orel—  Argentiferous  ores  that  do  not  contain  enough  lead  for  smelting 

DuckMuMne.— An  arrangement  of  two  boxes,  one  working  within  the 
other,  for  forcing  air  into  mines. 

Duelas  (Mexican).— Staves  of  a barrel  or  cask,  etc. 

Dumb’d. — Choked,  of  a sieve  or  grating.  . 

Dumb  Drift.- A short  tunnel  or  passage  connecting  the  mam  return  airways 
of  a mine  with  the  upcast  shaft  some  distance  above  the  furnace,  m order 
to  prevent  the  return  air  laden  with  mine  gases  from  passing  through  or 
over  the  ventilating  furnace.  . « .. 

Dump—  (1)  A pile  or  heap  of  ore,  coal,  culm,  slate,  or  rock.  (2)  The  tipple 
by  which  the  cars  are  dumped.  (3)  To  unload  a car  by  tipping  it  up. 

(4)  The  pile  of  mullock  as  discharged  from  a mine. 

Dumper.— A car  so  constructed  that  the  body  may  be  revolved  to  dump  the 
material  in  front  or  on  either  side  of  the  track. 

Durn  (Cornish).— A timber  frame. 

Durr  (German).— Barren  ground. 

Dust.— See  Coal  Dust. 

Dust  Gold. — Pieces  under  2 to  3 dwt.  . . _ , . 

Duty. — The  unit  of  measure  of  the  work  of  a pumping  engine  expressed  m 
foot-pounds  of  work  obtained  from  a bushel,  or  100  lb.,  or  other  unit  of 

Dyke* or  Dike.—{  1)  A wall  of  igneous  rock  passing  through  strata,  with  or 
without  accompanying  dislocation  of  the  strata.  (2)  A fissure  filled  with 
igneous  matter.  (3)  Barren  rock. 

Dzhu  (Cornish).— See  Dessue. 

Ear.— The  inlet  or  intake  of  a fan.  . , . , , 

Echadero  (Mexican). — A level  place  near  a mine  where  ore  is  cleaned,  piled, 
weighed,  and  loaded  on  mules  or  other  conveyance.  Also  called  patio  ot 
the  mine. 

Echado  (Mexican).— The  dip  of  the  vein.  . 

Edge  Coals  (English).— Highly  inclined  seams  of  coal,  or  those  having  a dip 
greater  than  30^* 

Efflorescence.— An  incrustation  by  a secondary  mineral,  due  to  loss  of  water 
of  crystallization. 

¥gf  Cool— Anthrac?^61 coal  that  will  pass  through  a 2*"  square  mesh  and 
over  a 2"  square  mesh  (see  page  434). 


586 


Elb 


GLOSSARY. 


Fal 


Elbow— A sharp  bend,  as  in  a lode  or  pipe. 

Electric  Blast—  Instantaneous  blasting  of  rock  by  means  of  electricity. 

Elevator  Pump—  An  endless  band  with  buckets  attached,  running  oyer  two 
drums  for  draining  shallow  ground. 

Elvan  — A Cornish  name  applied  to  most  dike  rocks  of  that  county,  irre- 
spective of  the  mineral  constitution,  but  in  the  present  day  restricted 
to  quartz  porphyries. 

Emborrascarse  (Mexican).— To  go  barren  by  the  vein  terminating  or  pinching 
out,  etc. 

Empties—  Empty  mine  or  railroad  cars. 

Encino  (Mexican).— Live  oak. 

End  Joint  (End  Cleat).— A joint  or  cleat  in  a seam  about  at  right  angles  to 
the  principal  or  race  cleats. 

Endless  Chain— A system  of  haulage  or  pumping  by  the  moving  of  an 
endless  chain. 

Endless  Rope— A system  of  haulage  same  as  endless  chain,  except  that  a 
wire  rope  is  used  instead  of  chain. 

End,  or  End-On— Working  a seam  of  coal  at  right  angles  to  the  principal 
or  face  cleats. 

Engine  Plane—  An  incline  up  which  loaded  cars  are  drawn  by  a rope 
operated  by  an  engine  located  at  the  top  or  bottom  of  the  incline.  The 
empty  cars  descend  by  gravity,  pulling  the  rope  after  them. 

Engineer— { 1)  One  who  has  charge  of  the  surveying  or  machinery  about  a 
mine.  (2)  One  who  runs  an  engine. 

Ensayes  (Mexican).— Assays. 

Entibar  (Mexican).— To  timber  a mine  or  any  part  thereof. 

Entry —A  main  haulage  road,  gangway,  or  airway.  An  underground  passage 
used  for  haulage  or  ventilation,  or  as  a manway. 

Entry  Stops— Pillars  of  coal  left  in  the  mouths  of  abandoned  rooms  to 
support  the  road,  entry,  or  gangway  till  the  entry  pillars  are  drawn. 

Erosion.— The  wearing  away  of  rocks  by  rains,  etc. 

Escaleras  (Mexican).— Ladders,  generally  made  of  notched  sticks. 

Escarpment  — A nearly  vertical  natural  face  of  rock  or  soil. 

Escoria  (Mexican).— Slag  or  cinders. 

Escorial. — Slag  pile. 

Escorificador  (Mexican).— A scorifier,  in  assaying. 

Espejuelo  (Mexican).— A mineral  gangue,  with  a faintly  reflecting  surface. 

Espeton  (Mexican).— The  tapping  bar  of  a smelting  furnace. 

Estano  (Spanish). — Tin. 

Estrujon  (Mexican).— A second  collection  of  amalgam,  generally  very  pasty. 

Exploder.— A chemical  employed  for  the  instantaneous  explosion  of  powder. 

Exploitation— The  working  of  a mine,  and  similar  undertakings;  the  exami- 
nation instituted  for  that  purpose. 

Exploration—  Development. 

Explosion.— Sudden  ignition  of  a body  of  firedamp. 

Eye  (English).— (1)  A circular  hole  in  a bar  for  receiving  a pin  and  for 
other  purposes.  (2)  The  eye  of  a shaft  is  the  very  beginning  of  a pit. 
(3)  The  eye  of  a fan  is  the  central  or  intake  opening. 

Face.— (1)  The  place  at  which  the  material  is  actually  being  WOTked,  either 
in  a breast  or  heading  or  in  longwall.  (2)  The  end  of  a drift  or  tunnel. 

Face-On. — When  the  face  of  the  breast  or  entry  is  parallel  to  the  face  cleats 
of  the  seam  (see  page  285).  . 

Face  Wall.— A wall  built  to  sustain  a face  cut  into  the  natural  earth,  in 
distinction  to  a retaining  wall,  which  supports  earth  deposited  behind  it. 

Faenas  (Mexican).— Dead  work,  in  the  way  of  development. 

Fahlband  (German). — A course  impregnated  with  metallic  sulphides. 

Faiscador  (Spanish).— A gold  washer. 

Fall.—{  1)  A mass  of  roof  or  side  which  has  fallen  in  any  part  of  a mine. 
(2)  To  blast  or  wedge  down  coal. 

False  Bedding.— Irregular  lamination,  wherein  the  laminae,  though  for 
short  distances  parallel  to  each  other,  are  oblique  to  the  general  strati- 
fication of  the  mass  at  varying  angles  and  directions. 

False  Bottom.— (1)  A movable  bottom  in  some  apparatus.  (2)  A stratum  on 
which  pay  dirt  lies,  but  which  has  other  layers  below  it. 

False  Cleavage.— A secondary  slip  cleavage  superinduced  on  slaty  cleavage. 

False  Set.— A temporary  set  of  timber  used  until  work  is  far  enough  advanced 
to  put  in  a permanent  set. 


Fam 


GLOSSARY ; 


Fla 


587 


Famp  (North  of  England).—' Thin  beds  of  soft  tough  shale. 

Fan!— A machine  for  creating  a circulation  of  air  in  a mine. 

Fan  Drift— A short  tunnel  or  conduit  leading  from  the  top  of  the  air-shaft  to 
the  fan.  , „ , A , . , 

Fanega  (Mexican).— A Spanish  measure  of  about  2£  bushels. 

Fang  (Derbyshire). — An  air-course. 

Fascines  (English).— Bunches  of  twigs  and  small  branches  for  forming 
foundations  on  soft  ground.  , 

j past  —(1)  A road  driven  in  a seam  with  the  solid  coal  at  each  side.  Fast 
at  an  end,”  or  “ fast  at  one  side,”  implies  that  one  side  is  solid  coal  and 
the  other  open  to  the  goaf  or  some  previous  excavation.  (2)  Bed  rock. 
Fast  End— A n end  of  a breast  of  coal  that  requires  cutting. 

Fat  Coals.— Those  containing  volatile  oily  matters. 

jfaS?.— i^fracture  or  disturbance  of  the  strata  breaking  the  continuity  of 

the  formation.  , , 

Feather  —A  slightly  projecting  narrow  rib  lengthwise  on  a shaft,  arranged 
to  catch  into  a corresponding  groove  in  anything  that  surrounds'  and 
slides  along  the  shaft.  , 

Feather  Edge  — (1)  A passage  from  false  to  true  bottom.  (2)  The  thin  end 
of  a wedge-shaped  piece  of  rock  or  coal. 

Feather  Ore. — Sulphide  of  lead  and  antimony.  ^ 

Feed.— Forward  motion  imparted  to  the  cutters  or  drills  of  rock-drilling  or 
coal-cutting  machinery,  either  hand  or  automatic. 

Feeder. — (1)  A runner  of  water.  (2)  A small  blower  of  gas. 

Feigh  (North  of  England). — Ore  refuse.  ^ , 

Fencing. — Fencing  in  a claim  is  to  make  a drive  round  the  boundaries  of 
an  alluvial  claim,  to  prevent  wash  dirt  from  being  worked  out  by 
adjoining  claim  holders.  , „ J , . , , 

Fend-OJf  (English).— A sort  of  bell-crank  for  turning  a pump  rod  past  the 
angle  of  a crooked  shaft. 

Fierros  (Mexican).— Iron  matte. 

Fiery.— Containing  explosive  gas.  1 

Fines— Very  small  material  produced  in  breaking  up  large  lumps. 

Fire—  (1)  A miners’  term  for  firedamp.  (2)  To  blast  with  gunpowder  or 
other  explosive.  (3)  A word  shouted  by  miners  to  warn  one  another 
when  a shot  is  fired.  , . , . . 

Fire-Bars  (English)  .—The  iron  bars  of  a grate  on  which  the  fuel  rests. 
Fireboard.—A  piece  of  board  with  the  word  fire  painted  upon  it  and  sus- 
pended to  a prop,  etc.,  in  the  workings,  to  caution  men  not  to  take  a 
naked  light  beyond  it,  or  to  pass  it  without  the  consent  of  the  foreman 
or  his  assistants.  _ , 

Fire  Boss.— An  underground  official  who  examines  the  mine  for  gas  and 
inspects  safety  lamps  taken  into  the  mine. 

Fireclay— Any  clay  that  will  withstand  a great  heat  without  vitrifying. 
Firedamp.— (1)  A mixture  of  light  carburetted  hydrogen  ( CIL)  and  air  m 
explosive  proportions;  often  applied  to  CH±  alone  or  to  any  explosive 
mixture  of  mine  gases. 

Fireman. — See  Fire  Boss.  . 

Fire-Setting.— The  process  of  Exposing  very  hard  rock  to  intense  heat,  ren- 
dering it  thereby  easier  for  breaking  down. 

First  Working. — See  Whole  Working. 

Firsts— The  best  ore  picked  from  a mine. 

Fish.—1 To  join  two  beams,  rails,  etc.  together  by  long  pieces  at  their  sides. 
Fissure— An  extensive  crack. 

Fissure  Vein—  Any  mineralized  crevice  in  the  rock  of  very  great  depth. 
Flags—  Broad  flat  stones  for  paving.  A , _ 

Flagstone—  Any  kind  of  a stone  that  separates  naturally  into  thm  tabular 
plates  suitable  for  pavements  and  curbing.  Especially  applicable  to 
sandstone  and  schists. 

Flang  (Cornish).— A double-pointed  pick. 

Flange  (English).— A projecting  ledge  or  rim. 

Flat.— (1)  A district  or  set  of  workings  separated  by  faults,  old  workings,  or 
barriers  of  solid  coal.  (2)  The  siding  or  station  laid  with  two  or  more 
lines  of  railway,  to  which  the  putters  bring  the  full  cars  from  the  work- 
ing face,  and  where  they  get  the  empty  cars  to  take  back.  (3)  The  area 
of  working  places,  from  which  coal  is  brought  to  the  same  station,  is  also 
called  “flat.” 


588 


Fla 


GLOSSARY. 


FrE 


Flat  Rod.— A horizontal  rod  for  conveying  power  to  a distance. 

Flats—  Narrow  decomposed  parts  of  limestones  that  are  mineralized. 

Flat  Sheet—  Sheet-iron  flooring  at  landings  and  in  the  plats,  chambers,  and 
junctions  of  drives,  to  facilitate  the  turning  and  management  of  trucks. 

Flat  Wall  (Cornish).— Foot-wall. 

Flintshire  Furnace— A kind  of  reverberatory  furnace  used  for  smelting  lead 

jpfo^—Broken  and  transported  particles  or  boulders  of  vein  matter. 

Float  Gold—  Gold  in  thin  scales,  which  floats  on  water. 

Float  Ore.— A term  applied  by  miners  to  ore  found  loose  in  the  clay  or  soil. 

Float  Stowes— Loose  boulders  from  lodes  lying  on  or  near  the  surface. 

Flood  Gate  (English).— A gate  to  let  off  excess  of  water  in  flood  or  other 
times. 

Floor  — (i)  The  stratum  of  rock  upon  which  a seam  of  coal  immediately 
lies.  (2)  That  part  of  a mine  upon  which  you  walk  or  upon  which  the 
road  bed  is  laid. 

Floram  (Cornish).— Very  fine  tin. 

Flour  Gold. — The  finest  alluvial  gold.  , 

Flouring.— Mercury  reduced  to  fine  globules  that  are  easily  contaminated 
and  will  not  amalgamate.  , . A ‘ . 

Flucan.—A  soft,  greasy,  clayey  substance  found  m the  joints  of  veins. 

Fluke.— A rod  for  cleaning  out  drill  holes. 

Flume.— An  artificial  watercourse.  „ . 

Pluming — Lifting  a river  out  of  its  bed  with  wooden  launders  or  pipes,  in 
order  to  get  at  the  bed  for  working.  ^ . ,, 

Flush .— (1)  To  clean  out  a line  of  pipes,  gutters,  etc.  by  letting  m a sudden 
rush  of  water.  (2)  The  splitting  of  the  edges  of  stone  under  pressure. 
(3)  Forming  an  even  continuous  line  or  surface.  (4)  To  fill  a mine 
with  fine  material. 

Fluthwerk  (German). — Fiver  prospecting.  . 

Flux—  Iron  ore,  limestone,  and  sand,  which  are  added  m various  propor- 
tions to  the  charge  in  a furnace  to  make  the  gangue  melt  up  and  flow 
off  easily.  „ , „ 

Fodder  (North  of  England).— 21  cwt.  of  lead. 

Following  Stone.— R oof  stone  that  falls  on  the  removal  of  the  seam. 

Foot  (Cornish).— 2 gallons,  or  60  lb.,  black  tin.  . 

Foot-Hole. — Holes  cut  in  the  sides  of  shafts  or  winzes  to  enable  miners  to 
ascend  and  descend.  , , , , , ... 

Foot- Piece.— (1)  A wedge  of  wood  or  part  of  a slab  placed  on  the  toot-wail 
against  which  a stull  piece  is  jammed.  (2)  A piece  of  wood  placed  on 
the  floor  of  a drive  to  support  a leg  or  prop  of  timber. 

Foot-  Wall. — The  lower  boundary  of  a lode. 

Footway.— Ladders  in  mines. 

Force  Fan—  See  Blowdown  Fan. 

Force  Piece—  Diagonal  timbering  to  secure  the  ground. 

Force  Pump— A pump  that  forces  water  above  its  valves.  . 

Forehay.— Penstock.  The  reservoir  from  which  water  passes  directly  to  a 
waterwheel. 

Foreyolinq. — Driving  the  poles  over  the  timbers  so  that  their  ends  project 
beyond  the  last  set  of  timber,  so  as  to  protect  the  miner  from  roof  falls; 
used  also  in  quicksand  or  other  loose  material.  . , 

Forewinninq—  The  first  working  of  a seam  in  distinction  from  pillar  drawing. 

Fork .— (1)  A deep  receptacle  in  the  rock,  to  enable  a pump  to  extract  the 
bottom  water.  A pump  is  said  to  be  “ going  in  fork  ” when  the  water  is 
so  low  that  air  is  sucked  through  the  windbore.  (2)  (Cornish)  Bottom 
of  sump.  (3)  (Derbyshire)  Prop  for  soft  ground.  . 

Formation.— A series  of  strata  that  belong  to  a single  geological  age. 

Fossickers  (Australian).— Grubbers  for  gold  in  the  beach  sand. 

Fossicking—  Overhauling  old  workings  and  refuse  heaps  for  gold. 

Fossil. — Organic  remains  or  impressions  of  them  found  in  mineral  matter. 

Fother  (North  of  England). — i chaldron.  ....  , 

Frame. — A table  composed  of  boards,  slightly  inclined,  over  which  water 
runs  to  wash  off  waste  from  sluice  tin. 

Frame  Set.— The  legs  and  cap  or  collar  arranged  so  as  to  support  a passage 
mined  out  of  the  rock  or  lode;  also  called  Framing.  . _ .. 

Free—  Coal  is  said  to  be  “ free  ” when  it  is  loose  and  easily  mined,  or  when  it 
will  “run”  without  mining. 

Free  Milling . — Ores  requiring  no  roasting  or  chemical  treatment. 


FRE 


GLOSSARY. 


Gob 


589 


Free  Miner.— Licensed  miner. 

Fresno  (Mexican).— An  ash  tree. 

Fronton  (Mexican).— Any  working  face. 

lT^oal  fc  or  near  the  bottom  of  an  upcast  shaft,  for  pro- 
dncing  a current  of  air  for  ventilating  the  mine. 

tridges.  '2)  To  melt. 

GaZap^^(MexiSn^^ASturtle-shaped  pig  of  lead. 

Gale.— A grant  of  mining  ground. 

Galiage.— Royalty. 

&Mex"-Ki0rs^me^  of  silver  or  gold  ore,  particularly  those 
-The*  frame  sufporiing  a pulley  over  which  the  hoisting  rope 
Gam&lMexi^-A  prospector  for  gold  placers  or  ores. 

Qanguet- Wasteniaterial  from  lodes. 

GamS^-^hard^ompacL^^^  ®rec^a^.'  smelting 

Gas  Coal  —Bituminous  coal  containing  a large  percentage  of  ga  . 

«5a aSSSSasif 48=*— 01  - 

GaZX-l  wono“lorTxed  in  an  airway  for  regulatlng  the  supply 

“ iS 

<>octa— Large  nodules  of  stone  v 

Geordie  — A safety  lamp  invented  by  George  btepnensou. 

with  a wedge-shaped  key  for  holding  pieces  together. 
RV«“-A  vertical  drum  and  framework  by  which  the  minerals 

or  waste  rock  when  it  arrives  at  the  surface.  degcribed  as  a p0st  roof 

“thmlta?  or^metal  roof  with  post  girdles,  according  as  the 

post  or  the  metal  predominates. 

t»,<2SffidSffSS*<K‘»&4S}  satr1 1"  l”°  *"1“d 
»qg-  “H-nasi 

, , v . 1 4.  ^„„iT„fnWo  in  thp  mine.  ( 


Gob 


that ' are*no t^marketabie  hi  the  mine.  (3)  To  stow  or  pack  any  useless 

«f  toe  coal  and  slack  in 

the  gob. 


590 


Gob 


GLOSSARY. 


Gut 


Gobbing  Up—  Filling  with  waste. 

Gob  Road,.— A roadway  in  a mine  carried  through  the  goaf. 

Going  Headways , or  Going  Bord.—A  headway  or  bord  laid  with  rails,  and 
used  for  conveying  the  coal  tubs  to  and  from  the  face. 

Golpeador  (Mexican).— A striker,  in  hand  drilling. 

Gossan.— A spongy  ferruginous  oxide,  left  after  the  soluble  substances  have 
been  dissolved  out  of  a lode. 

Goths  (Staffordshire). — Sudden  burstings  of  coal  from  the  face,  owing  to 
tension  caused  by  unequal  pressure. 

Gouge—  The  layer  of  clay,  or  decomposed  rock,  that  lies  along  the  wall  or 
walls  of  a vein.  It  is  not  always  valueless. 

Grade—  The  amount  of  fall  or  inclination  in  ditches,  flumes,  roads,  etc. 

Grain—  An  obscure  vertical  cleavage  usually  more  or  less  parallel  to  the  end 
or  dip  joints. 

Granza  (Mexican). — Metallic  minerals  from  the  size  of  rice  to  that  of 
hens’  eggs. 

Grasa  (Mexican). — Literally,  grease.  Slags. 

Grass.— The  surface  of  the  ground. 

Grassero  (Spanish). — Slag  heap. 

Grate  Coal. — See  Broken  Coal. 

Grating.— A perforated  iron  sheet  or  wire  gauze  placed  in  front  of  reducing 
machinery. 

Gravel.— Water- worn  stones  about  the  size  of  marbles. 

Gray  Metal.— Shale  of  a grayish  color. 

Graywacke. — A compact  gray  sandstone  frequently  found  in  Paleozoic 
formations. 

Greenstone. — A general  term  employed  to  designate  green-colored  igneous 
rocks,  as  diorite,  dolerite,  diabase,  gabbro,  etc. 

Grena  (Spanish).— Undressed  ore. 

Greta  (Mexican). — Impure  litharge  formed  in  a reverberatory  furnace. 

Griddle— A coarse  sieve  used  for  sifting  ores,  clay,  etc. 

Grizzly.— A grating  to  throw  out  large  stones  from  hydraulic  gold 
sluices. 

Ground  Rent.— Rent  paid  for  surface  occupied  by  the  plant,  etc.  of  a 
colliery. 

Groundsill.— A log  laid  on  the  floor  of  a drive  on  which  the  legs  of  a set  of 
timber  rest. 

Ground  Sluicing. — Washing  alluvial,  loosened  by  pick  and  shovel,  in  trenches 
cut  out  of  the  bed  rock,  using  bars  of  rock  as  natural  riffles.  Used  in 
shallow  placers,  hill  claims,  bank  claims,  and  stream  diggings. 

Grout  (English).— Thin  mortar  poured  into  the  interstices  between  stones 
and  bricks. 

Grove  (Derbyshire). — A mine. 

Grub  Stake.— The  mining  outfit  or  supplies  furnished  to  a prospector  on  con- 
dition of  sharing  in  his  finds. 

Grueso  (Mexican).— Lump  ore. 

Grundy.— Granulated  pig  iron. 

Guag  (Cornish).— Worked-out  ground. 

Gualdria  (Mexican).— A long  and  stout  beam,  generally  sustaining  other 
beams  or  some  heavy  weight. 

Guano.— A brown,  gray,  or  white,  light  powdery  deposit,  consisting  mainly 
of  the  excrement  of  sea  fowl  in  rainless  tracts,  or  of  bats  in  caves. 

Guarda  Raya  (Mexican). — A landmark;  a monument. 

Guardas  (Mexican).— The  country  seat  immediately  enclosing  any  metal- 
liferous vein  or  deposit. 

Gubbin.— Ironstone. 

Guia  (Mexican). — Indications  where  to  cut  a pay  streak  or  to  find  a vein. 

Guides.— See  Cage  Guides. 

Guija  (Spanish). — Quartz. 

Guijo  (Mexican).— A pointed  pivot,  upon  which  turns  the  upright  center 
piece  of  an  arrastre,  of  a door,  etc. 

Gunboat.— A self-dumping  car,  holding  from  5 to  8 tons  of  coal,  used  upon 
inclined  planes  or  slopes.  They  are  filled  by  emptying  the  mine  cars 
into  them  at  the  foot  of  the  slope. 

Gunnies  ( Cornish ) .—3  ft. 

Gurt  (Cornish).— Water  runnel  from  dressing  floor. 

Gutter—  (1)  A small  water-draining  channel.  (2)  The  lowest  part  of  a lead 
that  contains  the  most  highly  auriferous  dirt. 


Hac 


GLOSSAR  Y. 


Hea 


591 


Hacienda  de  Beneficio  (Mexican).-In  mining,  a metaUnrgioal  works;  any 
metallurgical  works,  usually  an  amalgamation  works. 

Hacienda  de  Fundicion  (Mexican).— A smelting  works. 

Hacienda  de  Maquila  (Mexican). — A custom  mill. 

Hade. — The  inclination  of  a vein  or  fault,  taking  the  vertical  as  zero. 

At°an  angle  of  45°  from  general  or  previous  course.  (2) 
Half  on  the  level  and  half  on  the  dip. 

Half  Set.— One  leg  piece  and  a cap. 

Halvans Gangue  containing  a little  ore. 

Hammer-and-Plate. — A signaling  apparatus.  , 

ft and  Barrow — A long  box  with  handles  at  each  enu. 

Hand  Dog— A kind  of  spanner  or  wrench  for  screwing  up  and  disconnecting 
the  joints  of  boring  rods  at  the  surface.  . 

Ha  strike  —A  wooden  lever  for  working  a capstan  or  windlass. 

Handwhip.—  An  apparatus  used  in  shallow  alluvial  workings,  consisting  of 
an  unright  at  the  top  of  which  is  balanced  a long  sapling,  at  the  thick 
end  of  the  sapling,  a bag  of  earth  is  fastened  to  counterbalance  the 

Th^man^thS'runs  the^^ded  cam  on  to  the  cages  and  gives 

Hangin^Spmr  JJod.-Wooden pump  rods  adjustable  by  screws,  etc.  by  which 

aSKSS"  "theiiratum  lying  geologically 

ffordtehi!—  Residue  from  tin  refining;  contains  much  iron  and  arsenic. 
Harrow.— Somewhat  like  an  agricultural  harrow;  it  is  fixed  to  the  pole  of  a 
puddling  machine  and  dragged  around  to  break  up  and  mix  the  aurifer- 
ous clays  with  water. 

ClWaped  like  a hat,  revolving  on  a 
vertical  pin,  for  guiding  inclined  haulage  ropes  around  curves. 

TTntter A miner  working  by  himself  on  his  own  account. 

Haulage  Clip—  Levers,  jaws,  wedges,  etc.  by  which  cars,  singly  or  in  trains, 

Hai^in^^^e^rawing6  or  conveying  of  the  product  of  the  mine  from  the 
working  places  to  the  bottom  of  the  hoisting  shaft,  or  slope. 
Haunches.—' The  parts  of  an  arch  from  the  keystone  to  the  skew  back. 

Hazle  (North  of  England). -Sandstone  mixed  with  shale. 

Head  — (11  Pressure  of  water  m pounds  per  square  inch.  (2)  Any  suoter 
ranean  passage  driven  in  solid  coal.  (3)  That  part  of  a face  nearest 

Headfor Staiee  Head  (Australia  and  New  Zealand)  .-A  supply  of  leu.  ft.  of 
water  per  second,  regardless  of  the  head,  pressure,  or  size  of  orifice. 

He<M  Block -( 1)  A stop  at  the  head  of  a slope  or  shaft  to  stop  cars  from 
going  down  the  shaft  or  slope.  (2)  A cap  piece.  . , . f 

Heakboard.—A  wedge  of  wood  placed  against  the  hanging  wall,  and  against 
which  one  end  of  the  stull  piece  is  jammed. 

Header  —(1)  A rock  that  heads  off  or  delays  progress.  (2)  A blast  hole  at  or 
above  the  head.  (3)  A stone  or  brick  laid  lengthwise  at  right  angles  to 
the  face  of  the  masonry.  (4)  The  Stanley  Header  is  an  entry  boring 
machine  that  bores  the  entire  section  of  the  entry  in  one  operation. 
Head-Gear  — The  pullev  frame  erected  over  a shaft.  . 

Head-House.— When  the  head-frame  is  housed  in,  the  structure  is  known  by 

Heading— (l)'  A continuous  passage  for  air  °r  for  use  as  a ^nway;  ^ Jgng- 
way  or  entry.  (2)  A connecting  passage  between  two  rooms,  breasts,  or 
other  working  places. 

Head-Piece. — A cap;  a collar.  , ,, 

Headrace— An  aqueduct  for  bringing  a supply  of  water  on  to  the  ground. 
Headstocks. — Gallows  frame;  head-frame.  . Tinrollol 

Headways—  (1)  A road;  usually  9 ft.  wide,  m a direction  parallel  to  the 
main-cleavage  planes  of  the  coal  seams,  "'hieh  ^rection  is  Killed 
“headways  course,”  and  is  generally  about  north  and  south  m t e 
Newcastle  coal  field.  It  is  termed  “on  end  .m  other  districts.  (2) 

He<we°—{ The^shifting  of  rocks,  seams,  or  lodes  on  the  face  of  a cross-course, 

etc. 


Hea 


GLOSSARY. 


Hyd 


Heaving. — The  rising  of  the  thill  (or  floor)  of  a seam  where  the  coal  has  been 
removed. 

Hechado  (Spanish).— Dip. 

Heel  of  Coal— A small  body  of  coal  left  under  a larger  body  as  a support. 

Heel  of  a Shot.— In  blasting,  the  front  of  a shot,  or  the  face  of  the  shot  farthest 
from  the  charge. 

Heep  Stead  (English).— The  entire  surface  plant  of  a colliery. 

Helper— A miner’s  assistant,  who  works  under  the  direction  of  the  miner. 

Helve.— A handle. 

Hewer. — A collier  that  cuts  coal;  a digger. 

High  Reef—  The  bed  rock  or  reef  is  frequently  found  to  rise  more  abruptly 
on  one  side  of  a gutter  than  on  the  other,  and  this  abrupt  reef  is  termed 
a high  reef. 

Hijuelas  (Mexican). — Literally,  little  children.  A small-sized  torta  made  up 
as  a sort  of  assay  on  a large  scale,  with  from  1 to  5 kilograms  of  argentif- 
erous mud. 

Hill  Diggings—  Placers  on  hills. 

Hilo  (Spanish). — A thin  metalliferous  vein. 

Hitch— { 1)  A fault  or  dislocation  of  less  throw  than  the  thickness  of  the 
seam  in  which  it  occurs.  (2)  Step  cut  in  the  rock  or  lode  for  holding 
stay-beams,  beams,  or  timber,  etc.  for  various  purposes. 

Hoarding— A temporary  close  fence  of  boards  placed  around  a work  in 
progress. 

Hogback.— A roll  occurring  in  the  floor  and  not  in  the  roof,  the  coal  being 
cut  out  or  nearly  so,  for  a distance. 

Hoister. — A machine  used  in  hoisting  the  product.  It  may  be  operated  by 
steampower  or  horsepower. 

Hole. — (1)  To  undercut  a seam  of  coal  by  hand  or  machine.  (2)  A bore 
hole.  (3)  To  make  a communication  from  one  part  of  a mine  to 
another. 

Holing. — (1)  The  portion  of  the  seam  or  underclay  removed  from  beneath 
tlie  coal  before  it  is  broken  down.  (2)  A short  passage  connecting  two 
roads.  (3)  See  Kirving. 

Holing  Through. — Driving  a passage  through  to  make  connection  with 
another  part  of  the  same  workings,  or  with  those  in  an  adjacent  mine. 

Hood.— See  Bonnet. 

Hopper— A coal  pocket;  a funnel-shaped  feeding  trough. 

Horn. — A piece  of  bullock’s  horn  about  8 in.  in  length,  cut  boat-shaped,  for 
concentrating  by  water  on  a small  scale. 

Horn  Coal. — Coal  worked  partly  end-on  and  partly  face-on. 

Horn  Silver. — Chloride  of  silver. 

Horse  Gin.— A gearing  for  winding  by  horsepower. 

Horsepower. — The  power  that  will  raise  33,000  lb.  1 ft.  high  per  minute. 

Horse,  or  Horsebacks. — (1)  Natural  channels  cut  or  washed  away  by  water  in 
a coal  seam,  and  filled  up  with  shale  and  sandstone.  Sometimes  a bank 
or  ridge  of  foreign  matter  in  a coal  seam.  (2)  A mass  of  country  rock 
lying  within  a vein  or  bed.  (3)  Any  irregularity  cutting  out  a portion 
of  the  vein.  See  Dirt  Fault  and  Rock  Fault. 

Horse  Whim.— A vertical  drum  worked  by  a horse,  for  hauling  or  hoisting. 
Called  also  Horse  Gin. 

Hose. — A strong  flexible  pipe  made  of  leather,  canvas,  rubber,  etc.,  and  used 
for  the  conveyance  of  water,  steam,  or  air  under  pressure  to  any  partic- 
ular point. 

H Piece—  The  portion  of  a column  pipe  containing  the  valves  of  the 
pump. 

Hueco  (Mexican). — See  Demasia. 

Hulk  (Cornish). — To  pick  out  the  soft  portions  of  a lode. 

Hundido  (Mexican). — See  Derrumbe. 

Hungry. — Worthless  looking. 

Hurdy  Gurdy. — A waterwheel  that  receives  motion  from  the  force  of 
traveling  water. 

Hushing—  Prospecting  by  laying  ground  bare  by  sudden  discharges  of 
pent-up  water. 

Hutch  (Cornish).— (1)  An  ore- washing  box.  (2)  (English)  A mine  car. 

Hydraulic  Cement. — A mixture  of  lime,  magnesia,  alumina,  and  silica  that 
solidifies  beneath  water. 

Hydraulicking. — Working  auriferous  gravel  beds  by  hydraulic  power. 

Hydrocarbons—  Compounds  of  hydrogen  and  carbon. 


IGN 


GLOSSARY. 


Jig 


593 


n i, _ TVin<sp  that,  have  been  in  a more  or  less  fused  state. 

'!nbyl '-tea toe<!tion  inward  toward  the  face  of  the  workings,  or  away  from 

Incline  — bnort,Cfor  inclined  plane.  Any  inclined  heading  or  slope  road  or 

In  -fort '-When  a pump  continues  working  after  water  has  receded  below 
the  holes  of  the  wind  bore. 

Tnaot  — A lump  of  cast  metal.  ...  . . . 

Tn  Place  —A  vein  or  deposit  in  its  original  position.  _ , 

mXpl-A a!^r0n°whfch  coal  is  raised  from  a lower  to  a higher 
Inspector^— A*  government  official  whose  duties  are  to  enforce  the  laws  regu- 
Instmto— Tlfe^ight^o  take  coai  from  a royalty  to  the  surface  by  a shaft  in 

Trp^tnne  ( Cornish) . — Any  hard  tough  stone.  . , , 

Iron  Hat  — Decomposed  ferruginous  mineral  capping  a lode. 

Iron  Man— A coal-cutting  machine. 

lahnnr'iiin  (Mexican)  — Decomposed  talcose  rock  or  hardened 

Jab7ound  to  a vtm  and  sometimes  indicating  the  proximity  of  a rich  strike. 

took ‘-A  ltnte?nSSape“  made  of  tin,  in  which  safety  lamps  are  carried 

-SSESSStfsa  “oi  suss 

Jack-Lmapl-A  Davy  lamp,  with  the  addition  of  a glass  cylinder  outside 

Jacoiittf/cA'hrazilian).— Ferruginous  ores  associated  with  gold. 

'(Mexica?).-Rlcli  tailings  or  middlings  from  concentration 

7orS0-lT?o!rdrillto'g,  two  long  links > which  take  up  the  shock  of  impact 
whpn  the  falling  tools  strike  the  bottom  of  the  hole.  . . , 

JenMn  - A road  cut-in  a pillar  of  coal  in  a bordways  direction,  that  is,  at 

Jia  -fl)1  A^elf-actingfnffiSe. ^Y^^machine  for  separating  ores  or  minerals 

5'from  iorthlcsrfock  by  meaiis  of  their  difference  in  specific  gravity; 

Jiane?-  m A*  Mnd'of  Ijo^pling  hook  for  connecting  cars  on  an  incline 
99 W)  An  allowance  of  FiquSr  sometimes  issued  to  workmen  (almost 

SeparatmgChea*vy  from  light  particles  by  agitation  in  water. 


594 


Joe 


GLOSSARY. 


Lag 


Jockey.— A self-acting  apparatus  carried  on  the  front  truck  of  a set  for  re- 
leasing it  from  the  hauling  rope. 

Joggle. — A joint  of  trusses  or  sets  of  timber  for  receiving  pressure  at  right 
angles,  or  nearly  so. 

Joints.— (1)  Divisional  planes  that  divide  the  rock  in  a quarry  into  natural 
blocks.  There  are  usually  two  or  three  nearly  parallel  series,  called  by 
quarrymen  end  joints,  back  joints,  and  bottom  joints,  according  to  their 
position.  (2)  In  coal  seams,  the  less  pronounced  cleats  or  vertical 
cleavages  in  the  coal.  The  shorter  cleats,  about  at  right  angles  to  the 
face  cleats  and  the  bedding  plane  of  the  coal. 

Jud.—(  1)  A portion  of  the  working  face  loosened  by  “ kirving”  underneath, 
and  “nicking”  up  one  side.  The  operation  of  kirving  and  nicking  is 
spoken  of  as  “making  a jud.”  (2)  The  term  jud  is  also  applied  to  a 
working  place,  usually  6 to  8 yd.  wide,  driven  in  a pillar  of  coal.  When 
a jud  has  been  driven  the  distance  required,  the  timber  and  rails  are 
removed,  and  this  is  termed  “ drawing  a jud.” 

Judge  (Derbyshire  and  North  of  England)  .—A  measuring  staff. 

Jugglei's,  or  Jugulars.— Timbers  set  obliquely  against  the  rib  in  a breast,  to 
form  a triangular  passage  to  be  used  as  a manway,  airway,  or  chute. 

Jump.— An  upthrow  or  a downthrow  fault. 

Jumper.— A hand  drill  used  in  boring  holes  in  rock  for  blasting. 

Kann  (Cornish).— Fluorspar. 

Kazen  (Cornish).— A sieve. 

Keckle-Meckle  — Poorest  lead  ore. 

Keeker—  An  official  that  superintends  the  screening  and  cleaning  of  the  coal. 

Keel  Wedge. — A long  iron  wedge  for  driving  over  the  top  of  a pick  hilt. 

Keeps , or  Keps.— Wings,  catches,  or  rests  to  hold  the  cage  at  rest  when  it 
reaches  any  landing. 

Keeve.—A  large  wooden  tub  used  for  the  final  concentration  of  tin  oxide. 

Kenner. — Time  for  quitting  work. 

Kerf.— The  undercut  made  to  assist  the  breaking  of  the  coal. 

Kerned  (Cornish).— Pyrites  hardened  by  exposure. 

Kerve  (North  of  England). — In  coal  mining,  to  cut  under. 

Kevil  (Derbyshire).— Calcspar  found  in  lead  veins. 

Key.—{  1)  An  iron  bar  of  suitable  size  and  taper  for  filling  the  key  ways  of 
shaft  and  pulley  so  as  to  keep  both  together.  (2)  A kind  of  spanner 
used  in  deep  boring  by  hand. 

Kibble—  See  Bowk.  Often  made  with  a bow  or  handle,  and  carrying  over  a 
ton  of  debris. 

Kickup.— An  apparatus  for  emptying  trucks. 

Kieve.— Tossing  tub. 

Killas  (Cornish).— Clay  slate. 

Kiln.— A chamber  built  of  stone  or  brick,  or  sunk  in  the  ground,  for  burning 
minerals  in. 

Kind. — (1)  Tender,  soft,  easy.  (2)  Likely  looking  stone. 

Kind-Chaudron.—A  system  of  sinking  shafts  through  water-bearing  strata. 

Kirving  (North  of  England).— The  cutting  made  beneath  the  coal  seam. 

Kist  — The  wooden  box  or  chest  in  which  the  deputy  keeps  his  tools.  The 
chest  is  always  placed  at  the  flat  or  lamp  station,  and  this  spot  is  often 
referred  to  by  the  expression  “at  the  kist.” 

Kit.— Any  workman’s  necessary  outfit,  as  tools,  etc. 

Kitty. — A squib  made  of  a straw  tube  filled  with  powder. 

Knee  Piece. — A bent  piece  of  piping. 

Knocker.— A lever  that  strikes  on  a plate  of  iron  at  the  mouth  of  a shaft,  by 
means  of  which  miners  below  can  signal  to  those  on  the  top. 

Knocker  Line— Tine  signal  line  extending  down  the  shaft  from  the  knocker. 

Koepe  System. — A system  of  hoisting  without  using  drums,  the  rope  being 
endless  and  passing  over  pulleys  instead  of  around  a drum. 

Labor  (Mexican).— Mine  workings  in  general.  Specifically,  a stope  or  any 
other  place  where  ore  is  being  taken  out. 

Ladderway,  Ladder  Road. — The  particular  shaft,  or  compartment  of  a shaft, 
used  for  ladders. 

Lagging—  (1)  Small  round  timbers,  slabs,  or  plank,  driven  in  behind  the 
legs  and  over  the  collar,  to  prevent  pieces  of  the  sides  or  roof  from  falling 
through.  (2)  Long  pieces  of  timber  closely  fitted  together  and  fastened 
to  the  drum  rings  to  form  a surface  for  the  rope  to  wind  on. 


Lam 


GLOSSARY. 


Lid 


595' 


Lamas  (Spanish).— (1)  Slimes.  (2)  Argentiferous  mud  treated  by  amalga- 
mation. 

Lamer o (Mexican)  .—Place  of  deposit  for  lamas. 

Laminae. — Sheets  not  naturally  separated,  but  which  may  be  forced  apart. 

Lampazo  (Mexican).— A sort  of  broom  formed  of  green  branches  on  the  end 
of  a long  stick,  to  dampen  the  flame  in  a reverberatory  furnace. 

Lamp  Men. — Cleaners,  repairers,  and  those  having  charge  of  the  safety  lamps 
at  a colliery.  , . , „ • , 

Lamp  Stations.— Certain  fixed  stations  m a mine  at  which  safety  lamps 
are  allowed  to  be  opened  and  relighted  by  men  appointed  for  that 
purpose,  or  beyond  which,  on  no  pretense,  is  a naked  light  allowed 
to  be  taken. 

Lander.— The  man  that  receives  a load  of  ore  at  the  mouth  of  a shaft. 

Lander's  Crook— A hook  or  tongs  for  upsetting  the  bucket  of  hoisted  rock. 

Landing—  (1)  A level  stage  for  loading  or  unloading  a cage  or  skip. 
(2)  The  top  or  bottom  of  a slope,  shaft,  or  inclined  plane. 

Land  Sate.— The  sale  of  coal  loaded  into  carts  or  wagons  for  local  consump- 
tion. 

Land-Sale  Collieries—  Those  selling  the  entire  product  for  local  consumption, 
and  shipping  none  by  rail  or  water. 

Lap. — One  coil  of  rope  on  a drum  or  pulley. 

Lappior  (Cornish). — An  ore  dresser. 

Large. — The  largest  lumps  of  coal  sent  to  the  surface,  or  all  coal  that  is  hand 
picked  or  does  not  pass  over  screens;  also,  the  large  coal  that  passes 
over  screens.  , „ , . . _ 

Larry—  (1)  A car  to  which  an  endless  rope  is  attached,  fixed  at  the  inside 
end  of  the  road,  forming  part  of  the  appliance  for  taking  up  slack  rope. 
See  Balance  Car.  (2)  See  Barney.  (3)  A car  with  a hopper  bottom  and 
adjustable  chutes  for  feeding  coke  ovens.  (4)  A hopper-shaped  car  for 
charging  coke  ovens.  , , . 

Latches. — (1)  A synonym  of  switch.  Applied  to  the  split  rail  and  hinged 
switches.  (2)  Hinged  switch  points,  or  short  pieces  of  rail  that  form 
rail  crossings. 

Lateral.— From  the  side. 

Lath.— A plank  laid  over  a framed  center  or  used  in  poling. 

Launder. Water  trough. 

Laundry  Box.— The  box  at  the  surface  receiving  the  water  pumped  up  from 
below. 

Lava.— A common  term  for  all  rock  matter  that  has  flowed  from  a volcano  or 
fissure. 

Lavadero  (Mexican).— A washer.  A tank  with  a stirring  arrangement  to 
loosen  up  the  argentiferous  mud  from  the  patio,  and  dilute  the  same 
with  water,  so  that  the  silver  amalgam  may  have  a chance  to  precipitate. 
An  agitator. 

Lazadores  (Mexican).— Men  formerly  employed  in  recruiting  Indians  for 
work  in  the  mines  by  the  gentle  persuasion  of  a lasso. 

Lazy  Back  (Staffordshire).— A coal  stack,  or  pile  of  coal. 

Leaching.— To  dissolve  out  by  some  liquid. 

Lead  (pronounced  teed).— ( 1)  Ledge  (America);  reef  (Australia);  lode  or 
vein  (England).  A more  or  less  vertical  deposit  of  ore  formed  after  the 
rock  in  which  it  occurs.  (2)  A bed  of  alluvial  pay  dirt  or  an  auriferous 
gutter.  (3)  The  distance  to  which  earth  is  hauled  or  wheeled. 

Leader.— A seam  of  coal  too  small  to  be  worked  profitably,  but  often  being  a 
guide  to  larger  seams  lying  in  known  proximity  to  it. 

Leat.—A  small  water  ditch. 

Leavings  (Cornish).— Hal  vans. 

Ledge.— See  Lead. 

Leg.— A wooden  prop  supporting  one  end  of  a collar. 

Leg  Piece.— An  upright  log  placed  against  the  side  of  a drive  to  support  the 
cap  piece. 

Lenador  (Mexican).— One  that  cuts,  carries,  or  furnishes  wood  for  com- 
bustible. 

Level. — A road  or  gangway  running  parallel  or  nearly  so  with  the  strike 
of  the  seam. 

Ley  (Mexican)  .—Law.  As  applied  in  mining  matters,  it  means  the  propor- 
tion of  precious  or  other  metals  contained  in  any  mineral  substance  or 
metallic  alloy. 

Lid.— A cap  piece  used  in  timbering. 


596 


LIP 


GLOSSARY. 


Lum 


Lift  — rn  The  vertical  height  traveled  by  a cage  in  a shaft.  (2)  The  lift  of  a 
'Dump  is  theoretical  height  from  the  level  of  the  water  m the  sump  to  the 
noint  of  discharge.  (3)  The  distance  between  the  first  level  and  the 
surface,  or  between  two  levels.  (4)  The  levels  of  a shaft  or  slope. 

Liftinq  Guards. — Fencing  placed  around  the  mouth  of  a shaft,  which  is 
lifted  out  of  the  way  by  the  ascending  cage. 

Lignite— A coal  of  a woody  character  containing  about  66$  carbon  and 
y having  a brown  streak.  . „ , , 

Limadura ( Mexican) . — Filings.  The  mercurial  globules  seen  when  a piece 
of  argentiferous  mud  from  a patio  is  washed  m a spoon  or  saucer  for 

T irru^Cartridae  — A charge  or  measured  quantity  of  compressed  dry  caustic 
lime  made  up  into  a cartridge  and  used  instead  of  gunpowder  for 
breaking  down  coal.  Water  is  applied  to  the  cartridge,  and  the  expan- 
sion breaks  down  the  coal  without  producing  a flame. 

Lime  Coal.— Small  coal  suitable  for  lime  burning. 

Lines  —Plumb-lines,  not  less  than  two  m number,  hung  from  hooks  driven 
in  wooden  plugs.  A line  drawn  through  the  centers  of  the  two  strings 
or  wires,  as  the  case  may  be,  represents  the  bearing  or  course  to  be 

driven  on.  , . . _ . 

Lining.— The  planks  arranged  against  frame-sets. 

Linnets  (Derbyshire).— Oxidized  lead  ores. 

Linternilla  ( Mexican)  .—The  drum  of  a Horse  Whim. 

Lip  Screen. — A small  screen  or  screen  bars,  placed  at  the  draw  hole  of  a coal 
pocket  to  take  out  the  fine  coal. 

Lis  (Mexican).—' The  flouring  of  mercury.  , , 

Little  Giant.— The  name  given  to  a special  sort  of  hydraulic  nozzle  used  for 

Live^Quartz.—A  variety  of  quartz  usually  associated  with  mineral. 

AZa^es^Mexic^in ) .—Horizontal  cross-beams  in  a shaft,  or  the  upright  pieces 
that  sustain  the  roof  beams  in  a drift  or  tunnel. 

Loaded  Track.- Track  used  for  loaded  cars.  . 

Loader—  One  that  fills  the  mine  cars  at  the  working  places. 

Loam. — Any  natural  mixture  of  sand  and  clay  that  is  neither  distinctly  sandy 

Locatiln^-The  first  approximate  staking  out  or  survey  of  a mining  claim,  in 
distinction  from  a Patent  Survey , or  a Patented  Claim. 

in  the  country  rock  filled  with  mineral; 
usually  applied  to  metalliferous  lodes.  In  general  miners 
vein  or  ledge  is  a tabular  deposit  of  valuable  minerals  between  definite 
boundaries  Whether  it  be  a fissure  formation  or  not  is  not  always 
known,  and  does  not  affect  the  legal  title  under  the  United  States  federal 
and  local  statutes  and  customs  relative  to  lodes.  But  it  m^st  not  be  a 
placer,  i.  e.,  it  must  consist  of  quartz  or  other  rock  in  place,  and  bearing 

Xodlstofor^ Magnetic  iron  ore.  (2)  Stone  found  in  veins  or  lodes. 

Logs. — Portions  of  trunks  of  trees  cut  to  lengths  and  built 

the  mouth  or  collar  of  a shaft  from  the  surface,  in  order  to  give  the 
reauisite  space  for  the  dumping  of  mullock  and  ore. 

Lonq-Pillar  Work— A system  of  working  coal  seams  in  three  separate  oper- 
tions*  (1)  large  pillars  are  left;  (2)  a number  of  parallel  headings  are 
driven  through  the  block;  and  (3)  the  ribs  or  narrow  pillars  are  worked 

LonTZt^-T woSdenltafce  about  24  ft.  long,  2 ft.  wide,  and  1 ft.  high,  for 
washing  auriferous  gravel. 

^ngwall.—  't  system  of  working  a seam  of  coal  in  J?® 

taken  out  and  no  pillars  left,  excepting  the  shaft  pillars,  and  sometimes 
the  main-road  pillars. 

Loob  (Cornish).— Sludge  from  tin  dressing. 

Loose  End— ( 1)  A portion  of  a seam  worked  on  two  sides.  (2)  A portion 
that  projects  in  the  shape  of  a wedge  between  previous  workings. 

Lumber—' Timber  cutto" the  various  sizes  and  shapes 

Lumbreras  (Mexican)  .-Ventilating  shafts  in  a mine  or  other  underground 
work. 


GLOSSARY. 


Mer 


597 


IrtJM  vr MJWK,****  - . 

TnllYnrn  r^ni  All  ooal  (anthracite  only)  larger  than  broken  coal,  or,  when 
co^  is  mXlumps  larger  than  this  size.  (2)  In  soft  coal,  all 
poai  nassing  over  the  nut-coal  screen.  . 

Lute.— An  adhesive  clay  used  either  to  protect  any  iron  vessel  from  too 
strong  a heat  or  for  securing  air-  and  gas-tight  joints. 

Lye  (English).— A siding  or  turnout. 

Marhote  ( Mexican). — A stake  or  permanent  bench  mark  fixed  in  an  under- 

M ground  working,  from  which  the  length  and  progress  thereof  is 
measured.  _ 

Magidr^  (Spanish) .—Roasted  copper  pyrites,  copper  sulphate,  etc.,  used  to 
reduce  silver  ores. 

the  north  end  of  the  magnetic 

Ma™eMc%eridian.-The  line  or  great  circle  in  which  the  magnetic  needle 

m i»%ada-a'h^Vprin?ipal‘  haulage  road  of  a mine  from  which  the  several 
crossroads  lead  to  the  working  face. 

IT  g&SfSSW  hSgt  the  rope  that  draws  the  loaded  cars 

MakU^as  (North  of  Englandl.-Small  coal  produced  in  kirving.  Fines. 

MaSte  (Mexican).— A Horse  Whim;  now  extended  to  any  hoisting  machine 
used  in  mines. 

KT-in^  and  supervision  of  a mine,  both 

Man^Er^ncs— An°apparatus  consisting  of  one  or  two  reciprocating  rods,  to 
which  suitable  stages  are  attached,  used  for  lowering  and  raising  men 

A^^  tTelXof  a gangway,  tunnel, 

or  slope  * (2)  A hole  in  cylindrical  boilers  through  which  a man  can 
get  into  the  boiler  to  examine  and  repair  it. 

which  ore  or  waste 

Maufeoa( Mexican)  .-The  act  of  hoisting  ore  or  waste  from  a mine. 

MSaj/M-AX2ll^a|eufeFS\  traveling  way  for  the  miner,  and  also 
often  used  as  an  airway  or  chute,  or  both. 

fScaXToUwork  “re  for  its  owner  on  shares  or  for  a money 
payment. 

Marco  (Mexican).— A weight  of  8 oz. 

tapered  round  iron,  used  in 

splicing  ropes.  j 

Marmajas  (Spanish). — Concentrated  sulphides. 

mZZrLamp- ‘“'type  of  safety  lamp  whose  chief  characteristic  is  the 

lKorshUfito?—  Cffn often  used  synonymously  with  Firedamp  (see  page  348). 

Match.— (1)  A charge  of  gunpowder  put  into  a paper  several  inches  long,  and 
used  for  igniting  explosives.  (2)  The  touch  end  of  a squib. 

>faffeS— A compound  of  iron  and  other  metals,  chiefly  copper,  with  sulphur, 
formed  during  smelting.  , _ ,.  . 

Mattock—  A kind  of  pick  with  broad  ends  for  digging. 

MaundHl^A  pick  with  two  shanks  and  points,  used  for  getting  coal,  etc. 

Mazo  (Mexican). — A stamp. 

Mear  (Derbyshire). — 32  yd.  along  the  vein. 

Measures—  Strata. 

Mecha  (Mexican).— A wick  for  a lamp  or  candle,  a torch. 

Merced  (Mexican).— A gift,  grant,  or  concession.  

Meridian.— A north  and  south  line,  either  true  or  approximate. 


598 


Met 


GLOSSARY ; 


Mou 


Metal.— {1)  In  coal  mining,  indurated  clay  or  slate.  (2)  An  element  that 
forms  a base  by  combining  with  oxygen  that  is  solid  at  ordinary  tem- 
perature (with  exception  of  quicksilver),  opaque  (except  in  the  thinnest 
possible  films),  has  a metallic  luster,  and  is  a good  conductor  of  heat 
and  electricity,  and,  as  a rule,  of  a higher  specific  gravity  than  the  non- 
metals.  (3)  (Mexican)  All  kinds  of  metalliferous  minerals  are  called 
“ metal”  in  Mexico.  Metal  de  Ayuda.— Fluxing  ore  of  any  kind.  Metal 
de  Cebo. — Very  rich  ore,  usually  treated  in  small  reverberatory  furnaces. 
Metal  Ordinario— Common  ore.  Metal  Pepena.—  The  best  class  of  selected 


ore. 

Metlapil  (Mexican).— See  Mano. 

Mill. — Works  for  crushing  and  amalgamating  gold  and  silver  ores. 

Mill  Cinder.— The  slag  from  the  puddling  furnace  of  a rolling  mill. 

Mill  Hole.— An  auxiliary  shaft  connecting  a stope  or  other  excavation  with 
the  level  below. 

Mill  Run.— The  test  of  a given  quantity  of  ore  by  actual  treatment  in  a mill. 

Mine.— A ny  excavation  made  for  the  extraction  of  minerals. 

Miner.— One  who  mines.  a 

Mineral— Any  constituent  of  the  earth’s  crust  that  has  a definite  com- 
position. 

Mineral  Oil.— Petroleum  obtained  from  the  earth,  and  its  distillates. 

Minero  (Mexican).— A mine  owner;  a mining  captain;  an  underground  boss. 

Mine  Road.— Any  mine  track  used  for  general  haulage. 

Mine  Run— The  entire  unscreened  output  of  a mine. 

Minero  Mayor  (Mexican).— The  head  mining  captain.  A mining  workman 
is  called  Operario. 

Miners'  Dial.— An  instrument  used  in  surveying  underground  workings. 

Miners'  Inch.— A measure  of  water  varying  in  different  districts,  being  the 
quantity  of  water  that  passes  through  a slit  1 in.  high,  of  a certain  width 
under  a given  head  (see  page  136). 

Miner's  Right.— An  annual  permit  from  the  Government  to  occupy  and  work 
mineral  land.  . _ V.  - , 

Mining—  In  its  broad  sense,  it  embraces  all  that  is  concerned  with  the 
extraction  of  minerals  and  their  complete  utilization. 

Mining  Engineer —A  man  having  knowledge  and  experience  in  the  many 
departments  of  mining.  , . , A , , 

Mining  Retreating.— A process  of  mining  by  which  the  vein  is  untouched 
until  after  all  the  gangways,  etc.  are  driven,  when  the  mineral  extraction 
begins  at  the  boundarv  and  progresses  toward  the  shaft. 

Mistress  (North  of  England).— A miner’s  lamp. 

Mock  Lead  (Cornish).— Zinc  blende. 

Mogrollo  (Mexican).— Same  as  Metal  de  Cebo.  . „ „ 

Moil— A short  length  of  steel  rod  tapered  to  a point,  used  for  cutting 
hitches,  etc.  . „ , . , . 

Molonque  (Mexican).— A rich  specimen  of  which  one-half  or  more  is  native 

silver. 

Monitor. — See  Gunboat. 

Monkey.— The  hammer  or  ram  of  a pile  driver. 

Monkey  Drift.— A small  drift  driven  in  for  prospecting  purposes,  or  a crosscut 
driven  to  an  airway  above  the  gangway. 

Monkey  Gangway.— A small  gangway  parallel  with  the  mam  gangway. 

Monkey  Rolls.—' The  smaller  rolls  in  an  anthracite  breaker. 

Monkey  Shaft.— A shaft  rising  from  a lower  to  a higher  level. 

Monoclinal—  Applied  to  an  area  in  which  the  rocks  all  dip  m the  same 


Mop— Some  material  surrounding  a drill  in  the  form  of  a disk,  to  prevent 
water  from  splashing  up.  ,, 

Mortar. — The  vessel  in  which  ore  is  placed  to  be  pulverized  by  a pestle. 
Mortise. — A hQle  cut  in  one  piece  of  timber,  etc.  to  receive  the  tenon  that 
projects  from  another  piece.  ....  , . 

Mote  (Moat).— A straw  filled  with  gunpowder,  for  igniting  a shot. 

Mother  Gate.— The  main  road  of  a district  in  longwall  working. 

Mother  Lode  (Main  Lode).— The  principal  vein  of  any  district.  , 

Motive  Column.— The  length  of  a column  of  air  whose  weight  is  equal  to  the 
difference  in  weight  of  like  columns  of  air  in  downcast  and  upcast  shafts. 
The  ventilating  pressure  in  furnace  ventilation  is  measured  by  the  differ- 
ence of  the  weights  of  the  air  columns  in  the  two  shafts. 

Mouth. — The  top  of  a shaft  or  slope,  or  the  entrance  to  a drift  or  tunnel. 


Moy 


GLOSSARY 


Ope 


599 


sharp  steel  point,  for  driving  into  clefts  when 


Moyle.— An  iron  with  a 

levering  off  rock.  . _ 

Muckle.— Soft  clay  overlying  or  underlying  coal. 

Mucks  (Staffordshire).— Bad  earthy  coal.  ^ , 

Muescas  (Mexican).— Notches  in  a stick;  mortises;  notches  cut  in  a round 
or  square  beam,  for  the  purpose  of  using  it  as  a ladder. 

Mueseler  Lamp.— A type  of  safety  lamp  invented  and  used  m the  collieries 
of  Belgium.  Its  chief  characteristic  is  the  inner  sheet-iron  chimney  for 
increasing  the  draft  of  the  lamp. 

Muffle. — A thin  clay  oven  heated  from  the  outside. 

Muller—  The  upper  grinding  iron  or  rubbing  shoe  of  amalgamating 
T3RHS  otc 

Mullock.— Country  rock  and  worthless  minerals  taken  from  a mine. 

Mundic  — Iron  pyrites. 

Naked  Light.— A candle  or  any  form  cf  lamp  that  is  not  a safety  lamp. 

Narrow  Work.—{  1)  All  work  for  which  a price  per  yard  of  length  driven  is 
paid,  and  which,  therefore,  must  be  measured.  (2)  Headings,  chutes, 
crosscuts,  gangways,  etc. 

Natas  (Mexican) —Same  as  Escoma  or  Grasa. 

Native  Metal.— A metal  found  naturally,  in  that  state. 

Natural  Ventilation.— Ventilation  of  a mine  without  either  furnace  or  otner 
artificial  means;  the  heat  imparted  to  the  air  by  the  strata,  men, 
animals,  and  lights  in  the  mine,  causing  it  to  flow  in  one  direction,  or 

to  ascend.  • 

Neck. — A cylindrical  body  of  rock  differing  from  the  country  around  it. 

Needle—  (1)  A sharp-pointed  metal  rod  with  which  a small  hole  is  made 
througn  the  stemming  to  the  cartridge  in  blasting  operations.  (2)  A 
hitch  cut  in  the  side  rock  to  receive  the  end  of  a timber. 

Negrillo  (Mexican).— Black  sulphide  of  silver. 

Nick. — To  cut  or  shear  coal  after  holing.  , fo. 

Nicking—  (1)  A vertical  cutting  or  shearing  up  one  side  of  a face  of  coal.  (2) 
The  chipping  of  the  coal  along  the  rib  of  an  entry  or  room  which  is 
usually  the  first  indications  of  a squeeze. 

Night  Shift.—’ The  set  of  men  that  work  during  the  night. 

Nip  —When  the  roof  and  floor  of  a coal  seam  come  close  together,  pinching 
the  coal  between  them.  ...  . . , • 

Nip  Out. — The  disappearance  of  a coal  seam  by  the  thickening  of  the  adjoin- 
ing strata,  which  takes  its  place. 

Nitro.—A  corrupted  abbreviation  for  nitroglycerine  or  dynamite. 

Nittings. — Refuse  of  good  ore. 

Nodular. — Blistered  or  kidney-shaped  ore.  . 

Nodules.— Concretions  that  are  frequently  found  to  enclose  organic  remains. 

Nogs  _ Logs  of  wood  piled  one  on  another  to  support  the  roof.  See  Chock. 

Nook  —The  corner  of  a working  place  made  by  the  face  with  one  side. 

Noria  (Spanish). — An  endless  chain  of  buckets.  . . 

Nozzle. — The  front  nose  piece  of  bellows  of  a blast  pipe  for  a furnace,  or  of  a 
w'ater  pipe. 

Nugget.— A natural  lump  of  gold  or  other  metal,  applied  to  any  size  above  2 

to  3 dwt.  , . . . 

Nut  Coal  — A contraction  of  the  term  chestnut  coal. 

Nuts. — Small  lumps  of  coal  that  will  pass  through  a screen  or  bars,  the  spaces 
between  which  vary  in  width  from  £ to  2£  in. 

Ocote  (Mexican). — Pitch  pine.  _ . . 

Odd  Work. — Work  other  than  that  done  by  contract,  such  as  repairing 
roads,  constructing  stoppings,  dams,  etc.  * _ 

Offtake  —The  raised  portion  of  an  upcast  shaft  ^bove  the  surface,  for  carrying 
off  smoke  and  steam,  etc.,  produced  by  the  furnaces  and  engines  under- 

Oil  IS!— Shale  containing  such  a proportion  of  hydrocarbons  as  to  be 
capable  of  yielding  mineral  oil  on  slow  distillation. 

Oil  Smellers.— Men  that  profess  to  be  able  to  indicate  where  petroleum  oil  is 
to  be  found. 

Old  Man. — Old  workings  in  a mine.  . ...  ..  „„„  ~ 

Oolitic.— A structure  peculiar  to  certain  rocks,  resembling  the  roe  of 
a fish. 

Open  Cast— Workings  having  no  roof. 


600 


Ope 


GLOSSARY. 


Pan 


Open  Cutting—  (1)  An  excavation  made  on  the  surface  for  the  purpose  of  get* 
ting  a face  wherein  a tunnel  can  be  driven.  (2)  Any  surface  excavation 

Openings , An  Opening—  Any  excavation  on  a coal  or  ore  bed,  or  to  reach  the 
same;  a mine.  * 

Openwork—  An  open  cut. 

Operario  ( Mexican ) .—A  working  miner. 

Operator  — The  individual  or  company  actually  working  a colliery. 

Ore— A mineral  of  sufficient  value  (as  to  quality  and  quantity),  to  be  mined 
with  profit.  . , , ^ 

Ores  .—Minerals  or  mineral  masses  from  which  metals  or  metallic  combina- 
tions can  be  extracted  on  a large  scale  in  an  economic  manner. 

Ore  Shoot—  A large  and  usually  rich  aggregation  of  mineral  in  a vein. 
Distinguished  from  pay  streak  in  that  it  is  a more  or  less  vertical  zone 
or  chimney  of  rich  vein  matter  extending  from  wall  to  wall,  and  having 
a definite  width  laterally. 

Oro  (Spanish).— Gold.  , . % . . . 

Oroche  (Spanish).— (1)  Retorted  bullion.  (2)  (Mexican)  Bullion  containing 
gold  and  silver.  A.A.  . _ _ _ 

Outburst —A  blower.  A sudden  emission  of  large  quantities  of  occluded  gas. 

Outbye. — In  the  direction  of  the  shaft  or  slope  bottom,  or  toward  the  outside. 

Outcrop. — The  portion  of  a vein  or  bed,  or  any  stratum  appearing  at  the  sur- 
face, or  occurring  immediately  below  the  soil  or  diluvial  drift. 

Outcropping.— See  Cropping  Out.  . 

Outlet.— A passage  furnishing  an  outlet  for  air,  for  the  miners,  for  water,  or 
for  the  mineral  mined.  , , , , , , . _ 

Output.— The  product  of  a mine  sent  to  market,  or  the  total  product  of  a mine. 

Outset.—' The  walling  of  shafts  built  up  above  the  original  level  of  the  ground. 

Outstroke  Rent.— The  rent  that  the  owner  of  a royalty  receives  on  coal  brought 
into  his  royalty  from  adjacent  properties.  . _ , . 

Outtake  — The  passage  by  which  the  ventilating  current  is  taken  out  of  the 
mine;  the  upcast. 

Overburden.— The  covering  of  rock,  earth,  etc.  overlying  a mineral  deposit 
that  must  be  removed  before  effective  work  can  be  performed. 

Overcast.— A passage  through  which  the  ventilating  current  is  conveyed  over 
a gangway  or  airway.  , „ „ A . 

Overhand  Stoping—  The  ordinary  method  of  stopmg  upwards. 

Overlap  Fault— A fault  in  which  the  shifted  strata  double  back  over  them- 

SG1VGS. 

Overman— One  who  has  charge  of  the  workings  while  the  men  are  in  the 
mine.  He  takes  his  orders  from  the  Underviewer. 

Overwind.—' To  hoist  the  cage  into  or  over  the  top  of  the  head-frame. 

Oyamel  (Mexican).— White  pine. 

Pack. — A rough  wall  or  block  of  coal  or  stone  built  up  to  support  the  roof. 

Packing. — The  material  placed  in  stuffingboxes,  etc.  to  prevent  leaks. 

Pack  Wall— A wall  of  stone  or  rubbish  built  on  either  side  of  a mine  road,  *o 
carry  the  roof  and  keep  the  sides  up. 

Pacos  (Spanish).— Ferruginous  silver  ores.  . ... 

Paddock. -( 1)  An  excavation  made  for  procuring  wash  dirt  in  shallow 
ground.  (2)  A place  built  near  the  mouth  of  a shaft  where  ore  is  stored. 

Paint  Gold.— The  very  finest  films  of  gold  coating  other  minerals. 

Paleozoic—  The  oldest  series  of  rocks  in  which  fossils  of  animals  occur. 

Palero  (Mexican). — A mine  carpenter.  „ ^ , , ,, 

Palm.— A piece  of  stout  leather  fitting  the  palm  of  the  hand,  and  secured  by 
a loop  to  the  thumb;  this  has  a flat  indented  plate  for  forcing  the  needle. 

Palm  Needle.— A straight  triangular-sectioned  needle,  used  for  sewing  canvas. 

Palo  (Mexican).— A stick;  a piece  of  timber 

Pan— A thin  sheet-iron  dish;16  in.  across  the  top,  and  10  in.  at  the  bottom, 
used  for  panning  gold. 

Panel— ( 1)  A large  rectangular  block  or  pillar  of  coal  measuring,  say, 
130  by  100  yd.  (2)  A group  of  breasts  or  rooms  separated  from  the  other 
workings  by  large  pillars.  . . ... 

Panel  Working.— A system  of  working  coal  seams  m which  the  colliery  is 
divided  up  into  large  squares  or  panels,  isolated  or  surrounded  by  solid 
ribs  of  coal,  in  each  of  which  a separate  set  of  breasts  and  pillars  is 
worked,  and  the  ventilation  is  kept  distinct,  that  is,  every  panel  has  its 
own  circulation,  the  air  of  one  not  passing  into  the  adjoining  one,  but 
being  carried  direct  to  the  main  return  airway. 


Pan 


GLOSSARY 


Pic 


601 


Panino  (Mexican).—1 The  peculiar  appearance,  form,  or  manner  in  which 
the  metalliferous  minerals  present  themselves  m any  given  distnc 

Panning ot’ Panning  Off.- Separating  gold  or  tin  from  its  accompanying 
minerals  by  washing  off  the  latter  in  a pan. 

a chattering  noise 

’ “s  t"nagcaeS 

nart  5 the  ores  in  place  of  wages.  Usually,  the  mine  owner  provides 
handles  nowder  and  steel,  and  keeps  the  drills  sharpened,  and  receive*, 
in  navment  of  royalty  and  supplies,  two-thirds  or  more  of  the  ore  taken 
^This  contract  is  renewed  weekly  or  monthly,  etc.,  and  the  proper - 
Son  ofoSe  retained  by  the  miners  is  more  or  less,  according  to  the  richness 
of The  stoves ^whlreUey  wSrk  This  is  a cheap  way  of  getting  ore  as  far 
as ^labor^^c^neemed.  But  the  miners  must  be  constantly  watched; 
otherwise  they  will  leave  the  mine  in  bad  state.  The  proportion  of  ore 
£3  to  the Miners  is  generally  bought  from  them  by  the  mine 

Parting!— (1 ^Any  ’ toto  “SK'  bed  of  earthy  material.  (2)  A side 
track  or  turnout  in  a haulage  road. 

down  ore  to  a lower  level  (21  A 
pas^ge  left  irSd  workings  for  men  to  travel  in  from  one  level  to 

PasSfy  — A siding  in  which  cars  pass  one  another  underground.  A turnout 

Pass- Into. — Wh en  one  mineral  gradually  passes  into  another  without  any 

PaMpZl-imlu  coal  mixed  with  8 to  10jt  of  pitch  or  tar,  and  compressed 

Patofe^ta^-A^fato  to  which  a patent  right  has  been  secured  from  the 

i government,  by  compliance  with  the  laws  relating  to  such  claims. 

Afent  Survey. — An^  accurate  survey  of  a claim  fjh?to^e  cllim  7 
required  by  law  m order  to  secure  a patent  right  to  the  claim. 

Pa(*WMerfcan)fl-Aiay  paved  enclosure  more  or  less  surrounded  by  build- 
toga  ^ av ^ A floor  Qr  yard  where  argentlferous  mud  is 

treated  by  amalgamation. 

ZJrt. — That  portion  of  an  alluvial  deposit  that  contains  gold  in  payable 
quantities. 

Pay  Out.— To  slacken  or  let  out  rope. 

Pay  Rock — Mineralized  rock. 

Pay  Streak—  Mineralized  part  of  rock. 

PeaCCoal.—l  smalTsize  o^nthracite  coal  (see  page  434). 

Peat — T^decomposed  partly  carbonized  organic  matter  ofbogs,  swamps,  eta 

Pebble  Jack.- Zinc  blende  in  small  crystals  or  pebble-like  forms  is  not 
attached  to  rock,  but  is  found  m clay  openings  m the  rock. 

Pee  (Derbyshire).— A fragment  of  lead  ore. 

Pdla , or  Plata  Pella  (Mexican).— Silver  amalgam. 

P^tHo'ji- -A^odfn  covering  for  the  protection  of  sinkers  working  in  a 

PerJice  — A*few  pieces  of  timber  laid  as  a roof  over  men’s  heads,  to  screen 
them  when  working  in  dangerous  places,  e.g.,  at  the  bottom  of  shafts. 

Pepenado  ( Spanish ) .—Dressed  ore. 

P^ZZonTabU^r-kintof  jolting  table  used  in  separating  very  tine  ores 
from  slimes.  . . , 

fSVi-To^  “tonally  decrease  in  thickness. 

Petlanque  (Mexican).— Ruby  silver. 

Petrifaction  — Organic  remains  converted  into  stone.  - 

i)  a tooffor  cutting  and  holing  coal.  (2)  To  dress  the  sides  Ox  face 

of  an  excavation  with  a pick. 


602 


Pic 


GLOSSARY. 


Pla 


Picker.— { 1)  A small  tool  used  to  pull  up  the  wick  of  a miner’s  lamp. 
(2)  A person  who  picks  the  slate  from  the  coal  in  an  anthracite-coal 
breaker. 

Picking  Chute. — A chute  in  an  anthracite  breaker  along  which  boys  are 
stationed  to  pick  the  slate  from  coal. 

Picking  Table— (1)  A flat  or  slightly  inclined  platform  on  which  anthracite 
coal  is  run  to  be  picked  free  from  slate.  (2)  A sorting  table. 

Pico  (Mexican). — A striking  or  sledge  hammer. 

Picture. — A screen  to  keep  off  falling  water  from  men  at  work. 

Piedras  de  Mano  (Mexican). — Hand  specimens. 

Pig— A piece  of  lead  or  iron  cast  into  a long  iron  mold. 

Pigsty  Timbering. — Hollow  pillows  built  up  of  logs  of  wood  laid  crosswise 
for  supporting  heavy  weights. 

Pike. — A pick. 

Pilar  (Mexican). — A pillar  of  rock  or  ore  left  to  sustain  some  portion  of  the 
mine. 

Pileta  (Mexican).— (1)  A sump.  (2)  The  basin  or  pot  where  melted  metal 
is  collected. 

Piling.— Long  pieces  of  timber  driven  into  soft  ground  for  the  purpose  of 
securing  a solid  base  on  which  to  build  any  superstructure. 

Pillar. — (1)  A solid  block  of  coal,  etc.  varying  in  area  from  a few  square 
yards  to  several  acres.  (2)  Sometimes  applied  to  a single  timber 
support. 

Pillar -and-Room  — A system  of  working  coal  by  which  solid  blocks  of  coal 
are  left  on  either  side  of  the  rooms,  entries,  etc.  to  support  the  roof  until 
the  rooms  are  driven  up,  after  which  they  are  drawn  out. 

Pillar-and-Stall. — See  Breast-and-Pillar . 

Pillar  Roads— Working  roads  or  inclines  in  pillars  having  a range  of  long- 
wall  faces  on  either  side. 

Pillion  ( Cornish)  .—Metal  remaining  in  slag. 

Pina  (Mexican).— Same  as  Pella. 

Pinch. — A contraction  in  the  vein. 

Pinch  Out. — When  a lode  runs  out  to  nothing. 

Pinta  (Mexican).— The  color,  weight,  grain,  etc.  of  ores,  whereby  it  is  pos- 
sible to  form  some  idea  of  their  richness  in  the  various  metals. 

Pipe—  An  elongated  body  of  mineral.  Also  the  name  given  to  the  fossil 
trunks  of  trees  found  in  coal  veins. 

Pipe  Clay.— A soft  white  clay. 

Piped  Air. — Air  carried  into  the  working  place  by  pipes  or  brattices. 

Piping— Undercutting  and  washing  away  gravel  before  the  water  nozzle. 

Pit.—(  1)  A shaft.  (2)  The  underground  portion  of  a colliery,  including  all 
workings.  (3)  A gravel  pit. 

Pit  Bank.— The  raised  ground  or  platform  where  the  coal  is  sorted  and 
screened  at  the  surface. 

Pit  Bottom.— The  portion  of  a mine  immediately  around  the  bottom  of  a shaft 
or  slope.  See  Shaft  Bottom. 

(1;  Rise  of  a seam.  (2)  Grade  of  an  incline.  (3)  Inclination.  (Cor- 
’'ish)  A part  of  a lode  let  out  to  be  worked  on  shares,  or  by  the  piece. 

Pit  Coal. — Generally  signifies  the  bituminous  varieties  of  coal. 

Pit  Frame.— See  Head-Frame. 

Pit  Headman—  The  man  who  has  charge  at  the  top  of  the  shaft  or  slope. 

Pitman. — A miner;  also,  one  who  looks  after  the  pumps,  etc. 

Pit  Prop.— A piece  of  timber  used  as  a temporary  support  for  the  roof. 

Pit  Rails. — Mine  rails  for  underground  roads. 

Pit  Room.— The  extent  of  underground  workings  in  use  or  available  for  use. 

Pit's  Eye. — Pit  bottom  or  entrance  into  a shaft. 

Pit  Top. — The  mouth  of  a shaft  or  slope. 

Place. — The  portion  of  coal  face  allotted  to  a hewer  is  spoken  of  as  his 
“working  place,”  or  simply  “place.” 

Placer. — A surface  accumulation  of  mineral  in  the  wash  of  streams. 

Placer  Mining. — Surface  mining  for  gold  where  there  is  but  little  depth  of 
alluvial. 

Plan.— (1)  The  system  on  which  a colliery  is  worked  as  Longwall,  Pillar- 
and-Breast , etc.  (2)  A map  or  plan  of  the  colliery  showing  outside 
improvements  and  underground  workings.  (3)  (Mexican)  The  very 
lowest  working  in  a mine.  Trabajar  de  Plan.— To  work  to  gain  depth. 

Plancha  —A  pig  of  lead,  etc.  A plate,  thick  sheet,  or  mass  of  any 


meta 


Pla 


GLOSSARY. 


Pop 


603 


Planchera  (Mexican).— A mold  of  sand,  earth,  or  iron,  to  form  pigs 
of  lead.  , , . . . . . , 

Plane—  A main  road,  either  level  or  inclined,  along  which  coal  is  conveyed 
by  engine  power  or  gravity. 

Plane  Table— A simple  surveying  instrument  by  means  of  which  one  can 
plot  on  the  field.  , , x ... 

Planilla  (Mexican).— An  inclined  plane  of  mason  work,  wood,  etc.,  on  which 
tailings  are  spread  out,  to  be  concentrated  by  jets  of  water,  skilfully 
applied. 

Planillero  (Mexican).— A workman  who  devotes  himself  to  concentrating 
tailings,  etc.  on  the  Planillas;  always  paid  by  weight,  measure,  or  con- 
centrates produced.  . . , _ . 

Plank  Dam.— A water-tight  stopping  fixed  m a heading  constructed  of 
timber  placed  across  the  passage,  one  upon  another,  sidewise,  and 
tightly  wedged.  „ , , . _ 

Plank  Tubbing—  Shaft  lining  of  planks  driven  down  vertically  behind 
wooden  cribs  all  around  the  shaft,  all  joints  being  tightly  wedged,  to 
keep  back  the  water. 

Plant.— The  shafts  or  slope,  tunnels,  engine  houses,  railways,  machinery, 
workshops,  etc.  of  a colliery  or  other  mine. 

Plat , or  Map—  A map  of  the  surface  and  underground  workings,  or  of 
either,  to  draw  such  a map  from  survey. 

Plata  ( Spanish ) .—Silver. 

Plata  Blanca  (Mexican).— Native  silver. 

Plata  Cornea  Amarillia  (Spanish).— Iodyrite. 

Plata  Cornea  Blanca  (Spanish).— Cerargy rite. 

Plata  Cornea  Verde  (Spanish).— Embolite. 

Plata  Mixta  (Spanish).— Gold  and  silver  alloy. 

Plata  Negra  (Spanish).— Argentite. 

Plata  Pasta  (Spanish).— Spongy  silver  bars  after  retorting. 

Plata  Piha  (Spanish).— Silver  after  retorting. 

Plata  Verde  (Spanish) .— Bromyrite. 

Plate  (North  of  England).— Scaly  shale  in  limestone  beds. 

Plates—  Metal  rails  4 ft.  long. 

Plenum— A mode  of  ventilating  a mine  or  a heading  by  forcing  fresh  air 


J.I/. 

Plomada  (Mexican).— A plumb-line  or  plumb-bob. 

Plomb  d' Oeuvre  (French).— Dressed  galena. 

Plomillos  (Mexican).— Shots  of  lead  found  in  slags. 

Plomo  (Spanish).— Lead,  galena.  , , 

Plugging—  When  drift  water  forces  its  way  through  the  puddle  clay  into 
the  shaft,  holes  are  bored  through  the  slabs  near  the  leakage  point,  and 
plugs  of  clay  forced  into  them  until  the  leakage  is  stopped. 

Plumb  ^ j 0^1(33,1 

Plummet.— (1)  A heavy  weight  attached  to  a string  or  fine  copper  wire  used 
for  determining  the  verticality  of  shaft  timbering.  (2)  A plumb-bob  for 
setting  a surveying  instrument  over  a point. 

Plunger—  The  solid  ram  of  a force  pump  working  in  the  plunger  case. 

Plunger  Case.— The  pump  cylinder  or  barrel  in  which  the  plunger  works. 

Plush  Copper.— Chalcotrichite. 

Plwm  (Welsh). — Lead. 

Poblar  (Mexican).— To  set  men  at  work  in  a mine. 

Pocket .— (1)  A thickening  out  of  a seam  of  coal  or  other  mineral  over  a small 
area.  (2)  A hopper-shaped  receptacle  from  which  coal  or  ore  is  loaded 
into  cars  or  boats. 

' Podar  (Cornish).— Copper  pyrites.  , . 

Pole  Tools. — Drilling  tools  used  in  drilling  in  the  old  fashion  with  rods,  now 
superseded  by  the  rope-drilling  method. 

Polroz  (Cornish).— Waterwheel  pit.  

Poling. — Refining  metal,  when  in  a molten  condition,  by  stirring  it  up  with  a 
green  pole  of  wood. 

Poll  Pick. — A pick  having  the  longer  end  pointed  and  the  shorter  ena  tiam- 
mer-shaped. 

Polvillos  (Spanish).— Rich  ores  or  concentrates. 

Polvoulla  (Spanish).— Black  silver. 

Poppet  Heads.— The  pulley  frame  or  hoisting  gear  over  a shaft. 

Poppet  {Puppet).— (1)  A pulley  frame  or  the  head-gear  oyer  a sliait.  (2)  A 
valve  that  lifts  bodily  from  its  seat  instead  of  being  hinged. 


GLOSSARY. 


Pun 


004 


Pos 


Post  _(1)  Any  upright  timber;  applied  particularly  to  the  timbers  used  for 
propping.  See  Prop.  (2)  Local  term  for  sandstone.  Post  stone  may  be 
“strong,”  “ framey,”  “ short,”  or  “ broken.” 

Post-and-Stall. — A system  of  working  coal  much  the  same  as  Pillar-and-Stall. 
Post  Ternary.— Strata  younger  than  the  Tertiary  formation. 

Pot  Bottom. — A large  boulder  in  the  roof  slate,  having  the  appearance  of  the 
rounded  bottom  of  a pot,  and  which  easily  becomes  detached. 

Pot  Growan  (Cornish).— Decomposed  granite.  . 

Pot  Hole  —A  circular  hole  in  the  rock  caused  by  the  action  of  stones  whirled 
around  by  the  water  when  the  strata  was  covered  by  water.  They  are 

generally  filled  with  sand  and  drift.  . . 

Power  Drill— A rock  drill  employing  steam,  air,  or  electricity  as  a motor. 
Prian  (Cornish). — Soft  white  clay.  , , . ' . . 

Pricker— ( 1)  A thin  brass  rod  for  making  a hole  m the  stemming  when 
blasting,  for  the  insertion  of  a fuse.  (2)  A piece  of  bent  wire  by  which 
the  size  of  the  flame  in  a safety  lamp  is  regulated  without  removing  the 
top  of  the  lamp.  x A _ , _ , . 

priU  — (l)  An  extra-rich  stone  of  ore.  (2)  A bead  of  metal. 

Prong  (English).— The  forked  end  of  the  bucket-pump  rods  for  attachment  to 
the  traveling  valve  and  seat.  _ A . . 

Prop.— A wooden  or  cast-iron  temporary  support  for  the  root. 

Propping. — The  timbering  of  a mine.  , , 

Prospect  —The  name  given  to  underground  workings  whose  value  has  not 
yet  been  made  manifest.  A prospect  is  to  a mine  what  mineral  is 
to  ore. 

Prospect  Hole— Any  shaft  or  drift  hole  put  down  for  the  purpose  of  prospect- 
ing the  ground.  , _ , 

Prospect  Tunnel  or  Entry— A tunnel  or  entry  driven  through  barren  measures 
or  a fault  to  ascertain  the  character  of  strata  beyond. 

Prospecting.— Examining  a tract  of  country  in  search  ol  minerals. 
Prospector—  One  engaged  in  searching  for  minerals. 

Protector  Lamp— A safety  lamp  whose  flame  cannot  be  exposed  to  the  out- 
ward atmosphere,  as  the  action  of  opening  the  lamp  extinguishes  the 

Prove ?— (1)  To  ascertain,  by  boring,  driving,  etc.,  the  position  and  character 
of  a coal  seam,  a fault,  etc.  (2)  To  examine  a mine  m search  of  fire- 
damp, etc.,  known  as  “ proving  the  pit.” 

Proving  Hole.—{  1)  A bore  hole  driven  for  prospecting  purposes.  (2)  A 
small  heading  driven  in  to  find  a bed  or  vein  lost  by  a dislocation  of 
the  strata,  or  to  prove  the  quality  of  the  mineral  in  advance  of  the 
other  workings. 

Pudding  Machine— A circular  machine  for  washing  pay  dirt. 

Pudding  Rock.— Conglomerate.  , . . , . 

Puddle.— (1)  Earth  well  rammed  into  a trench,  etc.,  to  prevent  leaking. 

(2)  A process  for  converting  cast  iron  into  wrought  iron. 

Pueble  (Mexican).— The  actual  working  of  a mine;  the  aggregation  ot 
persons  employed  therein.  . *T. 

Puertas  (Mexican).— Massive  barren  rocks,  or  “ horses,”  occurring  m a vein. 
Pug  Mill.— A mill  for  preparing  clay  for  bricks,  pottery,  etc. 

Pulley.— { 1)  The  wheel  over  which  a winding  rope  passes  at  the  top  ot  the 
head-gear.  (2)  Small  wooden  cylinders  over  which  a winding  rope  is 
carried  on  the  floor  or  sides  of  a plane.  . ...  „ 

Pulleying. — Overwinding  or  drawing  up  a cage  into  the  pulley  trame. 

Pulp.— Crushed  ore,  wet  or  dry. 

Pump— Any  mechanism  for  raising  water. 

Purnp  Ring —A  fiat  iron  ring  that,  when  lapped  with  tarred  baize  or  engine 
shag,  secures  the  joints  of  water  columns.  . . 

Pump  Rods. — Heavy  timbers  by  which  the  motion  of  the  engine  is  trans- 
mitted to  the  pump.  In  Cornish  and  bull  pumps,  the  weight  of  the  rods 
makes  the  effective  (pumping)  stroke,  the  engine  merely  lifting  the  rods 
on  the  up  stroke. 

Pump  Slope. — A slope  used  for  pumping  machinery.  to 

Pump  Station.— An  enlargement  made  in  the  shaft,  slope,  or  gangway,  to 

PumpCTree.  -Cast-iron  pipes,  generally  9 ft.  long,  of  which  the  column  or  set 
is  formed.  , . . . 

Punch-and-  Thirl.  — A kind  of  pillar-and-stall  system  of  working. 


Pun 


GLOSSARY. 


Ree 


605 


Punch  Prop— A short  timber  prop  set  on  the  top  of  a crown  tree,  or  used  in 

Put^Stonfs.- !oftPpfeces  of  decomposed  rock  found  in  placer  deposits. 

Pyran  (Cornish).— See  Prian. 

Pyrites—  Sulphide  of  iron.  . . , . , . 

Pyrometer—  An  instrument  for  measuring  high  degrees  of  heat. 

Marty  — ftT-An  ^op^^rllce0 excavation  for  working  valuable  rocks  or 
minerals.  (2)  An  underground  excavation  for  obtaining  stone  for 
stowage  or  pack  walls. 

Quartz  Bucket— A bucket  for  hoisting  quartz. 

^emadero  ’ ( T^xfcmi ) !— A burning  place;  a retorting  furnace  for  silver  or 

Qaem^dos '(MeScan ) .—Burnt  stuff.  Any  dark  cinder-like  mineral  encoun- 
H tered  in  a vein  or  mineral  deposit,  generally  mangamferous. 

Queme  (Mexican) .-A  roast  of  ore;  the  process  of  roasting  ore, 

Quick  (Adjective).— Soft,  running  ground;  an  ore  or  pay  streak  is  said  to  be 
Quickening  when  the  associated  minerals  indicate  richer  mineral 
ahead.  Quick  (Noun).— (1)  Productive.  (2)  Mercury 
Quicksand. — Soft  watery  strata  easily  moved,  or  readily  yielding  to  pressure. 
Quicksilver. — Mercury . 

^itapepena^ Mexican^— A watchman  that  searches  the  miners  as  they 
come  out  at  the  mouth  of  a mine. 

Rabban  (Cornish).— Yellow  dry  gossan. 

Rabbling. — Stirring  up  a charge  of  ore  in  a reverberatory  furnace  wit* 
specially  designed  iron  rods.  „ , .. 

Race  — A channel  for  conducting  water  to  or  from  the  piace  where  it  pei' 
forms  work.  The  former  is  termed  the  headrace,  and  the  latter  tiu 

tailrace.  . _ 

Rack  (Cornish).— A stationary  buddle.  . . 

Paff.—The  coarse  ore  after  crushing  by  Cornish  rolls. 

RataWheel°—A  revolving  wheel  with  side  buckets  for  elevating  the  raff. 
Rafter  Timbering.— That  in  which  the  timbers  appear  like  roof  rafters. 

Rag  Burning  (Cornish).— The  first  roasting  of  tin-witts. 

Rag-Wheel— Sprocket  wheel.  A wheel  with  teeth  or  pins  that  catch  into  th  e 

links  of  chains.  „ , A ..  , 

Rails  —The  iron  or  steel  portion  of  the  tramway  or  railroad.  . 

Rake  (Cornish).— (1)  A vein.  (2)  (Derbyshire)  Fissure  vein  crossing  strata. 
Pam  —(1)  The  plunger  of  a pump.  (2)  A device  for  raising  water. 

Ramal  (Mexican). — A branch  vein.  . . 

Ramalear  (Mexican). — To  branch  off  into  various  divisions. 

Ramble.— Stone  of  little  coherence  above  a seam  that  falls  readily  on  tne 
removal  of  the  coal.  See  Following  Stone. 

Rcmwr  -—A  iewev  with  a hammer  attached  at  one  end,  which  signals  by 
striking  a plate  of  metal,  when  the  signaling  wire  to  which  it  is  attached 

Pash  —A  term  used  to  designate  the  bottom  of  a mine  when  soft  and  slaty. 
Rastrillo  (Mexican).— A rake;  a stirrer  for  moving  ore  in  a furnace. 

Rastron  (Mexican).— A Chilian  mill. 

Raw  Ore—  Not  roasted  or  calcined. 

Reacher. — A slim  prop  reaching  from  one  wall  to  the  other. 

Reamer. — An  enlarging  tool. 

Reaming. — Enlarging  the  diameter  of  a bore  hole.  . . . . 

Receiving  Pit— A shallow  pit  for  containing  material  run  into  it. 

Red-Ash  CM— Coal  that  produces  a reddish  ash,  when  burnt. 

Red  Rab  (Cornish).— Red  slaty  rock.  . . ..  . .,  - 

Reduced— When  a metal  is  freed  from  its  chemical  associate  it  is  said  to  be 
reduced  to  the  metallic  state.  . 

Reduction  Works— Works  for  reducing  metals  from  their  ores. 

Peef.—i  l)  A vein  of  quartz.  (2)  Bed  rock  of  alluvial  claims. 

Reef  Drive.— In  alluvial  mines,  drives  made  in  the  country  rock  or  reef. 


606 


Ref 


GLOSSARY. 


' Riv 


Refining.— The  freeing  of  metals  from  impurities. 

Refractory.— Rebellious  ore,  not  easily  treated  by  ordinary  processes. 

Refuge  Hole.— A.  place  formed  in  the  side  of  an  underground  plane  in  which 
a man  can  take  refuge  during  the  passing  of  a train,  or  when  shots  are 
fired. 

Regulator.— A door  in  a mine,  the  opening  or  shutting  of  which  regulates  the 
supply  of  ventilation  to  a district  of  the  mine. 

Regulus. — See  Matte. 

Relampago , or  Relampaguear  (Mexican).— The  brightening  of  the  silver 
button  during  cupellation. 

Reliz  (Spanish).— Wall  of  lode. 

Rendir  (Mexican).— Is  when  all  the  silver  has  been  amalgamated  in  a heap 
of  argentiferous  mud  on  a patio. 

Rendrock.— A variety  of  dynamite. 

Repairman— A workman  whose  duty  it  is  to  repair  tracks,  doors,  brattices, 
or  to  reset  timbers,  etc.,  under  the  direction  of  the  foreman. 

Repaso-Repasar  (Mexican)  .—The  art  of  mixing  up  the  mud  heaps  in  the 
patio  process  of  amalgamation  by  treading  them  over  with  horses  or 
mules. 

Repos  Adero  (Mexican).— The  bottom  of  a crucible  or  pot  in  an  upright 
smelting  furnace. 

Rescatadores  (Mexican).— Ore  buyers. 

.Reserve.— Mineral  already  opened  up  by  shafts,  winzes,  levels,  etc.,  which 
mav  be  broken  at  short  notice  for  any  emergency. 

Reservoir—  An  artificially  built,  dammed,  or  excavated  place  for  holding  a 
reserve  of  water. 

Respaldos  (Mexican).— The  walls  enclosing  a vein.  Respdldo  Alto.— The 
hanging  wall.  Respaldo  Bajo. — The  foot-wall. 

Rests,  Keeps,  Wings.— Supports  on  which  a cage  rests  when  the  loaded  car 
is  being  taken  off  and  the  empty  one  put  on. 

Resue See  Stripping . 

Retort—  (1)  A vessel  with  a long  neck,  used  for  distilling  the  quicksilver 
from  amalgam.  (2)  The  vessel  used  in  distilling  zinc. 

Return.— The  air-course  along  which  the  vitiated  air  of  a mine  is  returned 
or  conducted  back  to  the  upcast  shaft. 

Return  Air.— The  air  that  has  been  passed  through  the  workings. 

Reverberatory.— A class  of  furnaces  in  which  the  flame  from  the  fire-grate  is 
made  to  beat  down  on  the  charge  in  the  body  of  the  furnace. 

Reversed  Fault— See  Overlap  Fault. 

Rib.— The  side  of  a pillar. 

Rib-and-Pillar.—A  system  of  working  similar  to  Pillar-and-Stall. 

Ribbon.— A line  of  bedding  or  a thin  bed  appearing  on  the  cleavage  surface 
and  sometimes  of  a different  color. 

Rick.— Open  heap  in  which  coal  is  coked. 

Ridding. — Clearing  away  fallen  stone  and  debris. 

Riddle.— An  oblong  frame  holding  iron  bars  parallel  to  each  other,  used  for 
sifting  material  that  is  thrown  against  it. 

Ride,  Riding.— To  be  conveyed  on  a cage  or  mine  car. 

Rider.— (1)  A guide  frame  for  steadying  a sinking  bucket.  (2)  Boys  that 
ride  on  trips  on  mechanical  haulage  roads.  (3)  A thin  seam  of  coal 
overlying  a thicker  one. 

Riffle,  or  Ripple.— Crosspieces  placed  on  the  bottom  of  a sluice  to  save  gold; 
or  grooves  cut  across  inclined  tables. 

Right  Shore— The  right  shore  of  a river  is  on  the  right  hand  when  descend- 
ing the  river. 

Rill.— The  coarse  ore  at  the  periphery  of  a pile. 

Rim  Rock.— Bed  rock  forming  a boundary  to  gravel  deposit. 

Ring.—{1)  A complete  circle  of  tubbing  plates  placed  round  a circular  shaft. 
(2)  Troughs  placed  in  shafts  to  catch  the  falling  water,  and  so  arranged 
as  to  convey  it  to  a certain  point. 

Ripping. — Removing  stone  from  its  natural  position  above  the  seam. 

Riscos  (Mexican).— Sharp  and  precipitous  rocks;  amorphous  quartz  found 
in  veins  or  outcrops.  . 

Rise.— The  inclination  of  the  strata,  when  looking  up  the  pitch. 

Rise  Workings.— Underground  workings  carried  on  to  the  rise  or  high  side 
of  the  shaft. 

River  Mining.— Working  beds  of  existing  rivers  by  deflecting  their  course 
or  by  dredging. 


Roa 


GLOSSARY ; 


Saf 


607 


Road.—(  1)  Any  underground  passageway  or  gallery.  (2)  The  iron  rails, 
etc.  of  underground  roads. 

Roasting—  Heating  ores  at  a temperature  sufficient  to  cause  a chemical 
change,  but  not  enough  to  smelt  them. 

Rob.— To  cut  away  or  reduce  the  size  of  pillars  of  coal. 

Robbing.—' The  taking  of  mineral  from  pillars. 

Robbing  an  Entry— See  Drawing  an  Entry. 

Rock— A mixture  of  different  minerals  in  varying  proportions. 

Rock  Breaker —A  machine  for  reducing  ore  in  size  by  crunching  it  between 
powerful  jaws. 

Rock  Chute.— See  Slate  Chute. 

Rock  Drill— A rock-boring  machine  worked  by  hand,  compressed  air,  steam, 
or  electrical  power. 

Rocker. — See  Cradle. 

Rock  Fault— A replacement  of  a coal  seam  over  greater  or  less  area,  by  some 
other  rock,  usually  sandstone. 

Rodding— The  operation  of  fixing  or  repairing  wooden  eye  guides  in 
shafts. 

Roll—  An  inequality  in  the  roof  or  floor  of  a mine. 

Roller.— A small  steel,  iron,  or  wooden  wheel  or  cylinder  upon  which  the 
hauling  rope  is  carried  just  above  the  floor. 

Rolleyway. — A main  haulage  road. 

Rolling  Ground— When  the  surface  is  much  varied  by  many  small  hills  and 
valleys. 

Rolls  -Cast-iron  cylinders,  either  plain  or  fitted  with  steel  teeth,  used  to 
break  coal  and  other  materials  into  various  sizes. 

Roof.— The  top  of  any  subterranean  passage. 

Room . — Synonymous  with  Breast. 

Room-and-Rance  — A system  of  working  coal  similar  to  Pillar-and-Stall. 

Rope  Roll—  The  drum  of  a winding  engine. 

Rosiclara  (Spanish).— Ruby  silver  ore. 

Roughs  (Cornish).— Second  quality  tin  sands. 

Round  Coal.— Coal  in  large  lumps,  either  hand-picked,  or,  after  passing  over 
screens,  to  take  out  the  small. 

Royalty.— The  price  paid  per  ton  to  the  owner  of  mineral  land-by  the  lessee. 

Rubbing  Surface.— The  total  area  of  a given  length  of  airway;  that  is,  the 
area  of  top,  bottom,  and  sides  added  together,  or  the  perimeter  multi- 
plied by  the  length. 

Rubble.— Coarse  pieces  of  rock. 

Rumbo  (Mexican).— The  course  or  direction  of  a vein. 

Run. — (1)  The  sliding  and  crushing  of  pillars  of  coal.  (2)  The  length  of  a 
lease  or  tract  on  the  strike  of  the  seam. 

Run  Coal.—Soit  bituminous  coal. 

Rung , Rundle , or  Round— A step  or  cross-bar  of  a ladder. 

Runner.— A man  or  boy  whose  duty  it  is  to  run  mine  cars  by  gravity  from 
working  places  to  the  gangway. 

Running  Lift.— A sinking  set  of  pumps  constructed  to  lengthen  or  shorten 
at  will,  by  means  of  a sliding  or  telescoping  wind  bore. 

Rush—  An  old-fashioned  way  of  exploding  blasts  by  filling  a hollow  stalk 
with  slow  powder  and  then  igniting  it. 

Rush  Gold.—G old  coated  with  oxide  of  iron  or  manganese. 

Rush  Together.— See  Caved  In. 

Rusty—  Stained  by  iron  oxide. 

Saca  (Mexican).— A bagful  of  ore.  A mine  is  said  to  be  de  buena  saca  when 
it  has  large  quantities  of  ore  easy  to  get  out. 

Saddle  .—An  anticlinal,  a hogback. 

Saddleback —A  depression  in  the  strata.  See  Roll. 

Saddle  Reef. — A reef  having  the  form  of  an-  inverted  V. 

Safety  Cage.— A cage  fitted  with  an  apparatus  for  arresting  its  motion  in  the 
shaft  in  case  the  rope  breaks. 

Safety  Car. — See  Barney. 

Safety  Catches.— Appliances  fitted  to  cages,  to  make  them  safety  cages. 

Safety  Door. — A strongly  constructed  door,  hinged  to  the  roof,  and  always 
kept  open  and  hung  near  to  the  main  door,  for  immediate  use. when 
main  door  is  damaged  by  an  explosion  or  otherwise. 

Safety  Fuse— A cord  with  slow-burning  powder  in  the  center  for  exploding 
charged  blast  holes. 


608 


Saf 


GLOSSARY. 


Seg 


Safety  Lamp— A miner’s  lamp  in  which  the  flame  is  protected  in  such  a 
manner  that  an  explosive  mixture  of  air  and  firedamp  can  be  detected 
by  the  mixture  burning  inside  the  gauze. 

Sag—  A depression,  e.g.,  in  ropes,  ranges  of  mountains,  etc. 

Sagre,  or  Seggar.—A  local  term  for  fireclay,  often  forming  the  floor  (or  thill,) 

of  coal  seams.  _ . 

Salting.— (1)  Changing  the  value  of  the  ore  m a mine  or  of  ore  samples 
before  they  have  been  assayed,  so  that  the  assay  will  show  much  higher 
values  than  it  should.  (2)  Sprinkling  salt  on  the  floors  of  underground 
passages  in  very  dry  mines,  in  order  to  lay  the  dust. 

Sampler.— (1)  An  instrument  or  apparatus  for  taking  samples.  (2)  One  whose 
duty  it  is  to  select  the  samples  for  an  assay,  or  to  prepare  the  mineral 
to  be  assayed,  by  grinding  and  sampling.  . . . , . . , 

Sampling  Wor ks.— Works  for  sampling  and  determining  the  values  obtained 
in  ores;  where  ores  are  bought  and  sold. 

Samson  Post.— An  upright  supporting  the  working  beam  that  communicates 
oscillatory  motion  to  pump  or  drill  rod. 

Sand  Bag— A bag  filled  with  sand  for  preventing  a washout  by  obstructing 

Sand^ Pump. ‘—A  sludger;  a cylinder  provided  with  a stem  (or  other)  valve, 
lowered  into  a drill  hole  to  remove  the  pulverized  rock. 

Scaffolding. — Incrustations  on  the  inside  of  a blast  furnace. 

Scale. — (1)  A small  portion  of  the  ventilating  current  in  a mine  passing 
through  a certain  size  of  aperture.  (2)  The  rate  of  wages  to  be  paid, 
which  varies  under  certain  contingencies. 

Scale  Door. — See  Regulator.  . 

Scallop  —To  hew  coal  without  kirving  or  nuking  or  shot  firing. 

Schist  — Crystalline  or  metamorphic  rocks  having  a slaty  structure. 

Scissors  Fault— A fault  of  dislocation,  in  which  two  beds  are  thrown  so  as  to 
cross  each  other.  , 

Scoop— A large-sized  shovel  with  a scoop-shaped  blade. 

Scoria. — Ashes. 

Scorifier.— A small  dish  used  in  assaying. 

Scovan  (Cornish).— A tin  lode  showing  no  gossan  at  surface. 

Scove  (Cornish).— Purest  tin  ore.  „ ,. 

Scramming. — Cleaning  up  small  bodies  or  patches  of  ore  left  in  the  ordinary 

Scraper.— {!)  T tool ' for  cleaning  the  dust  out  of  the  bore  hole.  (2)  A 
mechanical  contrivance  used  at  colleries  to  scrape  the  culm  or  slack 
along  a trough  to  the  place  of  deposit.  . 

Scrapper  — A local  name  given  to  parties  that  pick  up  the  ore  left  on  dumps. 

Screen. — (1)  A mechanical  apparatus  for  sizing  materials.  (2)  A cloth  brat- 
tice or  curtain  hung  across  a road  in  a mine,  to  direct  the  ventilation. 

Serin  (Derbyshire). — A small  vein.  . 

Scrowl  (Cornish).— Loose  ore  where  a vein  is  crossed. 

Sculping. — Fracturing  the  slate  along  the  grain,  l.  e.,  across  the  cleavage. 

Scupper  Nails.— Nails  with  broad  heads,  for  nailing  down  canvas,  etc. 

Sea  Coal. — That  which  is  transported  by  sea.  • . . ^ e 

Sealing—  Shutting  off  all  air  from  a mine  or  a part  of  a mine  by  stoppings. 

Seam.—{  1)  Synonymous  with  Bed , Vein , etc.  (2)  (Cornish)  A horse  load 

Seam-Oid.— A term  applied  to  a shot  or  blast  that  has  simply  blown i out  a softer 
stratum  of  the  deposit  in  which  it  was  placed,  without  dislodging  the 
other  strata  or  layers  of  the  seam.  . 

Second  Outlet  ( Second  Opening).— A passageway  out  of  a mine,  for  use  in  case 
of  accident  to  the  main  outlet. 

Seconds.—1 The  second-class  ore  of  a mine  that  requires  dressing. 

Second  Working.— The  operation  of  getting  or  working  out  the  pillars  .ormed 

Section1— (LtoA  verticaf  or  horizontal  exposure  of  strata.  (2)  A drawing  or 
sketch  representing  the  rock  strata  as  cut  by  a vertical  or  a horizontal 

Sed&ntary  Rocks.—  Rocks  formed  from  deposits  of  sediment  by  wind  or 

SeeFbeup— A water-tight  packing  of  flaxseed  around  the  tube  of  a drill  hole, 
to  prevent  the  influx  into  the  hole  of  water  from  above. 

Segregations.— Detached  portions  of  veins  in  place. 


Sel 


GLOSSARY. 


Sho 


609 


Self-Acting  Plane— An  inclined  plane  upon  which  the  weight  or  force  of 
gravity  acting  on  the  full  cars  is  sufficient  to  overcome  the  resistance  of 
the  empties;  in  other  words,  the  full  car,  running  down,  pulls  the  other 
car  up. 

Self-Detaching  Hook.— A self-acting  hook  for  setting  free  a hoisting  rope  m 
case  of  overwinding.  ■ 

Self-Feeders— Automatic  appliances  for  feeding  ore-dressing  machines. 
Selvage— The  clay  seam  on  the  walls  of  veins;  gouge. 

Separation  Doors.—  The  main  doors  at  or  near  the  shaft  or  slope  bottom, 
which  separate  the  intake  from  the  return  airways. 

Separation  Valve— A massive  cast-iron  plate  suspended  from  the  roof  of  a 
return  airway  through  which  all  the  return  air  of  a separate  district 
flows,  allowing  the  air  to  always  flow  past  or  underneath  it;  but  in 
the  event  of  an  explosion  of  gas,  the  force  of  the  blast  closes  it  against 
its  frame  or  seating,  and  prevents  a communication  with  other  districts. 
The  blast  being  over,  the  weight  of  the  valve  allows  it  to  return  ^o  its 
normal  position. 

Set. — To  fix  in  place  a prop  or  sprag.  ...  , 

Set  Hammer.— The  flat-faced  hammer  held  on  hot  iron  by  a blacksmith  when 
shaping  or  smoothing  a surface  by  aid  of  his  striker’s  sledge. 

Set  of  Timber—  The  timbers  which  compose  any  framing,  whether  used  in 
a shaft,  slope,  level,  or  gangway.  Thus,  the  four  pieces  fuming  a single 
course  in  the  curbing  of  a shaft,  or  the  three  or  four  pieces  forming 
the  legs  and  collar,  and  sometimes  the  sill  of  an  entry  framing  are 
together  called  a set  of  timber,  or  timber  set.  . 

Shackle.— A U-shaped  link  in  a chain  closed  by  a pm;  when  the  latter  is  with- 
drawn the  chain  is  severed  at  that  point. 

Shadd  (Cornish).— Rounded  fragments  of  ore  overlying  a vein. 

Shaft.— A vertical  or  highly  inclined  pit  or  hole  made  through  strata,  through 
which  the  product  of  the  mine  is  hoisted,  and  through  which  the  ventila- 
tion is  passed  either  into  or  out  of  the  mine.  A shaft  sunk  from  one 
seam  to  another  is  called  a “blind  shaft.” 

Shaft  Pillar.— Solid  material  left  unworked  beneath  buildings  and  around 
the  shaft,  to  support  them  against  subsidence.  . 

Shaking  Table.— An  inclined  table  for  concentrating  fine  grains  of  ore,  which 
is  rapidly  shaken  by  a short  motion 

Shale— (1)  Strictly  Speaking,  all  argillaceous  strata  that  split  up  or  peel  off 
in  thin  laminae.  (2)  A laminated  and  stratified  sedimentary  deposit  of 
clay,  often  impregnated  with  bituminous  matter. 

Shank.—1 The  body  portion  of  any  tool,  up  from  its  cutting  edge  or  bit. 
Shearing— Cutting  a vertical  groove  in  a coal  face  or  breast.  The  cutting  of 
a “ fast  end”  of  coal.  . 

Shear  Legs.— A high  wooden  frame  placed  over  an  engine  or  pumping  shaft 
fitted  with  small  pulleys  and  rope  for  lifting  heavy  weights. 

Shears , or  Sheers  (English).— Two  tall  poles,  with  their  feet  some  distance 
apart  and  their  tops  fastened  together,  for  supporting  hoisting  tackle. 
Shear  Zone.— Hogback. 

Sheave— A wheel  with  a grooved  circumference  over  which  a rope  is  turned 
either  for  the  transmission  of  power  or  for  winding  or  hauling. 

Sheet  Pump.— See  Sludger , . , _ . 

Sheets  .—Coarse  cloth  curtains  or  screens  for  directing  the  ventilating  current 
underground.  _ _ _ _ _ 

Shelly— A name  applied  to  coal  that  has  been  so  crushed  and  fractured  that 
it  easily  breaks  up  into  small  pieces.  The  term  is  also  applied  to  a lami- 
nated roof  that  sounds  hollow  and  breaks  into  thin  layers  of  slate  or 
shale. 

Shet  (Staffordshire). — Fallen  roof  of  coal  mine.  . _ 

Sheth. — An  old  term  denoting  a district  of  about  eight  or  nine  adjacent  bords. 

Thus,  a “ sheth  of  bords,”  or  a “ sheth  of  pillars.” 

Shift— {1)  The  number  of  hours  worked  without  change.  (2)  A gang  or 
force  of  workmen  employed  at  one  time  upon  any  work,  as  the  day  shift, 
or  the  night  shift. 

Shoad  (Cornish).— See  Shadd. 

Shoading  (Cornish). — Prospecting.  . , 

Shoe. — (1)  A steel  or  iron  guide  piece  fixed  to  the  ends  or  sides  of  cages,  to 
fit  or  run  on  the  conductors.  (2)  The  upper  working  face  of  a stamp  or 
grinding  pan.  (3)  The  lower  capping  of  any  post  or  pile,  to  protect  its 
end  while  driving.  (4)  A wooden  or  sheet-iron  frame  or  muff  arranged 


610 


Sho 


GLOSSARY. 


Sin 


at  the  bottom  of  a shaft  while  sinking  through  quicksand,  to  prevent  the 
inflow  of  sand  while  inserting  the  shaft  lining. 

Shoot,  Chute,  Shute .— (1)  A run  of  rich  material  in  a vein.  (2)  An  inclined 
or  vertical  trough  or  pipe  for  conveying  materials  from  a higher  to  a 
lower  level. 

Shoot.—1 To  break  rock  or  coal  by  means  of  explosives. 

Shooting—  Blasting  in  a mine. 

Shore  (English).— A studdle  or  thrusting  stay. 

Shore  Up. — To  stay,  prop  up,  or  support  by  braces. 

Shot.— (1)  A charge  or  blast.  (2)  The  firing  of  a blast.  (3)  Injured  by  a 
blast. 

Shot-Firer.— See  Shot  Lighter. 

Shot  Hole—  The  bore  hole  in  which  an  explosive  substance  is  placed  for 
blasting. 

Shot  Lighter,  or  Shot  Firer.—A  man  specially  appointed  by  the  manager  of 
the  mine  to  fire  off  every  shot  in  a certain  district,  it,  after  he  has 
examined  the  immediate  neighborhood  of  the  shot,  he  finds  it  free  from 
gas,  and  otherwise  safe. 

Shotty  Gold— Granular  pieces  like  shot. 

Show.— When  the  flame  of  a safety  lamp  becomes  elongated  or  unsteady, 
owing  to  the  presence  of  firedamp  in  the  air,  it  is  said  to  show. 

Showing. — The  first  appearance  of  float,  indicating  the  approach  to  an  out- 
cropping vein  or  seam.  Blossom. 

Shroud.— A housing  or  jacket. 

Shute. — See  Chute,  Shoot,  and  Schute. 

Shutter.— (1)  A movable  sliding  door,  fitted  within  the  outer  casing  of  a 
Guibal  or  other  closed'  fan,  for  regulating  the  size  of  the  opening  from 
the  fan,  to  suit  the  ventilation  and  economical  working  of  the  machine. 
(2)  A slide  covering  the  opening  in  a door  or  brattice,  and  forming  a 
regulator  for  the  proportionate  division  of  the  air-current  between  two 
or  more  districts  of  a mine. 

Sickening.— A coating  of  impurities  on  quicksilver  that  retards  amalgama- 
tion or  the  coalescence  of  the  globules  of  quicksilver. 

Siddle. — Inclination. 

Side.—{  1)  The  more  or  less  vertical  face  or  wall  of  coal  or  goaf  forming  one 
side  of  an  underground  working  place.  (2)  Rib.  (3)  A district. 

Side  Chain.— A chain  hooked  on  to  the  sides  of  cars  running  on  an  incline  or 
along  a gangway,  to  keep  the  cars  together  in  case  the  coupling 
breaks 

Sidelong  Reef.— An  overhanging  wall  of  bed  rock  in  alluvial  formations 
running  parallel  with  the  course  of  the  gutter;  generally  only  on  one 
side  of  it. 

Siding— A short  piece  of  track  parallel  to  the  mam  track,  to  serve  as  a 
passing  place.  , . 

Siding  Over.— A short  road  driven  in  a pillar  in  a head  wise  direction. 

Sight—  (1)  A bearing  or  angle  taken  with  a compass  or  transit  when  making 
a survey.  (2)  Any  established  point  of  a survey. 

Sights . — Bobs  or  weighted  strings  hung  from  two  or  more  established  points 
in  the  roof  of  a room  or  entry,  to  give  direction  to  the  men  driving  the 
entry  or  room.  , , . , 

Sill.—(1)  The  floor  piece  of  a timber  set,  or  that  on  which  the  track  rests; 
the  base  of  any  framing  or  structure.  (2)  The  floor  of  a seam. 

Silver. — (1)  A certain  white  ductile  and  valuable  metal.  (2)  Short  for  quick- 
silver. . 

Sing. — The  noise  made  by  a feeder  of  gas  issuing  from  the  coal. 

Singing  Coal.— Coal  from  which  gas  is  issuing  with  a hissing  sound. 

Singing  Lamp. — A safety  lamp,  which,  when  placed  in  an  atmosphere  ol 
explosive  gas,  gives  out  a peculiar  sound  or  note,  the  strength  of  the 
note  varying  in  proportion  to  the  percentage  of  firedamp  present. 

Single-Entry  System.— A system  of  opening  a mine  by  driving  a single  entry 
only,  in  place  of  a pair  of  entries:"  The  air-current  returns  along  the 
face  of  the  rooms,  which  must  be  kept  open. 

Single-Intake  Fan— A ventilating  fan  that  takes  or  receives  its  air  upon  one 
side  only.  , . ...  . . 

Single-Rope  Haulage.— A system  of  underground  haulage  m which  a single 
rope  is  used,  the  empty  trip  running  in  by  gravity.  This  is  engine-plane 
haulage.  , . . , 

Sink— To  excavate  a shaft  or  slope;  to  bore  or  put  down  a bore  hole. 


Sin 


GLOSSARY. 


Sli 


611 


Sinker.— A.  man  who  works  at  the  bottom  of  a shaft  or  face  of  a slope  during 
the  course  of  sinking. 

Sinker  Bar.— In  rope  drilling,  a heavy  bar  attached  above  the  jars,  to  give 
force  to  the  up  stroke,  so  as  to  dislodge  the  bit  in  the  hole. 

Sinking—  The  process  of  excavating  a shaft  or  slope  or  boring  a hole. 

Siphon.— A simple,  effective,  and  economical  mode  of  conveying  water  over 
a hill  whose  height  is  not  greater  than  what  the  atmospheric  pressure 
will  raise  the  water.  Its  form  is  that  of  an  iron  pipe,  bent  like  an 
inverted  U;  the  vertical  height  between  the  surface  of  the  water  in  the 
upper  basin  and  the  top  of  the  hill  is  called  the  lift  of  the  siphon;  while 
the  vertical  height  between  the  surfaces  of  the  water  in  the  upper  and 
lower  basins  is  called  the  fall  of  the  siphon. 

Sizing.— To  sort  minerals  into  sizes. 

Skew  Back.— The  beveled  stone  from  which  an  arch  springs,  and  upon  which 
it)  rests 

Skids. — Slides  upon  which  heavy  bodies  are  slid  from  place  to  place. 

Skimpings  (Cornish).— The  poorest  ore  skimmed  off  the  jigger. 

Skip .— (1)  A mine  car.  (2)  A car  for  hoisting  out  of  a slbpe.  (3)  A thin 
slice  taken  off  from  a breast  or  pillar  or  rib  along  its  entire  length  or 
part  of  its  length. 

Skirting.— Road  opened  up  or  driven  next  a fall  of  stone,  or  an  old  fallen  place. 

Skit  (Cornish). — A pump. 

Slab.—  Split  pieces  of  timber  from  2 in.  to  3 in.  thick,  4 ft.  to  6 ft.  long,  an<J  * 
7 in.  to  14  in.  wide,  placed  behind  sets  or  frames  of  timber  in  shafts  or 
levels.  . 

Slack.— (1)  Fine  coal  that  will  pass  through  the  smallest  sized  screen.  The 
fine  coal  and  dust  resulting  from  the  handling  of  coal,  and  the  disinte- 
gration of  soft  coal.  (2)  The  process  by  which  soft  coal  disintegrates 
when  exposed  to  the  air  and  weather. 

Slag.— The  liquid  refuse  from  a smelting  operation,  which  floats  on  top  of 
the  metal. 

Slant.— (1)  An  underground  roadway  driven  at  an  angle  between  the  full 
rise  or  dip  of  the  seam  and  the  strike  or  level.  (2)  Any  inclined  road 
in  a seam. 

Slant  Chutes—  Chutes  driven  diagonally  across  a pillar,  to  connect  a breast 
manway  with  a manway  chute. 

Slate.— (1)  A hardened  clay  having  a peculiar  cleavage.  (2)  About  coal 
mines,  slate  is  any  shale  accompanying  the  coal,  also  sometimes  applied 
to  bony  coal. 

Slate  Picker.— (1)  A man  or  boy  that  picks  the  slate  or  bony  coal  from 
anthracite  coal.  (2)  A mechanical  contrivance  for  separating  slate  and 
coal. 

Slate  Chute.— (1)  A chute  for  conveying  slate  or  bony  coal  to  a pocket  from 
which  it  is  loaded  into  “ dumpers.”  (2)  A chute  driven  through  slate. 

Sleek  (Derbyshire).— Mud  in  a mine. 

Sled.— A drag  used  to  convey  coal  along  the  face  to  the  road  head  where  it  is 
loaded,  or  to  the  chute. 

Sledge.— A heavy  double-handed  hammer. 

Sleeper  (English). -The  foundation  pieces  or  cross-ties  on  which  rails  rest. 

Sleeping  Tab'e  (Cornish). — A buddle. 

Sleeve.— A hollow  cylinder  fitting  over  two  pieces,  to  hold  them  together. 

Slickensides—  Polished  surfaces  of  vein  walls. 

Slide—  Loose  deposit  covering  the  outcrop  of  a seam. 

Slides—  See  Guides. 

Sliding  Scale.— A mode  of  regulating  the  wages  paid  workingmen  by  taking 
as  a basis  for  calculation  the  market  price  of  coal,  the  wages  rising  and 
falling  with  the  state  of  trade. 

Sliding  Wind  Bore  (English).— The  bottom  pipe  or  suction  piece  of  a sinking 
set  of  pumps  having  a lining  made  to  slide  like  a telescope  within  it,  to 
give  length  without  altering  the  adjustment  of  the  whole  column 
of  pipes. 

Slime,  Sludge. — (1)  The  pulp  or  fine  mud  from  a mill  or  from  a drill  hole. 
(2)  Silt  containing  a very  fine  ore,  which  passes  off  in  the  water  from 
the  jigs. 

Slings.— Pieces  of  ropes  or  chains  to  be  put  around  stones,  etc.  for  raising 
them. 

Slip.— (1)  A fault.  (2)  A smooth  joint  or  crack  where  the  strata  have 
moved  upon  each  other. 


612 


Sli 


GLOSSAR  Y. 


Spi 


Slip  Cleavage.— Microscopic  folding  and  fracture  accompanied  by  slippage; 
quarryinen’s  “ false  cleavage.” 

Slit.— A short  heading  put  through  to  connect  two  other  headings. 

"slope — A plane  or  inclined  roadway,  usually  driven  in  the  seam  from  the 
surface.  A rock  slope  is  a slope  driven  across  the  strata,  to  connect  two 
seams;  or  a slope  opening  driven  from  the  surface,  to  reach  a seam  below 
that  does  not  outcrop  at  an  accessible  point. 

fludger  Sludge  Pump.— A cylinder  having  an  upward  opening  valve  at  the 
bottom,  which  is  lowered  into  a bore  hole,  to  pump  out  the  sludge  or  fine 
rock  resulting  from  drillings.  „ . , . _ , . , , , 

Sluice. (1)  A long  channel  in  rock  or  built  of  timber,  with  checks  to  catch 

gfold.  (2)  Anv  overflow  channel. 

Sluice  Box.— A trough  with  ripples  or  false  bottom  for  catching  gold. 

Sluice  Head,  or  Head  (Australia  and  New  Zealand).— A supply  of  1 cu.  ft.  of 
water  per  second,  regardless  of  the  head,  pressure,  or  size  of  orifice. 
Sluicing. — Ground  sluicing  is  working  gravel  by  excavating  with  pick  and 
shovel,  and  washing  the  debris  m trenches  with  water  not  under 
pressure.  , 

Slurry  (North  of  Wales).— Half-smelted  ore. 

Small. — See  Slack. 

Smeddum  — Lead-ore  dust.  . . . , .. 

Smelting. — Method  of  extracting  a precious  metal  from  its  ores 
Smift  Snifi  —A.  bit  of  touch  paper,  touch  wood,  etc.  attached  by  a bit  of 
ciay  or  grease  to  the  outside  end  of  the  train  of  gunpowder  when 

Smitton.— Fine  gravel-like  ore,  occurring  free  in  mud  openings,  or  derived 
from  the  breaking  of  the  ore  in  blasting. 

^^Tn^Piece^-1 The°holein  the  lower  part  of  a sinking  or  Cornish  pump, 

Soa^^A^lnZ^^ea  by  the  miner  to  any  soft,  unctuous 

Socabon  {Mexican) .— A mining  tunnel;  an  adit.  Socavon  dhilo  de  vela.  A 
drift  tunnel.  Socavon  crucero. — A crosscut  tunnel  or  adit. 

Socket. — (1)  The  innermost  end  of  a shot  hole,  not  blown  away  after  finng. 
(2)  A wrought-iron  contrivance  by  means  of  which  a wire  rope  is 
securely  attached  to  a chain  or  block. 

Sole  Sole  Plate.— A piece  of  timber  set  underneath  a prop. 

Sollar. — A wooden  platform  fixed  in  a shaft,  for  the  ladders  to  rest  on. 
Sondear  (Mexican).— To  bore  for  prospecting  purposes. 

Sondeo  (Mexican).— A boring  for  prospecting  purposes. 

Soplete  (Mexican).— A blowpipe.  Ensayeal  Soplete  — A blow  pipe  assay. 
Sorting. — Separating  valuable  from  worthless  material.  „ . , 

Sounding.— (1)  Knocking  on  a roof  to  see  whether  it  is  sound  ^fe  to  work 
under.  (2)  Rapping  on  a pillar  so  that  a person  on  the  other  side  of  it 
may  be  signaled  to,  or  to  enable  him  to  estimate  its  width.  „ 

S0u\—{  1)  A tool  used  for  sharpening  drills.  (2)  Iron  deposits  at  the  bottom 

Spall. — To  break  up  rocks  with  a large  hammer,  for  hand  sorting. 

Spalls.— The  chips' and  other  waste  material  cut  from  a block  of  stone  in 

Spnr!-An\m/gfve™to  certain  white  quartz-like  minerals,  e.  g„  calcspar, 
feldspar,  fluorspar. 

Spears. — Pump-rods. 

I^rbal^fdeo'r  anttmonide  of  iron,  often  containing  nickek 
P cobalt,  lead,  bismuth,  copper,  etc.,  having  a metallic  luster  of  high 
specific  gravity  and  a strong  tendency  tow  ard  crystallization. 

but  has  not  done  its  work, 

Spew  —The  extension  of  mineral  matter  on  the  surface,  past  the  ordinary 
limits  of  the  lode. 

Spiders—  See  Drum  Rings. 

Svieaeleisen.— Manganiferous  white  cast  iron.  ...  „ 

Spiking  Curbs.— A light  ring  of  wood  to  which  planks  are  spiked  when 

plank  tubbing  is  used. 


Spi  GLOSSARY.  Sta  613 


Spiles  (Cornish).— A temporary  lagging  driven  ahead  on  levels  in  loose 
ground.  Short  pieces  of  planking  sharpened  flatways,  and  used  for 
driving  into  watery  strata  as  sheath  piling,  to  assist  in  checking  the 
flow;  used  much  in  sinking  through  quicksands. 

Spiling—  A process  of  timbering  through  soft  ground. 

Spiral  brum.— See  Conical  Brum. 

Splint , or  Splent  — A laminated,  coarse,  inferior,  dull-looking,  hard  coal,  pro- 
ducing much  white  ash,  intermediate  between  cannel  and  bituminous 
coal. 

Split.— (1)  To  divide  an  air-current  into  two  or  more  separate  currents.  (2) 
Any  division  or  branch  of  the  ventilating  current.  (3)  The  workings 
ventilated  by  that  branch.  (4)  Any  member  of  a,  coal  bed  split  by  thick 
partings  into  two  or  more  seams.  (5)  A bench  separated  by  a consider- 
able interval  from  the  other  benches  of  a coal  bed. 

Spoil.— D6bris  from  a coal  mine. 

Spoon. — A slender  iron  rod  with  a cup-shaped  projection  at  right  angles  to 
the  rod,  used  for  scraping  drillings  out  of  a bore  hole. 

Spout.— A short  underground  passage  connecting  a main  road  with  an  air- 
course. 

Sprag.— (1)  A short  wooden  prop  set  in  a slanting  position  for  keeping  up 
the  coal  during  the  operation  of  holing.  (2)  A short  round  piece  of  hard 
wood,  pointed  at  both  ends,  to  act  as  a brake  when  placed  between  the 
spokes  of  mine-car  wheels.  (3)  The  horizontal  member  of  a square  set 
of  timber  running  longitudinally  with  the  deposit. 

Spragger.— One  who  attends  to  the  spragging  of  cars. 

Sprag  Road— A mine  road  having  such  a sharp  grade  that  sprags  are  needed 
to  control  the  speed  of  the  car. 

Spreader.— A timber  stretched  across  a shaft  or  stope. 

Spring  Beams.— Two  short  parallel  timber  beams,  built  with  a Cornish  pump- 
ing engine  house,  nearly  on  a level  with  the  engine  beam,  for  catching 
the  beam,  etc.,  and  preventing  a smash  in  case  of  a breakdown. 

Spring  Latch—  The  latch  or  tongue  of  an  automatic  switch,  operated  by  a 
spring  pole  at  the  side  of  the  track. 

Spring  Pole— An  elastic  wooden  pole  from  which  boring  rods  are  suspended. 
Used  also  to  operate  a spring  latch. 

Sprocket  Wheel  (English).— Rag  wheel.  A wheel  with  teeth  or  pins  which 
catch  in  the  links  of  a chain. 

Spud,  Spad.—A  horseshoe  nail  with  a hole  in  the  head,  for  driving  into  the 
mine  timbers,  or  into  a wooden  plug  fitted  into  the  roof,  to  mark  a sur- 
veying station. 

Spur.—(  1)  A short  ridge  or  offsetting  pointed  branch  from  a main  ridge  or 
mountain.  (2)  A short  branch  or  feeder  from  the  main  lode  of  a vein. 

Square  Set— A variety  of  timbering  for  large  excavations. 

Squat  (Cornish).— Tin  ore  mixed  with  spar. 

Squeeze— See  Creep. 

Squib. — A straw,  rush,  paper,  or  quill  tube  filled  with  a priming  of  gun- 
powder, with  a slow  match  on  one  end. 

Stage. — A platform  on  which  mine  cars  stand. 

Staging. — A temporary  flooring  or  scaffold,  or  platform. 

Stage  Pumping—  Draining  a mine  by  means  of  two  or  more  pumps  placed  at 
different  levels,  each  of  which  raises  the  water  to  the  next  pump  above, 
or  to  the  surface. 

Stage  Working. — A system  of  working  minerals  by  removing  the  strata  above 
the  beds,  after  which  the  various  beds  are  removed  in  steps  or  stages. 

Stalactites.— Icicle-shaped  formations  of  mineral  matter  depending  from  roof 
strata. 

Stalagmites.— Accumulations  of  mineral  matter  that  form  on  the  floor,  caused 
by  the  continual  dripping  of  water  impregnated  with  mineral  matter. 

Stall.— A narrow  breast,  or  chamber. 

Stall  Gate— A road  along  which  the  mineral  worked  in  a stall  is  conveyed  to 
the  main  road. 

Stamp  Mill , Stomps. —Machine  for  crushing  ore. 

Stanchion. — A vertical  prop  or  strut. 

Standage. — Pump  reservoir. 

Standing. — Not  at  work,  not  going  forwards,  idle. 

Standing  Gas.— A body  of  firedamp  known  to  exist  in  a mine,  but  not  in  cir- 
culation; sometimes  fenced  off. 

Standing  Sett  (English).— A fixed  lift  of  pumps  in  a sinking  set. 


614 


Sta 


GLOSSARY. 


STO 


^taple^—{ 1)  ^shallow  pit  within  a mine.  (2)  An  underground  shaft. 

Starter. — A man  who  ascends  a chute  to  the  battery  and  starts  the  coal  to 

Starved  (English), -When  a pump  is  choked  at  the  brass  holes. 

Station.— A plat  or  convenient  resting  place  in  a shaft  or  level. 

Stavi  Englfsh). — Props,  struts,  or  ties  for  keeping  anything  in  its  place. 
Steamboat  Coal.- In  anthracite  only,  coal  small  enough  to  pass  through  bars 
set  6 to  8 in.  apart,  but  too  large  to  pass  through  bars  from  3 9 to  5 in. 
Comparatively  few  collieries  make  steamboat  coal  except  to  fill  special 
contracts  or  orders.  . . 

Steam  Coal.— A hard,  free-burning,  non-caking  coal.  - 

Steam  Jet.— A system  of  ventilating  a mine  by  means  of  a number  °f  jets  of 
steam,  at  high  pressure,  kept  constantly  blowing  off  from  a series  of  pipes 
in  the  bottom  of  the  upcast  shaft.  . • 

Steel  Mill An  apparatus  for  obtaining  light  in  a fiery  mine.  It  consisted  of 

a reviving  steel  wheel,  to  which  a piece  of  flint  was  held,  to  produce 

Steel^Needlef—  An  instrument  used  in  preparing  blasting  holes,  before  the 
safety  fuse  was  invented. 

Steening.  ot  Steining.— The  brick  or  stone  lining  of  a shaft. 

stpmmer A copper  or  wooden  bar  used  for  stemming.  , 

Stemming  —(1)  Fine  shale  or  dirt  put  into  a shot  hole  after  the  powder,  and 
rammed  hard.  (2)  Tamping  a shot.  . . .,  . . __ 

Stev  (English)  —(1)  The  cavity  in  a piece  for  receiving  the  pivot  of  an 
uprifht  sLft,  or  the  end  of  an  upright  piece.  (2)  The  shearing  m a 

Stird^ The  amount  of  work  to  be  done  by  a man  in  a specified  time. 

Stobb. A lqng  steel  wedge  used  in  bringing  down  coal  after  it  has  been 

Sioctoort'-A  rock  run  through  with  a number  of  small  veins  close 
together,  the  whole  of  which  has  to  be  worked  when  mining  such 

Stonfp.  - A ‘short  wooden  plug  fixed  in  the  roof  of  a level,  to  serve  as  a bench 
mark  for  surveys.  , . ..  v , 

Stone  Coal. — Anthracite ; also  other  hard  varieties  of  coal. 

TTpnd A heading^  or  gangway  driven  m stone.  A tunnel.  ... 

Stone  Tubbing. — Water-tight  stone  walling  of  a shaft  cemented  at  the 

Stoo Jb-A  pillar  of  coal  about  4 yd.  square  being  the  last  portion  of  a full- 

sized  pillar  to  be  worked  away  in  bord-and-pillar  workings. 

Stook-and-Feather.—A  wedge  for  breaking  down  coal,  worked  by  hydraulic 
power,  the  pressure  being  applied  at  the  extreme  inner  end  of  t e 
drilled  hole. 

itoo?-a7id-Soom.— ^system  of  working  coal  very  similar  to  pillar-and-stall. 
Stop!—  Any  cleat  or  beam  to  check  the  descent  of  a cage,  car,  pu^  rods^e  ^ 
Stope. (1)  To  excavate  mineral  m a series  of  steps.  (2)  A place  in  a mine 

Stop^.—WoCkh^  out  ore  between  two  levels  or  on  the 

steps.  Stoping  Overhand.— Mining  a stope  upwards,  the  flight  of  steps 
being  inverted.  Stoping  Underhand— Mining  a stope  in 

such  a series  that  it  presents  the  appearance  of  a flight  of  steps. 
Stovvinq.— An  air-tight  wall  built  across  any  passageway  in  a mine. 

Stove  Coal. — In  anthracite  only;  two  sizes  of  to1 2^mesh 

lar^e  stove,  known  as  No.  3,  passes  through  a z4  to  z mesn 
and  over  all"  to  1£"  mesh;  small  stove,  known  as  No.  4,  passes  through 
a to  1-"  mesh  and  over  a l\"  to  1"  mesh.  Only  one  size  of  stove  coal 
fs^ow  usually  made.  It  passes  through  a 2"  square  mesh  and  over  H" 

Stov%»roriOTed.-Upset.  When  a rod  of  iron  heated  at  one  end  is  ham- 
mered  endwise  the  diameter  of  that  end  is  enlarged,  and  it  is  said  to  be 

Stow.— To  pack  away  rubbish  into  goaves  or  old  workings. 

Th^  tack  of  a miner  and  which  supports 

the  roof  or  hanging  wall  of  the  excavation. 


I 


GLOSSARY. 


Swi 


615 


Str 


Straight  Ends  and  Walls.— A system  of  working  coal  somewhat  similar  to 
bord-and-pillar.  Straight  ends  are  headings  from  4 ft.  6 in.  to  6 ft.  in 
width.  Walls  are  pillars  30  ft.  wide. 

Straight  Work.— A system  of  getting  coal  by  headings  or  narrow  work. 

Strake.— A slightly  inclined  table  for  separating  heavier  minerals  from 
lighter  ones. 

Stratification.— Arrangement  in  layers. 

Stratum  (plural,  strata).— A layer  or  bed  of  rocks,  or  other  deposit. 

Streak.— The  color  of  the  mark  made  when  a mineral  is  scratched  against  a 
white  surface.  ' 

Strett.— The  system  of  getting  coal  by  headings  or  narrow  work.  See 
Bor  d-and- Pillar. 

Strike  (of  a seam  or  vein).— The  intersection  of  an  inclined  seam  or  a vein 
with  a horizontal  plane.  A level  course  in  the  seam.  The  direction  of 
strike  is  always  at  right  angles  to  the  direction  of  the  dip  of  the  seam. 

Strike  Joints—  Joints  or  cleavages  that  are  parallel  to  the  strike  of  the  seam. 

Striking  Deal.— Planks  fixed  in  a sloping  direction  just  within  the  mouth  of 
a shaft,  to  guide  the  tub  to  the  surface. 

Stringer  (English).— Any  longitudinal  timber  or  beam. 

Stringpump.—A  system' of  pumping  whereby  the  motion  of  the  engine  is 
transmitted  to  the  pump  by  timbers  or  stringers  bolted  together. 

String  Rods —A  line  of  surface  rods  connected  rigidly  for  the  transmission 
of  power;  used  for  operating  small  pumps  in  adjoining  shafts  from  a 
central  station. 

Strip.— (1)  To  remove  the  overlying  strata  of  a bed  or  vein.  (2)  Mining  a 
deposit  by  first  taking  off  the  overlying  material. 

Strut  {English). —A  prop  to  sustain  compression,  whether  vertical  or  inclined. 

Struve  Ventilator. — A pneumatic  ventilating  apparatus  consisting  of  two 
vessel-like  gas  holders,  which  are  moved  up  and  down  in  a tank  of 
water.  By  this  means,  the  air  is  sucked  out  of  the  mine  as  required. 

Studdle.—A  piece  of  squared  timber  placed  vertically  between  two  sets  of 
timber  in  a shaft. 

Stull.— A post  for  supporting  the  wall  or  roof  in  a mine;  a prop  timber. 

Stump.— The  pillar  between  the  gangway  and  each  room  turned  off  the  gang- 
way. Sometimes  the  entry  pillars  are  called  stumps. 

Stumping. — A kind  of  pillar-and-stall  plan  of  getting  coal. 

Stup. — Powdered  coke  or  coal  mixed  with  clay. 

Sturt.— A tribute  bargain  profitable  to  the  miner. 

Stuttle,  or  Sprag. — The  horizontal  member  of  a square  set  of  timber  running 
longitudinally  with  the  deposit. 

Stythe. — Carbonic-acid  gas  (blackdamp). 

Sucker  Rod. — The  pump  rod  of  an  oil  or  artesian  well. 

Suction  Pump  (English).— A pump  wherein,  by  the  movement  of  the  piston, 
water  is  drawn  up  into  the  vacuum  caused. 

Sulphur.— { 1)  One  of  the  elements.  (2)  Iron  pyrites. 

Sulphuret. — See  Sulphide. 

Sulphide. — A combination  of  sulphur  and  a base. 

Sump,  or  Sumpt. — A catch  basin  into  which  the  drainage  of  a mine  flows  and 
from  which  it  is  pumped  to  the  surface. 

Surface  Deposits.— Those  that  are  exposed  and  can  be  mined  from  the  surface. 

Swab  Stick. — A short  wooden  rod,  bruised  into  a kind  of  stumpy  brush  at  one 
end,  for  cleaning  out  a drill  hole. 

Swally,  or  Swelly.—A  trough,  or  syncline,  in  a coal  seam. 

Swamp —A  depression  or  natural  hollow  in  a seam.  A basin. 

Sweeping  Table.— A stationary  buddle. 

Sweet—  Free  from  deleterious  gases. 

Sweet  Roast—  To  roast  dead  or  completely. 

Swing.— The  arc  or  curve  described  by  the  point  of  an  instrument,  such  as  a 
pick  or  hammer,  when  being  used. 

Swinging  Plate. —Amalgamated  copper  plates  hung  in  sluices,  to  catch  float 
gold. 

Switch—  (1)  The  movable  tongue  or  rail  by  which  a train  is  diverted  from 
one  track  to  another.  (2)  The  junction  of  two  tracks.  (3)  A movable 
arm  for  changing  the  course  of  an  electrical  current. 

Switchboard.— A board  where  several  electrical  wires  terminate,  and  where, 
by  means  of  switches,  connection  may  be  established  between  any  of 
these  wires  and  the  main  wire. 

Swither.—A  crevice  branching  from  a main-lead  lode. 


616 


Syn 


GLOSSARY. 


Tee 


Sfw nrh’nal  Axis  — The  line  or  course  of  a syncline.  ... 

Syncline  —The  point  or  axis  of  a basin  toward  which  the  strata  upon  either 
‘ side  dip.  An  inverted  anticline.  , A basin. 

Tarkle  (English)  —(1)  Ropes,  chain,  detaching  hooks,  cages,  and  all  other 
appamtus  for  raising  coal  or  ore  in  shafts.  (2)  Any  rope  for  hoisting,  as 

Ta/ion^^eScan^— An  arrastre  moved  by  water-power.  Tahonero.—' The 

rail^alk^When  the  firedamp  ignites  and  the  flame  is  elongated  or  creeps 
backwards  against  the  current  of  air,  it  is  said  to  tail-bacx. 

d etritus  from  reduction  or  gold-washing  machinery. 

flows  after  it  has  done  its  work 

Tail-Rope  — (1)  In  a tail-rope  system  of  haulage,  the  rope  that  is  used l to 
draw  the  empties  back  into  the  mine.  (2)  A wire  rope  attached  beneath 

TaU-^o^e  Haulage —A  haulage  system  in  which  the  fulltnpis 

drawn  out  by  the  main  rope,  and  the  empty  trip  is  drawn  m by  the  tail- 
rope,  these  ropes  being  attached  to  the  opposite  ends  of  the  trip  (see 

TaiLShmve0- The  sheave  at  the  inbye  end  of  any  haulage  system.  See  Turn 

TaketheVAir.-(l)  To  measure  the  ventilating  current.  (2)  Applied  to  a 
ventilating  fan  as  working  well,  or  working  poorly.  . _ 

Taladn)  (Mexican)  .—A  drill  for  mechanical  or  mining  purposes.  Taladrar .. 

Talhi ^bmeArrnark  or  number  placed  by  the  miner  on  every  car  of  coal  sent 
2 out  of  Ms  place  usually  a tin  ticket.  By  counting  these,  a tally  is  made 
of  all  th(f (Eireof  coaf he  sends  out.  (2)  Any  numbering,  or  counting,  or 

TaT/S^T^fil^^bor ea holef  after  inserting  the  charge,  with  some  substance 
Thich  is  rammed  hard  ’as  it  is  put  into  the  hole  Vertical  holes  are  often 
tamped  with  water,  when  blasting  with  dynamite. 

Tamnina  —The  process  of  stemming  or  filling  a bore  hole.  . 

Taping  Bar.-A  copper-tipped  bar,  for  ramming  the  tamping  or  stem- 

Tanafesf  Mexican) . — Leather,  hide,  or  jute  bags,  to  carry  ore  or  waste  rock 
within  or  out  of  a mine.  Tanatero.— A laborer  or  bag  c^I™r- 
Tap  —(1)  To  cut  or  bore  into  old  workings,  for  the  purpose  of liberating  accu- 
Emulations  of  gas  or  water.  (2)  To  pierce  or  open  any  gas  or  water 
feeder  (3)  To  win  coal  in  a new  district.  . „ 

Tnneytle  (Mexican)  —A  working  platform  or  stage  built  up  in  a stope  or  any- 
in  Srie;  a landing  place  between  two  flights  of  ladders. 

TeZiHj' Tro«grft°-APtrougli  into  which  the  water  from  a mine  is  pumped 
rSapft  -Asheetdron  trough-shaped  chute,  for  conveying  coal  or  slate 

goM)  containing  tellurium. 

Temesquitale  (Mexican).— The  earthy  part  of  ground-up  ore. 

Temner—  (1)  To  change  the  hardness  of  metals  by  first  beating  aim  tnen 
plunging  them  into  water,  oil,  etc.  (2)  To  mix  mortar,  or  to  prepare 

The  actlf  reheating  and  properly  cooling  a bar  of  metal  to  any 
to  rope^riUing,  a screw  for  gradually  lowering  the  clamped 
TenonV— A 'pro^cttog^ongue8 fitting  into  a corresponding  cavity  called  a 

white  emd^ Siallo w^ssS^rf6 any  kin^^to^certa^n^e^amimnt^of 

metallic  portions  of  any  mineral,  and  to  cause  the  earthy  portions  to  be 

TepdSeAM exi can)  .—An y rock  or  earth  found  in  a mine,  which  does  not 
contain  the  metal  sought  for. 


Teq 


GLOSSARY. 


Tea 


617 


Tequio  (Mexican).— A task  set  for  a drillman  or  for  any  laborer  in  a mine,  to 
be  regarded  as  a day’s  work. 

Terrace—  A raised  level  bank,  such  as  river  terraces,  lake  terraces,  etc. 

Terrero  (Mexican).— The  dump  of  a mihe. 

Test.— (1)  A trial  of  an  engine,  fan,  or  other  appliance  or  substance.  (2)  An 
iron  framework  that  is  filled  with  bone  ash  for  cupeling  on  a large  scale. 

Theodolite—  An  instrument  used  in  surveying,  for  taking  both  vertical  and 
horizontal  angular  measurements.  An  engineer’s  large  transit,  with 
attachments. 

Thill.— See  Floor. 

Thimble—  (1)  A short  piece  of  tube  slid  over  another  piece,  to  strengthen  a 
joint,  etc.  (2)  An  iron  ring  with  a groove  around  it  on  the  outside,  used 
as  an  eye  when  a rope  is  doubled  about  it. 

Thirl.— See  Crosscut. 

T hr ough-and-  Through.— A system  of  getting  bituminous  coal,  without  regard 
to  the  size  of  the  lump. 

Throw.— (1)  A fault  of  dislocation.  (2)  The  vertical  distance  between  the 
two  ends  of  a faulted  bed  of  coal. 

Thrown—  Faulted;  broken  by  a fault. 

Thrust—  Creep  or  squeeze  due  to  excessive  weight,  hard  floor,  and  too 
small  pillars. 

Thurl  (Staffordshire).— To  cut  through  from  one  working  into  another. 

Ticketing—  English  periodical  markets  for  the  sale  of  ores. 

Tie-Back.— ( 1)  A beam  serving  a purpose  similar  to  a fend-off  beam,  but 
fixed  at  the  opposite  side  of  the  shaft  or  inclined  road.  (2)  The  wire 
ropes  or  stayrods  which  are  sometimes  used  on  the  side  of  the  tower 
opposite  the  hoisting  engine,  in  place  of  or  to  reenforce  the  engine 
braces. 

Tierras  (Spanish).— Earth  impregnated  with  mercury  ore. 

T terras  de  Labor  (Mexican). — Dirt  from  a stope,  mixed  with  particles  of  ore. 

Tierras  de  Llunque  (Mexican).— Chips  made  in  breaking  and  sorting  ore. 

Tiff. — Calcite  or  carbonate  of  lime. 

Timber—  (1)  Props,  bars,  collars,  legs,  laggings,  etc.  (2)  To  set  or  place 
timber  in  a mine  or  shaft. 

Timberer,  Timberman.—A  man  who  sets  timber. 

Time.— (1)  Hours  of  work  performed  by  workmen.  (2)  To  count  the 
strokes  of  a pump  or  revolutions  of  an  engine  or  fan. 

Tin-Can  Safety  Lamp.— A Davy  lamp  placed  inside  a tin  can  or  cylinder 
having  a glass  in  front,  air  holes  near  the  bottom,  and  open-topped, 
making  the  lamp  safer  in  a rapid  current  of  air. 

Tin- Witts  (Cornish).— Product  of  first  dressing  of  tin  ores,  containing,  also, 
wolfram  and  sulphides. 

Tip.— A dump.  See  Tipper , or  Tipple. 

Tipper , or  Tipple— An  apparatus  for  emptying  cars  of  coal  or  ore,  by  turning 
them  upside  down,  and  then  bringing  them  back  to  original  position, 
with  a minimum  of  manual  labor. 

Tipple—  The  dump  trestle  and  tracks  at  the  mouth  of  a shaft  or  slope,  where 
the  output  of  a mine  is  dumped,  screened,  and  loaded. 

Tiro  (Mexican).— A mining  shaft.  Tiro  Vertical.— A vertical  shaft. 

Token.— (1)  A mutually  understood  mark  placed  upon  a bucket  of  ore  when 
it  is  hoisted  or  lowered  into  a shaft,  to  acquaint  the  lander  or  filler  of 
some  important  matter.  (2)  A piece  of  leather  or  metal  stamped  with 
the  hewer’s  or  putter’s  number  or  distinctive  mark,  and  fastened  to  the 
tub  he  is  filling  or  putting. 

Ton.— A measure  of  weight.  Long  ton  is  2,240  lb.;  short  ton  is  2,000  lb.; 
metric  ton  is  1,000  kilograms  = 2,204.6  lb. 

Top.— (1)  See  Roof.  (2)  Top  of  a shaft;  surface  over  a mine. 

Topit. — A kind  of  brace  head  screwed  to  the  top  of  boring  rods,  when  with- 
drawing them  from  the  hole. 

Torta  (Mexican).— A pie  or  cake;  the  heaps  of  argentiferous  mud  that  are 
treated  in  the  patio  process  of  amalgamation. 

Tossing—  Shaking  powdered  ore  in  water,  to  effect  separation  of  heavy  and 
light  particles. 

Tovera  (Mexican).— The  tuyere  of  a smelting  furnace. 

Track.— Railways  or  tramways. 

Tracking—  Wooden  rails. 

Train  Boy.— A boy  that  rides  on  a trip,  to  attend  to  rope  attachments,  signal 
in  case  of  derailment  of  cars,  etc.  Trip  rider. 


618 


Tra 


GLOSSARY. 


Tum 


Train  or  Trip.— The  cars  taken  at  one  time  by  mules,  or  by  any  motor,  oi 
run  at  one  time  on  a slope,  plane,  or  sprag  road,  always  together. 

Tram—  A mine  car,  or  the  track  on  which  it  runs. 

Trammer.— One  who  pushes  cars  along  the  track. 

Tramroad. — A mine  track  or  railroad.  . 

Tram’  Rone. — A hauling  rope,  to  which  the  cars  are  attached  by  a clip  or 
chain,  either  singly  or  in  trips.  . 

Tramway— A small,  roughly  constructed  iron  track  for  running  wagons  or 

Transfer  Carriage. — Movable  platform  or  truck  used  to  transfer  mine  cars 
from  one  track  to  another.  .... 

Transome  ( English ) —A  heavy  wooden  bed  or  supporting  piece. 

Trap —( 1)  A steep  heading  along  which  men  travel.  (2)  A fault  of  dislo- 
cation. (3)  An  eruptive  rock.  (4)  A dangerous  place. 

Tran  Door. — A small  door,  kept  locked,  fixed  in  a stopmg,  for  giving  access 
to  firemen  and  certain  others  to  the  return  airways,  dams,  or  other 
unused  portions  of  the  mine.  . - . . . 

Tran  Dike— A fault  (not  necessarily  accompanied  by  displacement  of  strata) 
m which  the  spaces  between  the  fractured  edges  of  the  beds  are  filled  up 
bv  a thick  wall  of  igneous  rock. 

Trapiche  (Spanish).— A primitive  grinding  mill 

Trapper.—  A boy  employed  underground  to  tend  doors. 

Traveling  Road. — An  underground  passage  or  way  used  expressly,  though 
not  always  exclusively,  for  men  to  travel  along  to  and  from  their  work- 

TreenaiF— Along  wooden  pin  for  securing  planks  or  beams  together. 

TrdooUng  (Cornish).— Stirring  tin  slimes  in  water. 

Trend.— The  course  of  a vein,  fault,  or  other  feature. 

Tribute. — A method  of  working  mines  by  contract,  whereby  the  miners 
receive  a certain  share  of  the  products  won.  Tribute)  s.  Miners  paid 
bv  results. 

Trig. — A sprag  used  to  block  or  stop  a wheel  or  any  machinery. 

Tritta  (Mexican). — The  same  as  Torta.  . 

Trip  —The  mine  cars  in  one  train  or  set.  See  Train.  ^ Txnrnl1o1 

Triple-Entry  System.— A system  of  opening  a mine  by  driving  three  parallel 
entries  for  the  main  entries. 

Triturate.— To  grind  or  pulverize.  , „ . , , , 

Trolley. -{1)  A small  four-wheeled  truck,  used  for  carrying  the  ore  bucket 
underground.  (2)  An  electric  motor.  (3)  The sarm  of  a motor  ^ con- 
ducts the  electric  current  from  the  wire  above  the  track  to  the  machine. 

Trommel. — A drum,  consisting  of  a cylinder-  or  cone-shaped  sheet-iron 
mantle  (generally  punched  with  holes)  that  revolves;  used  for  washing 

Trmnpal Mefican)  — A funnel-shaped  mouthpiece  of  cooled  slag  that  forms 
within  a smelting  furnace  over  the  tuyere  opemng. 

Trompe. — An  apparatus  for  producing  ventilation  by  the  fall  of  water  down 

SL  slldift 

Trouble. — A dislocation  or  fault;  any  irregularity  in  the  bed. 

Trouah  Fault.— A wedge-shaped  fault,  or,  more  correctly,  a mass  of  rock, 
coal  etc.  let  down  in  between  two  faults,  which  faults,  however,  are 

through  a pillar  to  connect  two  rooms. 

Truck. — Used  svnonymously  with  Barney. 

Truck  System. — Paying  miners  in  food  instead  of  money. 

Trunnions. — Cylindrical  projections  or  journals,  attached  to  the  sides  of 
a vessel,  so  that  it  can  rotate  in  a vertical  plane. 

Truing  the  Lamp— The  examination  of  the  flame  of  a safety  lamp  for  tne 
purpose  of  forming  a judgment  as  to  the  quantity  of  firedamp  mi  ed 

Tulh—O.)*  A6  mine  car.  (2)  An  iron  or  wooden  barrel  used  in  a shaft,  for 

TuWi^—cSt iron,  and  sometimes  timber,  lining  or  walling  of  a circular 
Wedges.— Small  wooden  wedges  hammered  between  the  joints  of 

TuMn^.— 1 Iron  pipes  or  tubes  used  for  lining  bore  holes,  to  prevent  caving. 

Tumbar  (Mexican).— To  knock  down  ore.  etc. 

Tumbe{  Mexican).— The  act  of  knocking  down  and  taking  out  ore. 


Tun 


GLOSSARY. 


Yen 


619 


Tunnel.— A.  horizontal  passage  driven  across  the  measures  and  open  to  day  at 
both  ends;  applied  also  to  such  passages  open  to  day  at  only  one  end,  or 
not  open  to  day  at  either  end. 

Turbary.— A peat  bog. 

Turbine.— A rapidly  revolving  waterwheel,  impelled  by  the  pressure  of  water 
upon  blades. 

Turn.— (1)  The  hours  during  which  coal,  etc.  is  being  raised  from  the  mine. 
(2)  See  Shift.  (3)  To  open  rooms,  headings,  or  chutes  off  from  an  entry 
or  gangway.  (4)  The  number  of  cars  allowed  each  miner. 

Turnout— A siding  or  passing  on  any  tram  or  haulage  road. 

Turn  Pulley.— A sheave  fixed  at  the  inside  end  of  an  endless-  or  tail-rope 
hauling  plane,  around  which  the  rope  returns.  See  Tail-Sheave. 

Turntable.— A revolving  platform  on  which  cars  or  locomotives  are  turned 
around. 

Tut  Work. — Breaking  ground  at  so  much  per  foot  or  fathom. 

Tuyere—  The  tubes  through  which  air  is  forced  into  a furnace.  • 

Two-Throw.— When,  in  sinking,  a depth  of  about  12  ft.  has  been  reached,  and 
the  debris  has  to  be  raised  to  the  surface  by  two  lifts  or  throws  with  the 
shovel,  one  man  working  on  staging  above  another. 

Tye.— An  inclined  table  used  for  dressing  ores. 

Unconformability.— When  one  layer  of  rock,  resting  on  another  layer,  does  not 
correspond  in  its  angle  of  bedding. 

Undercast. — An  air-course  carried  under  another  air-course  or  roadway. 

Underclay.— A bed  of  fireclay  or  other  less  clayey  stratum,  lying  immediately 
beneath  a seam  of  coal. 

Undercut— To  remove  a small  portion  of  the  bottom  of  the  bed  or  the  under- 
clay, so  that  the  mass  of  coal  or  mineral  can  be  wedged  or  blasted  down. 

Underhand  Stoping. — See  Stoping  Underhand. 

Underhand  Work. — Picking  or  drilling  downwards. 

Underholing , Undermining.— To  mine  out  a portion  of  the  bottom  of  a seam 
or  the  underclay,  by  pick  or  powder,  thus  leaving  the  top  unsupported 
and  ready  to  be  blown  down  by  shots,  broken  down  by  wedges,  or  mined 
with  a pick  or  bar. 

Underlie , or  Underlay. — The  inclination  of  a lode  at  right  angles  to  its  course, 
or  strike;  the  true  dip. 

Underviewer,  or  Underlooker.— An  inside  foreman. 

Unit.—{  1)  The  unit  of  metals  is  1$  of  whatever  ton  is  used.  Generally,  the 
20-cwt.  ton,  equal  to  2,240  lb.,  is  employed,  but,  when  dealing  with 
copper  ores,  the  21-cwt.  ton  of  2,352  lb.  is  taken;  therefore,  the  respective 
units  are  22.4  lb.  and  23.52  lb.  (F.  Danvers  Powers).  (2)  Ores  are  quoted 
at  a certain  price  per  unit  or  per  cent,  of  valuable  material  in  the  ore. 
If  an  iron  ore  contains  40^  of  metallic  iron  that  is  worth  5 cents  per  unit, 
the  value  of  the  ore  is  $2  per  ton. 

Unwater.— To  drain  or  pump  the  water  from  a mine,  or  shaft. 

Upcast.— The  shaft  through  which  the  return  air  ascends. 

Upraise. — An  auxiliary  shaft,  a mill  hole,  or  heading  carried  from  one  level 
up  toward  another. 

Upthrow.— A fault  in  which  the  displacement  has  been  upward. 

Vapor  (Mexican).— Steam;  heated  and  stinking  gas  sometimes  found  in 
mines,  which  causes  candles  to  burn  dimly  and  go  out. 

Vaso  (Mexican).— A reverberatory  furnace  used  for  smelting  rich  ore,  or  for 
cupeling  silver. 

Vat.— Large  wooden  tub  used  for  leaching  or  precipitation. 

Vein.— See  Lode.  Often  applied  incorrectly  to  a seam  or  bed  of  coal  or  other 
mineral. 

Veinstone. — The  non-metallic  portion  of  a vein  associated  with  the  ore. 

Vena  (Mexican).— A thin  vein,  not  over  3 in.  thick— a knife-blade  vein. 

Vend  (North  of  England).— Total  sales  of  coal  from  a mine. 

Vent,  or  Vent  Hole. — (1)  A small  passage  made  with  a needle  through  the 
tamping,  which  is  used  for  admitting  a squib,  to  enable  the  charge  to  be 
lighted.  (2)  Any  opening  made  into  a confined  space. 

Ventilating  Column.— See  Motive  Column. 

Ventilating  Pressure— The  total  pressure  or  force  required  to  overcome  the 
friction  of  the  air  in  mines;  the  unit  of  ventilating  pressure  or  pressure 
per  sq.  ft.  of  area  multiplied  by  the  area  of  the  airway. 

Ventilation. — Circulation.  The  atmospheric  air  circulating  in  a mine. 


620 


Yen 


GLOSSARY. 


Wat 


Ventilator.— Any  means  or  apparatus  for  producing  a current  of  air  in  mine 
or  other  airways. 

of  rock;  a true  fissure  vein  Loosely, 

direction  or  course.  Veta  Soda. — A vein  that  joins  another.  1 eta  Ramal. 
—A  branch  vein.  Veta  Recostada.— An  inclined  vein.  . 

Viewer. — The  general  manager  or  mining  engineer  of  one  or  more  collieries, 
who  has  control  of  the  whole  of  the  underground  works,  and  also  gen- 
erally of  those  on  the  surface. 

when  all  impurities  have 

been  removed  from  the  silver  under  treatment. 

Vug,  or  Vugh  (Cornish).— A cavity  in  the  rock. 

'iVagon  Brea  ft— A ' breast  in  which  the  mine  cars  are  taken  up  to  the 
working  face.  „ „ 

Wailing. — Picking  stones  and  dirt  from  among  coals. 

Wale  (North  of  England).— Hand-dressing  coal. 

Walking  Beam.— See  Working  Beam. 

Wall.—(  1)  The  face  of  a long  wall  working  or  breast.  (2)  A nb  of  solid  coal 
between  two  breasts. 

Walling—  See  Steening.  . . .u 

Walling  Cribs—  Oak  cribs  or  curbs  upon  which  walling  is  built. 

Walling  Stage.— A movable  wooden  scaffold  suspended  from  a crab  °u  the 
surface,  upon  which  the  workmen  stand  when  walling  or  lining  a shaft. 

Wall  Plates.— The  two  longest  pieces  of  timber  in  a set  used  in  a rectan- 

Warners  — Apparatus  consisting  of  a variety  of  delicately  constructed 
machines^  actuated  by  chemical,  physical,  electrical  and 
properties,  for  indicating  the  presence  of  small  quantities  of  £redamp  m 
the  mines.  At  present,  most  of  these  ingenious  contrivances  are  more 
suited  to  the  laboratory  than  for  practical  application  underground. 

Warning  Lamp. — A safety  lamp  fitted  with  certain  delicate  apparatus,  for 
indicating  very  small  proportions  of  firedamp  in  the  atmosphere  of  a 
mine  As  small  a quantity  as  3$  can  be  determined  by  this  means. 

Wash—  Drift,  clay,  stones,  etc.  overlying  the  strata. 

wTs^Dirt— That  portion  of  alluvial  working  in  which  most  of  the  gold  is 

WashUFcwlt.— A portion  of  a seam  of  coal  replaced  by  shale  or  sandstone. 

Washing  Apparatus,  or  Washer  y.-(l)  Machinery  and  applianceserected  on 
the  surface  at  a colliery,  generally  in  c^nectmn  with  °vens,  for 
extracting,  by  washing  with  water,  the  impurities  mixed  with  the  coa^ 
dust  or  small  slack.  (2)  Machinery  for  removing  impurities  from  small 

Washout^- The^r^^  appreciable  extent  of  a coal  seam  by  aqueous 

Wash  PZace.— A place  where  the  ores  are  washed  and  separated  from  the 
waste,  usually  applied  to  places  where  the  hand  jigs  ap  used. 

Waste  — m See  Goaf.  (2)  Very  small  coal  or  slack.  (3)  The  portion  of  a 
mine  occupied  by  the  return  airways.  (4)  A1%^d  bo „d/?^ihge 
spaces  between  the  pack  walls  m the  gob  of  longwall  working.  (5)  Refuse 
material 

Waste  Gate  (English). — A door  for  regulating  discharge  of  surplus  water. 

Water  Blast.— The  sudden  escape  of  air  pent  up  in  rise  f ° ^ 

siderable  pressure  from  a head  of  water  that  has  accumulated  m a 

Wat^Cartridge.—A  waterproof  cartridge  surrounded  by  an  ou|er  case. 
The  snace  between  being  filled  with  water,  which  is  employed  to 
destroy  the  flame  produced  when  the  shot  is  fired,  thereby  lessens  the 
chance  of  an  explosion  should  gas  be  present  in  the  Place. 

Water  Gauge.— An  instrument  for  measuring  the  pressure  per  square  foot 

Water  JTammfr.— 1 Thlfhammering  noise  caused  by  the  intermittent  escape 
of  gas  through  water  in  pipes. 


Wat 


GLOSSARY. 


Won 


621 


Water-Jacket. — A jacket  filled  with  water,  to  keep  cool  a cylinder  or  furnace. 

Water  Level— An  underground  passage  or  heading  driven  very  nearly  dead 
level  or  with  sufficient  grade  only  to  drain  off  the  water. 

Water  Right. — The  privilege  of  taking  a certain  quantity  of  water  from  a 
watercourse. 

Watershed.— The  elevated  land  or  ridge  that  divides  drainage  areas. 

Waterwheel  (English).— Overshot,  undershot,  breast  wheels.  A wheel  pro- 
vided with  buckets,  which  is  set  in  motion  by  the  weight  or  impact  of  a 
stream  of  water. 

Weather. — To  crumble  by  exposure  to  the  atmosphere. 

Weather  Door— See  Trap  Door. 

Web.— The  face  of  a longwall  stall  in  course  of  being  holed  and  broken  down 
for  removal.  The  length  of  breast  or  face  brought  down  by  one  mining. 

Wedging.— The  material,  moss  or  wood,  used  to  render  the  shaft  lining 
tight. 

Wedging  Crib.— A curb  or  crib  of  wood  or  cast  iron  wedged  tightly  in  place 
and  packed,  in  order  to  form  a water-tight  joint  and  upon  which  tubbing 
is  built. 

Wedging  Down.— Breaking  down  the  coal  at  the  face  with  hammers  and 
wedges  instead  of  by  blasting. 

Weeldon.— Old  ironstone  workings. 

Weigh  Bridge  (English).— A platform  large  enough  to  carry  a wagon,  resting 
on  a series  of  levers,  by  means  of  which  heavy  bodies  are  weighed. 

Weize. — A band  or  ring  of  spun  yarn,  rope,  rubber,  lead,  etc.  put  in  between 
the  flanges  of  pipes  before  bolting  them  together,,  in  order  to  make  a 
water-tight  joint.  , „ 

Well.—(1)  The  well  of  a furnace  is  the  deepest  lying  portion  or  hollow  in 
which  the  metal  collects.  (2)  A sump,  or  a branch  from  the  sump. 

Whim,.— A winding  drum  worked  by  a horse. 

W.him  Shaft— A shaft  through  which  coal,  ore,  water,  etc.  are  raised  from  a 
mine  by  means  of  a whim. 

Whin. — A hard,  compact  rock. 

Whin  Dike.— A fault  or  fissure  filled  with  whin  and  the  debris  of  other 
rocks,  sometimes  accompanied  by  a dislocation  of  the  strata. 

Whip. — A hoisting  appliance  consisting  of  a pulley  supporting  the  hoisting 
rope  to  which  the  horse  is  directly  attached. 

W hitedamp . —Carbonic  oxide  (CO).  A gas  found  in  coal  mines,  generally 
where  ventilation  is  slack.  A product  of  slow  combustion  in  a limited 
supply  of  air.  It  burns  and  will  support  combustion.  It  is  extremely 
poisonous. 

White  Tin—  The  commercial  name  for  metallic  tin. 

Whits. See  Tin-  Witts. 

Whole  Working. — The  first  working  of  a seam,  which  divides  it  into  pillars. 

Wild  Lead. — Zinc-blende. 

Wild  Rock.— Anv  rock  not  fit  for  commercial  slate. 

Win.— To  sink  a'  shaft  or  slope,  or  drive  a drift  to  a workable  seam  of  mineral 
in  such  a manner  as  to  permit  its  being  successfully  worked. 

Winch , or  Windlass —A  hoisting  machine  consisting  of  a horizonal  drum 
operated  by  crank-arm  and  manual  labor. 

Wind  Bore  (England).— The  bottom  or  suction  pipe  of  a lift  of  pumps,  which 
has  suitable  brass  holes  or  perforations  for  suction  of  water  or  air. 

Wind  Gauge— An  anemometer,  for  testing  the  velocity  of  air  in  mines. 

Winding. — The  operation  of  raising  or  hauling  by  means  of  a steam  engine 
and  ropes,  the  product  of  a mine. 

Winding  Engines—  Hoisting  or  haulage  engines. 

Wind  Method.— A system  of  separating  coal  into  various  sizes,  and  extracting 
the  dirt  from  it,  whibh  in  principle  depends  on  the  specific  gravity  or 
size  of  the  coal  and  the  strength  of  the  current  of  air. 

Wind  Sail.—' Tim top  part  of  canvas  piping,  which  is  used  for  conveying  air 
down  shallow  shafts. 

Wing  Bore.— A side  or  flank  bore  hole. 

Wings. — See  Rests  and  Keeps. 

Winning.— A sinking  shaft,  a new  coal,  ironstone,  clay,  shale,  or  other  mine 
of  stratified  material.  A working  place  in  a mine. 

Winnowing  Gold. — Air-blowing.  Tossing  up  dry  powdered  auriferous  mate- 
rial in  the  air,  and  catching  the  heavier  particles  not  blown  away. 

Winze—  Interior  shaft  connecting  levels,  sometimes  used  as  an  ore  chute. 

ITon.— Proved,  sunk  to,  and  tested. 


622 


WOR 


GLOSSARY. 


ZON 


Work.-(  1)  To  mine.  (2)  Applied  to  mine  working  when  affected  by  squeeze 
or  creep. 

Workable—  Any  seam  that  can  be  profitably  mined.  : p 

Worked  Out— When  all  available  mineral  has  been  extracted  from  a mine,  it 

is  worked  out. 

Working. — Applied  to  mine  workings  when  squeezing. 

Wolunl  imm^fiEngHshb— ^beam^aving'a^ertieal  motion  on  a rock  shaft 
at ifs ceXr  onge  end  being  connected  with  the  piston  rod  and  the  othei 
with  a crank  or  pump  rod,  etc.  . 

Working  Cost— The  total  cost  of  producing  the  mineral. 

Working  Face—  See  Face.  , . frnm  thp 

Working  Home.— Getting  or  working  out  a seam  of  coal,  etc.,  from  the 
boundary  or  far  end  of  the  mine  toward  the  shaft  bottom. 

Working  on  Air—  A pump  works  on  air  when  air  is  sucked  up  wit 

Worting^but.— Working  outwards  or  in  the  direction  of  the  boundaries  ol 

WorUngFla^1.— The  actual  place  in  a mine  at  wliich  the  coal  is  being  mmed. 
Workings.— The  openings  of  a colliery,  including  all  roads,  ways,  levels, 
dips,  airways,  etc. 

Work  Lead—  Base  bullion,  silver  lead.  . . 

Wrought  Iron.— Iron  in  its  minimum  state  of  carburization. 

Wythern  (Wales). -Lode. 

Xacal  (Mexican).— A miner’s  cabin;  a storehouse  for  mining  goods;  a shaft 
house. 

pricns),'  paid  for  ?oads  of  certain  widths,  and  driven  in  certain  directions. 
Yellow  Ore  (Cornish).— Chalcopyrite. 

Yield— The  proportion  of  a seam  sent  to  market. 

7onp Tn  coal-mining  phraseology,  this  word  means  a certain  series  of  coal 

Z°neseams  wfthTheir IcSompanyifg  shales,  etc.,  which  eonmn  for  exampie 
much  firedamp,  called  a fiery  zone,  or,  if  much  water,  a watery  zone. 


INDEX 


Absolute  Pressure,  195,  345. 

temperature  and  pressure,  344, 345. 
Abuse  of  instruments,  80. 

Abutments  (dams),  154. 

Acceleration  in  jigging,  440. 

on  inclined  planes,  399. 

Acid  waters,  Pumps  for,  165. 

Acres  to  square  feet,  4. 

Adiabatic  compression,  195,  198. 
Adjustable  bars,  432. 

Adjustment  of  Burt’s  solar  attach- 
ment, 48. 
of  compass,  38. 
of  level,  53. 
of  transit,  41. 

Afterdamp,  351. 

Agonic  line  chart,  40. 

Air  and  mercury  columns,  347. 
brattice,  394. 
bridges,  393. 

columns  in  furnace  ventilation, 
384. 

Compressed,  194. 
compression,  Theory  of,  194. 
compression,  Horsepower  neces- 
sary for,  406. 

Air  compressors,  194. 

Classification  of,  194. 
Compound,  194. 

Construction  of,  194. 

Cooling,  195. 

Dry,  196. 

Duplex,  194. 

Horizontal,  cross-compound, 
194. 

Rating  of,  195. 

Simple,  194. 

Stage,  194. 

Straight-line,  194. 

Vertical,  194. 

Wet,  196. 

Air  currents,  Conducting,  393. 
currents,  Splitting  o£  373,  378. 
leaks,  186. 
lift  pumps,  164. 
required  for  ventilation,  362. 
transmission,  196. 

Airways,  Similar,  372. 

Alabama  method  of  mining,  297. 
Alternating  current,  217. 
current  dynamos,  224. 
current  motors,  226. 

Alternators,  225. 

Multiphase,  225,  226. 

Single-phase,  225. 

Three-phase,  226. 

Two-phase,  226. 

Altitude,  Effect  of,  on  air  compres- 
sion, 195. 

Aluminum,  Electric  properties  of, 
209. 


American  coals,  168. 
gauge  wire,  208. 
measures  of  area,  4. 
measures  of  length,  2. 
measures  of  volume,  5. 

Amount  crushed  by  rolls,  424. 
of  charge,  blasting,  331. 
of  gas  liberated  per  ton  of  coal, 352. 
Analyses  of  American  coals,  168. 
Analysis  of  coal,  173. 

Andre’s  formula  for  shaft  pillars,  285. 
Aneroid  barometer,  339. 

Angle  of  inertia,  398. 

of  rolling  friction,  398. 
reading,  45. 

Annunciator  system,  232. 

Anthracite  coal,  169. 

Cubic  feet  in  ton  of,  449. 
Handling,  443. 

Sizes,  of  434. 

Specific  gravity  of,  109. 
mining,  Costs  of,  323. 
mining  methods,  305. 

Percentages  of  different  sizes  of, 
323,  326. 

Preparation  of,  442. 
screens,  Duty  of,  434. 

Tests  of  compressive  strength  of, 
290. 

Apothecaries’  weight,  1. 

Appliances  in  mine  ventilation,  381. 
Arc,  Error  in,  76. 

lamps,  214. 

Area,  Measures  of,  4. 
of  circle,  31. 
of  ellipse,  32. 

of  largest  square  inscribed  in  a 
circle,  28. 

of  parallelogram,  28. 

of  polygons,  30. 

of  tract  of  land,  To  find,  52. 

of  trapezium,  30. 

of  trapezoid,  30. 

of  triangle,  28. 

Areas,  Calculation  of,  77. 

of  circles,  1 to  1,000,  Table  of,  545. 
of  circles,  to  100,  Table  of,  561. 
Arithmetic,  15. 

Arithmetical  progression,  20. 
Armature,  216. 

Arrangement  of  drill  holes,  244,  335. 
of  mine  plan,  381. 
of  slope  tracks,  413. 

Ascensional  ventilation,  381. 

Ash  (coal),  171. 

Ashworth  - Hepplewhite  - Gray  lamp, 
358. 

Asphyxiation,  451. 

Atmosphere,  Composition  of,  337. 

Weight  of.  337. 

Atmospheric  pressure,  339. 


INDEX . 


624 


Atom,  341. 

Atomic  volume,  341. 
weight,  344. 

Austrian  measures  of  length,  3. 
Avoirdupois  weight,  2. 


Back  of  Ore,  Caving  a,  320. 

Balancing  a conical  drum,  396. 

Ball  mills,  427. 

Barometer,  339. 

Barometric  elevations,  340. 

variations,  339. 

Barrell,  J.,  62. 

Barrier  pillars,  287. 

Bar  signals,  236. 

Base  lines,  46. 

Batteries,  Electric,  229. 

Battery  ceils,  Composition  of,  231. 
wa*ter,  430. 
working,  307. 

Beams,  102,  105. 

Bearing  in,  283. 

value  of  masonry,  107. 

Bedded  deposits,  279. 

materials,  Prospecting  for,  238. 
Bell  wiring,  230. 

Belting  and  velocity  of  pulleys,  193. 
Bending  rails,  412. 

Bends  in  pipes,  153. 

Bent  plumb-line  method  of  slope  sur- 
veying, 73. 

Biram’s  ventilator,  387. 

Bitumen,  Prospecting  for,  249. 
Bituminous  coal,  169. 

Cubic  feet  in  ton  of,  449. 
Handling,  443. 

Blackdamp,  350. 

Blacksmith  coal,  173. 

Blake  crushers,  419. 

Blasting  by  electricity,  332. 

Bleeding  from  scalp  wounds,  451. 
Blossburg  method  of  mining,  298. 
Blower  fans,  386. 

Board  measure,  13. 

Boiler,  176. 

Care  of,  185. 
capacity,  181. 

Choice  of,  179,  180. 

cleaning,  186. 

coverings,  183. 

feed-pumps,  161. 

iron,  thickness  required,  187. 

scale,  181. 

tests,  188. 

Boltheads,  Weight  of,  116. 

Bolts  per  mile  of  track,  117. 

Bolts,  Weight  of,  116. 

Bonnett,  268. 

Bord-and-pillar,  280. 

Bore-hole  records,  244,  250. 
holes,  242. 

Bottoms,  Slope,  413. 

Boxes  for  electric  fuses,  224. 

Box  regulator,  375,  377. 

Boyle’s  law,  195.  345. 

Brass,  Weight  of,  111,  112,  114,  115. 
Brattice,  Air,  ^94. 


Breast  boards,  270. 

, wheels,  157. 

Bridges,  Air,  393. 

Briqueting,  448. 

British  imperial  measure  (liquid  and 
dry),  5. 

measures  of  area,  4. 
measures  of  length,  2. 
measures  of  volume,  5. 
thermal  unit,  168. 

Brown  coal,  170. 

Brown’s  method  of  mining  anthra- 
cite, 306. 

Brown  & Sharpe  gauge,  208. 

Buckets,  Conveying,  446. 

Buggy  breasts,  291. 

Buildings,  283. 

Bulling,  330. 

Buntons,  270. 

Burt’s  sdlar  attachment,  47. 

Butt  cleats,  284. 


Cables,  Electric,  209. 

Cableways  in  mining,  122b,  278. 

Calculation  of  areas,  77. 
of  mine  resistance,  366. 
of  wires  for  electric  transmission, 
210. 

California  method  of  mining,  300. 
stamps,  428. 

Calorie,  168. 

Calumet  classifier,  435. 

Cams  for  stamps,  429. 

Cannel  coal,  170. 

Capacity  of  boilers,  181. 
of  electric  cables,  209. 
of  mining  machines,  337. 
of  pumps,  161. 
of  shaking  screens,  432. 
of  standard  steel  buckets,  446. 

Capell  ventilator,  389. 

Carat,  12. 

Carbonic-acid  gas,  350. 
oxide  gas,  349. 

Castings,  Weight  of  iron,  copper,  lead, 
brass,  or  zinc,  111. 

Caving  a back  of  ore,  320. 
methods,  320. 
waste  only,  320. 

Cells,  Various  types  of,  231. 

Ppntprs!  RQ 

Centigrade  to  Fahrenheit,  366. 
to  Reaumur,  366. 

Centrifugal  fans,  386. 
pumps,  164. 
roller  mills,  426. 

Chain,  Surveyor’s,  42. 
cutter  machines,  337. 
pillars,  287. 

Chains,  Iron,  129. 

Chamber-and-pillar  method,  318. 

Chambering,  330. 

Channels,  Flow  in,  142. 

Character  of  floor  and  roof  on  size  of 
pillars,  Influence  of,  280. 

Charging  a hole,  330. 

Charles’  law,  345. 


INDEX. 


625 


Chemical  compounds,  341. 
equations,  341. 
symbols,  341. 

Chemistry  of  gases,  341. 

Chimneys,  189. 

Chinese  measures  of  length,  4. 

Chock,  268. 

Choice  of  a boiler,  179, 180. 

Chokedamp,  350. 

Churn  drills,  242. 

Chute  breasts,  292. 
mining,  309. 

Circles,  31.  _ __  r 

areas  of,  1 to  1,000,  Table  of,  545. 
areas  of,  & to  100,  Table  of,  561. 
Circuit,  Electric,  205. 

Circular  mil,  207. 

Circulation  of  boilers,  181. 
Circumferences,  1 to  1,000,  Table  of, 
545. 

to  100,  Table  of,  561. 

Clanny  lamp,  356. 

Classifiers,  Hydraulic,  434. 

Classifying  apparatus,  431. 

C’eaning  safety  lamps,  358. 

Clearfield  method  of  mining,  295. 

Cleats,  284. 

Clinometer,  44. 

Closed  work,  279.  . 

Close  workings,  Shots  in,  361. 

Closing  surveys,  68. 

Coal,  169. 

Analyses,  168. 
analysis,  173. 

Anthracite,  169. 

Bituminous,  169. 

Blacksmith,  173. 

Brown,  170. 

Calorific  Power,  168. 

Cannel,  170. 

Coking,  170. 

Composition  of,  170. 
dealers’  computing  table,  452. 
Domestic,  173. 
dust,  Effect  of,  360. 

Free-burning,  170. 

Gas,  173. 

Hardness  of,  171. 

Iron-making,  172. 

Lignite,  170. 

Preparation  of,  418. 

Prices  of,  326,  327. 

Production  of  U.  S.,  326. 
Prospecting  for,  238. 

Running  of,  312. 

Semianthracite,  169. 
Semibituminous,  169. 

Sizes  of,  173,  434. 

Specific  gravity  of,  109, 171. 

Splint,  170. 

Steaming,  171. 

Storage  of,  291. 

Strength  of,  171. 
washers,  436. 

Weight  of,  170. 

Coals,  Cubic  feet  in  ton  of  various, 
109,  170. 

Cockermegs,  268. 


Coefficient  of  contraction  (water), 
135. 

of  discharge  (water),  135. 
of  discharge  with  weirs,  140. 
of  rolling  friction,  398. 
of  roughness  for  water  channels, 
144. 

of  velocity  (water),  135. 

Coefficients  of  friction  for  various 
materials,  95,  96. 
of  friction  of  air  in  mines,  367. 

Cog,  268. 

Coins,  10. 

Coke,  172. 

ovens,  Cost  of,  328. 

Coking  coals,  170. 

coal,  Cost  of,  328. 

Collar,  268. 

Collimation,  Line  of,  53. 

Colorado  method  of  mining,  302. 

Color  of  coal  ash,  171. 

Columns,  Safe  loads  for,  106. 
Combustibles,  166. 

Combustion,  Spontaneous,  291. 
Common  fractions,  15. 

Commutator,  216. 

Comparison  of  aluminum  and  copper 
for  electric  use,  209. 
of  hydraulic  formulas,  149. 
of  methods  of  shaft  sinking,  262. 
of  vacuum  and  plenum  systems  of 
ventilation,  386. 

Compass,  38. 

To  adjust,  38. 

To  use,  39. 
vernier,  39. 
field  notes,  44. 

Complement  of  angle,  34. 

Composition  of  atmosphere,  337. 
of  coals,  170. 
of  forces,  95. 
of  fuels,  169. 

Compound,  Chemical,  341. 
lever,  92. 

wound  dynamos,  219. 

Compressed  air,  194. 

haulage,  403. 
haulage  problems,  404. 
Compressibility  of  liquids,  133. 
Compressive  strength  of  anthracite, 
289. 

Condensers,  176.  . 

Conducting  power  of  various  sub- 
stances, 184. 

Conductors  (guides),  398. 

(electrical),  207. 
for  electric-haulage  plants,  214. 
Cone,  33. 

Conical  drums,  394. 

drum,  To  balance,  396.  . 

Connecting  outside  and  inside  sur- 
veys, 68.  . . 

Connections  for  continuous-current 
motors,  223.  . . 

Connellsville  method  of  mining,  293. 
Constant-current  circuit,  206. 
potential  circuits,  206. 
power,  372. 


626 


INDEX. 


Constant  pressure  , 372. 
pressure  circuits,  206. 
quantity,  372. 
velocity,  372. 

Constants  for  mine  gases,  349. 

for  wooden  beams,  103. 
Construction  of  air  compressors,  194. 
of  dams,  133. 
of  a mine  furnace,  383. 

Contents  of  a coal  seam,  To  find,  52. 
of  cylinders,  6. 

Continuous-current  motors,  Connec- 
tions for,  223. 
vernier,  45. 

Contraction,  Coefficient  of  ( water)  ,135. 
Control  of  roof  pressure,  284. 
Conversion  factors  (hydraulic),  141. 
of  thermometer  readings,  366. 
tables,  7,  10. 

Conveyors,  Horsepower  of,  445. 
Coordinates,  51. 

Copper,  Electric  properties  of,  209. 
Weight  of,  111,  112,  114,  115. 

Wire,  208. 

Cornish  pumps,  158. 
rolls,  423. 

underhand  stoping,  316. 

Corps,  Mine,  66. 

Corresponding  mercury  and  air  col- 
umns, Table  of,  347. 

Corrugated  rolls,  422. 

Cosecant,  35,  454. 

Cosine,  35,  453. 

Cost  of  briqueting,  449. 
of  coke  ovens,  328. 
of  coking  coal,  328. 
of  drilling,  244-247. 
of  haulage,  409. 
of  mining  anthracite,  322. 
of  sinking,  263. 
of  stamping,  430. 
of  unloading  coal,  447. 
of  well  drilling,  242. 

Cotangent,  35,  453. 

Cotangents,  Natural,  Table  of,  464. 
Coverings,  Boiler  and  pipe,  183. 
Coversed  sine,  35. 

Coyoting,  321. 

Cracking  rolls,  421. 

Crib,  268. 

Cribbing,  270. 

Cross-section  of  electric  wires,  207. 
Cross-sections,  Construction  of,  249. 
Crushing  load  of  wood,  105. 
machinery,  418,  431. 
mills,  426. 
rolls,  423. 

rolls,  Table  of,  425,  426. 

Cube,  33. 

root,  19,  545. 
roots,  Table  of,  545. 

Cubes,  Table  of,  545. 

Cubic  feet  occupied  by  ton  of  various 
coals,  449. 

Culm,  Flushing  of,  314. 

Current  estimates,  212. 

motors,  157. 

Curtains,  394. 


Curves  for  mine  roads,  411. 

' Railroad,  78. 

on  slopes,  Vertical,  416. 

Cylinder,  33. 

Cylinders,  Contents  of,  6. 
in  a pump,  Ratio  of,  160. 
of  a hoisting  engine,  To  find  size 
of,  397. 

To  find  contents  of,  in  U.  S.  gal- 
lons or  bushels,  5. 

Cylindrical  boiler,  Maximum  work 
of,  178. 

boilers,  Economy  of,  188. 
drums,  394. 

drum,  To  find  period  of  winding, 
397. 

rings,  34. 


Dams,  154. 

Debris,  156. 

Earth,  156. 
in  mines,  133. 

Masonry,  156. 

Stone,  155. 

Wing,  156. 

Danish  measures  of  length,  3. 

Darcy’s  formulas  (hydraulic),  148. 
Davy  lamp,  356. 

Debris  dams,  156. 

Decimals,  16. 

Decimals  of  a foot  for  each  & inch  , 3. 
Declination,  Magnetic,  39. 

of  Polaris,  46. 

Deflected  angle,  45. 

Deflections  in  p o w e r - transmission 
ropes,  Table  of,  122. 

Density  of  a gas,  344. 

Departures,  537. 

Deposits  over  8 ft.  thick,  318. 

Depth  of  shafts,  Calculation  of,  340. 
of  suction,  162. 

Derangement  of  ventilating  current, 
359. 

Detaching  hooks,  398. 

Detection  of  small  percentages  of  gas, 
356. 

Detonation,  331. 

Diagram  for  reporting  on  mineral 
lands,  252. 

Diameter  of  holes  (blasting),  330. 
Diamond  drill,  243. 

weight,  12. 

Dies  for  stamps,  429. 

Differential  pulley,  94. 

Diffusion  of  gases,  346,  348. 

Dip  and  strike  from  bore-hole  records, 
250. 

workings,  Ventilation  of,  382. 
Direct-current  circuits,  210. 
dynamos,  215. 
motors,  220. 

Direction  of  face,  284. 

Directions  for  blasting  by  electricity, 
332. 

Discharge,  Coefficient  of  (water),  135. 
gates  (dams),  154. 
through  V notch,  138. 


INDEX . 


627 


Disintegrating  rolls,  423. 

Disk  fans,  385. 

Distance,  Errors  in,  77. 

from  center  to  center  of  breasts, 
Table,  287. 

Distribution  of  air  in  mine  ventila- 
tion, 373. 

Ditches,  142. 

Banks  of,  143. 

Capacity  of,  143. 

Grades  of,  143. 

Velocity  in,  142. 

Division  of  air-current,  Proportional, 
375. 

D.,  L.  & W.  telephone  system,  234. 
Dodge  crushers,  419. 

Domestic  coals,  173. 

Door  regulator,  375,  377.  # 

regulator,  Size  of  opening  for,  377. 
Doors,  393. 

Double-chute  battery,  309. 
cylindrical  drums,  394. 
entry,  284. 

Draft,  190.  . , . 

Drainage  in  shaft  sinking,  263. 
Drawbar  pull  of  electric  locomotives, 
407. 

Drawing  pillars,  289. 

Dredge  (centrifugal  pump),  164. 
Dredging,  279. 

Dressing  of  ores,  418. 

Drift  of  drill  holes,  243. 

Drill,  Diamond,  243. 
holes,  243. 

holes,  Arrangement  of,  335. 
records,  244,  250. 

Drilling,  242,  330. 

Driving  the  gangway,  264. 

Dron’s  formula  tor  shaft  pillars,  285. 
Drop  for  stamps,  428. 

Drums,  Conical,  394. 

Double-cylindrical,  394. 
for  wire  rope,  12,21. 

Dry  measure  (U.  S.),  5. 

Dunn’s  table  of  size  of  pillars,  286. 
Duplex  pumps,  158. 

Dust  briquets,  448. 

Effect  of,  360. 

Duty  of  anthracite  screens,  434. 
of  miners’  inch,  137. 
of  stamps,  430. 

Dynamite,  Thawing,  329. 

Dynamos,  215. 

Alternating-current,  224. 
Compound-wound,  219. 
Series-wound,  219. 

Shunt-wound,  219. 

Earth  Augers,  242. 

dams,  156. 

Economizers,  185. 

Effect  of  altitude  on  air  compression, 
195. 

Efficiency,  Manometrical,  390. 
Mechanical,  390. 
of  water-power,  156.  . 

Electrical  Expressions  and  Equiva 
lents,  205. 

Electric  blasting,  332. 


Electric  circuit,  205. 
exploder,  332. 
haulage,  406. 

haulage  plants,  Conductors  for, 
214. 

haulage  problem,  407. 
locomotives,  Drawbar  pull  of,  407. 
locomotives,  Hauling  capacity  of, 
408. 

power,  204. 

pumps,  162.  . 

resistance,  Estimation  of,  209. 

signaling,  229-235. 

units,  203. 

wiring,  207. 

Electricity,  203. 

Electromotive  force,  203,  218. 

Elements,  341. 

in  ventilation,  363. 
of  mechanics,  91. 

Table  of,  342. 

Elevating  capacity  of  buckets,  446. 
Elevation  of  rails  for  mine  roads,  412. 
Elevations,  Barometric,  340. 

Elevators,  Water,  164. 

Ellipse,  32. 

End  cleats,  284. 
on,  285. 
plates,  270. 

Endless-rope  haulage,  401. 

Engine  drivers,  Rules  for,  191. 

planes,  399. 

Engines,  Sinking,  263. 

Steam,  190. 

Entries,  Number  of,  284. 

Equal  settling  factors,  Table  of,  439. 
settling  particles,  439. 
shadows,  47. 
splits  of  air,  374. 

Equations,  Chemical,  341. 

Equilibrium  of  liquids,  130. 
Equivalent  orifice,  367. 

Errors,  76. 
in  arc,  76. 
in  distance,  77. 
in  measurement,  77. 
in  surveying,  66,  76. 

Eschka’s  method  of  analysis  for  sul- 
phur, 174. 

Establishing  a meridian  wi*h  solar 
attachment,  47. 

Estimates  of  current,  212. 

Evolution,  19,  545. 

Excitation  of  dynamos,  218. 

Exhaust  fans,  386. 

Expansion  of  gases,  344. 

Exploder,  Electric,  332. 

Exploring  workings,  361. 

Explosions,  Exploring  workings  after 
361. 

in  boilers,  179. 

Explosive  conditions  in  mines,  359. 
Explosives,  329. 

Pressures  developed  by,  334. 
Relative  strengths  of  various 
brands  of,  330. 

Values  of,  335. 

Eytelwein’s formulas  (hydraulic),  148 


628 


INDEX. 


Face  Cleats,  284. 

Direction  of,  284. 
on,  285. 

Factor  of  a mine,  Potential,  367. 
Factors,  Conversion  (hydraulic),  141. 
Fahrenheit  to  centigrade,  366. 

Fan  construction,  Principles  of,  391. 
tests,  392. 

ventilation,  373,  385.  « 

Fans,  Ventilating,  386. 

Fastenings  for  wire  rope,  126. 

Feeders  of  gas,  352. 

Feed-pumps,  161,  186. 

Feedwater  for  boilers,  186. 

Field  excitation  of  dynamos,  218, 
magnet,  216. 

notes  for  outside  compass  survey* 
44. 

Filling  methods,  319. 

Finger  bars,  432. 

Firedamp,  351. 

Fires,  Gob,  291. 

Firing  a boiler,  186. 
blasts,  331. 
by  detonation,  331. 

Fixed  carbon  in  coal,  171.  174. 

Flash  signals,  234. 

Flat  deposits,  318. 

Flat  ropes,  119,  394. 

Flights,  Capacity  of,  446. 

Flow  of  water  in  channels,  142,  144. 
in  rivers,  145. 
through  flumes,  146. 
through  orifices,  135. 
through  pipes,  147, 150. 
Flumes,  145,  443. 

Flow  of  water  through,  146. 

Grade  of,  145. 

Flushing  of  culm,  314. 

Foaming  (boilers),  186. 

Forced  draft,  190. 

Force  fans,  386. 

Forces,  Composition  of,  95. 

Foreign  coins,  Values  of,  11. 
Forepoling,  260,  270. 

Form  of  roll  teeth,  422, 

Forms  of  mine  timbering,  267. 
Formulas  for  air  splitting,  378. 
for  inclined  planes,  399. 
in  ventilation,  370. 

Foster’s  formula  for  shaft  pillars,  286. 
Foundations  (dams),  154. 

Fractions,  15. 

Common,  15. 

Decimal,  16. 

Table  of  equivalent  decimal,  16. 
Fragmental  deposits,  Mining  of,  278. 
Free-burning  coals,  170. 

gold  per  ton  of  ore,  Value  of,  241 
Freezing  process,  260. 

Friction,  95. 

coefficients  for  air  in  mines,  367. 
coefficients  for  various  materials, 
95,  96. 

in  knees  and  bends,  153. 
of  air  in  pipes,  201. 
of  mine  cars,  96. 
of  water  in  pipes,  151. 


Friction  pull  on  endless  rope.  402. 
Frictional  resistance  of  shafting,  96. 
Frozen  ground,  Mining  of,  322. 
Frustums.  34. 

Fuel  dust  briquets,  448. 

Fuels,  166. 

Composition  of,  169, 

Furnace  stack,  385. 

Construction  of  ventilating,  383. 
ventilation,  373. 

ventilation,  Air  columns  in,  384. 
Fuse  boxes,  224. 

Fuses,  224. 

Fusible  plugs,  186. 


Galvanic  Action  Around  Boilers,  187. 

Gangway  driving,  264. 

timbers,  268. 

Gas  coals,  173. 
feeders,  352. 

Testing  for,  354. 

Outbursts  of,  352,  360. 

Gases,  Chemistry  of,  341. 

Diffusion  of,  346;  348. 
enclosed  in  the  pores  of  coal,  353. 
found  in  mines,  348. 

Pressure  of,  345. 

Properties  of,  344. 

Transpiration  of,  346,  348. 

Gate  for  jig,  438. 

Gates  crusher,  Table  of,  422. 

Gauge  cocks,  186. 

of  mine  tracks,  411. 

Pressure,  185. 

Water,  365. 

Wire,  122k,  207,  208. 

Gauging  by  weirs,  138. 
water,  136. 

Gay-Lussac’s  law,  195,  345, 

Gears,  Train  of,  92. 

Gems  and  precious  stones,  Prospect- 
ing  for,  241. 

General  mathematical  principles,  14. 

remarks  on  surveying,  49. 
Geological  maps,  Construction  of,  249. 
periods,  237. 

Geometrical  problems,  25. 

progression,  21. 

Geometry,  24. 

Geordy  lamp.  356. 

George’s  creek  method  of  mining,  297. 
Gilpin  county  stamps,  428. 

Glossary  of  mining  terms,  565. 

Gob  fires,  291. 

Gold  coins,  10. 

mine,  Opening  of,  258. 

; Gonda  type  of  cell,  230. 

Gophering,  321. 

Gould’s  formulas  (hydraulic),  148. 
Grade  of  mine  road,  410. 

Gradient,  Hydraulic,  147. 

Graham’s  law,  346. 

Gravity  planes,  398. 

Specific,  107. 
specific,  Table  of,  108. 
stamps,  427. 
i Gray  lamp,  358. 


INDEX. 


629 


Grizzlies,  431. 

Guibal  ventilator,  388. 
Guides,  398. 

Gyratory  crushers,  420. 


Half  on,  285. 

Hammer  crushers,  423. 

Handling  of  material,  443. 

Hard  coal,  169,  313. 

Hardness  of  coal,  171. 

Haulage,  398.  . 

by  compressed  air,  403. 

Cost  of,  409. 

Electric,  214,  406. 

Motor,  402. 
problems,  399,  407. 
road  signals,  235. 
rope.  120, 122,  400. 

Speed  of,  408. 

Hauling  capacity  of  electric  locomo- 
tives, 408.  . i 

Ha wksley’s  formula  (hydraulic),  148. 

Head-bars,  431. 
block,  268. 
frames,  275,  397. 
frames,  Sinking,  262. 
gears,  275. 
sheaves,  397. 

Headboard,  268. 

Heating  surface  of  a boiler,  1/7. 
values  of  American  coals,  168. 

Heberle  gate,  438. 

High  explosives,  329. 

Hill,  E.,  198.  . 

Hints  for  mining  small  seams,  313. 
to  beginners  in  surveying,  80. 

Hoisting,  394. 

engine  cylinders,  397. 
engine,  To  find  size  of,  396. 
problems,  396. 

ropes,  Starting  strain  on,  124,  126. 
ropes,  Stress  in,  1221. 

Hooks,  Detaching,  398. 

Horizontal  distances,  50,  87,  537. 
distances,  Stadia  table  of,  87. 

Horsepower  for  box  regulators,  377. 
for  bucket  elevators,  445. 
for  door  regulators,  377. 
necessary  to  compress  air,  406. 
of  air-currents,  363. 
of  boilers,  177. 
of  coal  conveyor,  445. 
of  engine,  190. 
of  manila  ropes,  126. 
of  stamps,  430. 
of  a stream,  157. 
required  to  raise  water,  161. 

Hughes’s  formula  for  shaft  pillars, 
286. 

Hydraulic  classifiers,  434. 
gradient,  147. 
placer  mining,  278. 

Hydraulics,  135. 

Hydrocarbons,  349. 

Hydrogen  disulphide  H^S,  350. 
Sulphuretted,  350. 

Hydrostatics,  130. 


I Beams,  Safe  Loads  for,  104 

Illuminating  power  of  safety  lamps, 
359. 

Impulse  wheels,  158. 

Incandescent  lamps,  213. 

Inch,  Miners’,  136. 

Inclined  plane,  93. 

plane,  Stress  in  hoisting  ropes  on, 
1221. 

roads,  Calculation  of  power  for, 
402. 

roads,  Haulage  on,  398. 
shafts,  Surveying,  73. 

Included  angle,  45. 

Incrustation  and  scale,  182. 

Indiana  method  of  mining,  298. 
Individual  angle,  45. 

Induction  motors,  227. 

Inertia,  Angle  of,  398. 

Influence  of  furnace  stack  on  venti- 
lation, 385. 

of  seasons  on  ventilation,  382. 
Injector,  186.  . 

Area  of  nozzle  of,  187. 

Delivery  in  gallons  per  hour  oi, 
187. 

Inside  surveys,  56,  67. 

Inspection  of  boilers,  181. 

Insulated  wires,  212. 

Interstitial  currents,  439. 

factors,  440. 

Involution,  19,  545. 

Iowa  method  of  mining,  299. 

Iron  beams,  103. 
for  track,  117. 
pipe,  Weight  of,  113. 
supports,  272. 

Weight  of  flat,  115. 

Weight  of  wrought,  114, 

Irregular  mining  deposits,  321. 
Isogonic  chart,  40.  . 

Isothermal  compression,  195, 198. 


Jaw  Crushers,  419. 

Jeffrey-Robinson  coal  washer,  436. 
Joints  in  mine  timbering,  267. 

Kind-Chaudron  Method  of  Sinking,  262. 

Knees  in  pipes,  153. 

ICoepe  system  of  hoisting,  395. 

Lamp  Tests  for  Gas,  354. 

Lamps,  Arc,  214. 

Incandescent,  213. 

Safety,  355. 

Testing,  355. 

Lancashire  boiler,  177. 

Landings,  Timbering  of,  2/2. 

Large  deposits  over  8 ft.  thick,  Min- 
ing, 318. 

Latches,  413. 

Latitude,  50,  537. 

with  Burt’s  solar,  48. 

Launders,  443. 


630 


INDEX. 


Law  of  settling  particles,  439. 

Laws  in  regard  to  air  splitting,  373. 
in  regard  to  quantity  of  air,  363. 
of  volume,  341. 

Leaching  methods  of  mining,  322. 
Lead,  Weight  of,  111,  113,  114,  115. 
Leclanche  cell,  229. 

Lehigh  region,  Costs  of  mining  in, 
323. 

Length,  Measures  of,  2. 

of  steep  pitch  on  inclined  plane, 
399. 

Leveling,  53. 

Trigonometric,  56. 

Level  notes,  55,  62. 

roads,  Haulage  on,  398. 
timbers,  268. 

Levels  (gangways),  316, 
in  metal  mines,  264. 

Levers,  91. 

Lid,  268. 

Life  of  shoes  and  dies,  429. 

of  wire  rope,  1221 
Lignite,  170. 

Line  shafting,  110. 

Liquid  measure  (U.  S.),  5. 

Liquids,  Compressibility  of,  133. 

Load  for  wire  rope,  125. 

that  a hoisting  engine  will  start, 
To  find,  396. 

Locating  errors,  76. 

special  work,  77. 

Locks  for  lamps,  358. 

Locomotive  haulage,  402. 

Logarithmic  functions,  Table  of,  492. 
Logarithms,  22,  473. 

of  numbers,  Table,  473. 
of  trigonometric  functions,  Table 
of,  492. 

Log  washer,  436. 

Long-hole  process  of  shaft  sinking, 
262. 

horn,  285. 
section,  64. 
splice,  128. 

Longitudinal  back  stoping  with  fill- 
ing, 319. 

Longwall  method,  281,  302. 
Modifications  of,  302. 

Timbering,  283. 

Loss  in  transmitting  air,  198. 
of  blood,  449. 

of  head  in  pipe  by  friction,  151. 
of  heat  from  steam  pipes,  184. 
of  pressure  of  air  in  pipes,  202. 
Low  explosives,  329. 

Lubricants  for  different  purposes,  102. 
Lubrication,  100, 124b. 


Machine  Mining,  336. 

Magnetic  prospecting,  248. 
variation,  39. 

Malleable-iron  buckets,  446. 

Manila  ropes,  Power  transmitted  by, 
126. 

Manometrical  efficiency,  390. 
Mapping,  74. 


Maps,  Geological,  249. 

Mariotte’s  law,  345. 

Marsaut  lamp,  358. 

Marsh  gas,  348. 

Masonry,  Bearing  value  of,  107. 
dams,  156. 
supports,  272. 

Material,  Handling  of,  443. 
Mathematical  signs,  14. 

Mathematics,  14. 

Measurement,  Error  jn,  77. 
of  temperature,  366. 
of  ventilating  currents,  364. 
Measures  of  area,  4. 

American,  4. 

British,  4. 

Metric,  4. 

Measures  of  Length,  2. 

American,  2. 

Austrian,  3. 

British,  2. 

Chinese,  4. 

Danish,  3. 

Metric,  3. 

Norwegian,  3. 

Prussian,  3. 

Russian,  3. 

Swedish,  4. 

Measures  of  volume,  5. 

American,  5 
British,  5. 

Metric,  5. 

Mechanical  efficiency,  390. 
mixture,  341. 
ventilators,  385. 

Mechanics,  91. 

Mensuration,  28. 
of  solids,  33. 
of  surfaces,  28. 

Mercurial  barometer,  339. 

Mercury  and  air  columns,  347. 

column  corresponding  to  water 
column,  340. 

Meridians,  46. 

Merivale’s  formula  for  shaft  pillars, 
285. 

Mesh  for  shaking  screens,  433. 

of  revolving  screens  for  anthra* 
cite,  434. 

Size  of,  433. 

Metal  linings  for  shafts,  260. 

Methods  and  appliances  in  mine  ven- 
tilation, 381. 

Methods  of  mining,  277. 

Alabama,  297. 
anthracite,  305. 

Blossburg,  298. 

Brown’s,  306. 

California,  300. 

Clearfield,  295. 

Colorado,  302. 

Connellsville,  293. 

George’s  creek,  297. 

Indiana,  298. 

Iowa,  299. 

mineral  deposits,  316. 
Newcastle,  Colo.,  302. 
Pittsburg,  295. 


INDEX . 


631 


Methods  of  Mining,  Reynoldsville, 
295 

Tesla,  Cal.,  300. 

West  Virginia,  296. 

Williams’,  312. 

Methods  of  surveying,  67. 

Metric  conversion  tables,  7-10. 
measures  of  area,  4. 
measures  of  length,  3. 
measures  of  volume,  5, 
system,  1,  2,  3,  9,  10. 
weight,  2. 

Mil,  207. 

Milling  system,  278. 

Mine-car  friction  tests,  98. 
cars,  Friction  of,  96. 
corps,  66. 
dams,  133. 
explosions,  361. 
gases,  348. 
gases,  Table  of,  349. 

Opening  a,  257. 
plan,  Arrangement  of,  381. 
resistances,  364,  366. 
roads,  410b. 
sampling,  174. 
telephones,  233. 
timber  and  timbering,  265. 
tracks  410b. 

Mineral  available  in  a prospect,  251. 
deposits,  Methods  of  mining,  316. 
lands,  Report  on,  252. 

Miners’  inch,  136. 

Mining  terms,  Glossary  of,  565. 

Mixture,  Mechanical,  341. 

Moisture  in  coal,  171, 174. 

Molecule,  341. 

Money,  Tables  of,  10. 

Morris,  W.  H.,  127. 

Motor  haulage,  402. 

Motors,  214,  215. 

Current  (water),  157. 

Induction,  227. 

Regulation  of  speed  of,  222. 

Synchronous,  226. 

Movable  bars,  432. 

pulley,  94. 

Mueseler  lamp,  358. 

Multiphase  alternators,  225. 

Murphy  ventilator,  389. 


Nails,  Sizes,  Etc.  of,  114. 

Nasmyth  fan,  387. 

Natural  division  of  air-currents,  374. 
functions,  Tables  of,  453. 
gas,  Prospecting  for,  249. 
splitting,  Calculation  of,  374. 
ventilation,  381. 

Needling,  268. 

Neville’s  formula  (hydraulic),  148. 
Newcastle,  Colorado,  method  of 
mining,  302. 

Nitrogen,  348. 

Non-conductors,  Relative  values  of, 
185. 

Norwegian  measures  of  length,  3. 
Notes  (survey),  60. 


Notes,  Compass  field,  44. 

for  outside  compass  survey,  44. 
Level,  55,  62. 
on  mapping,  74. 

Side,  60,  61. 

Stope-book,  62. 

Transit,  60. 

Nozzle,  Injector,  187. 

Number  of  cars  in  a trip  on  a self- 
acting incline,  399. 

Nuts,  Weight  of,  116. 


Occluded  Gases,  352.  _ 

Occurrence  of  gases  in  mines,  351. 
Ohm’s  law,  204. 

Oils  for  safety  lamps,  356. 

Lubricating,  100, 102. 

Open  channels,  142. 
work,  277. 

Opening  a mine,  257. 

in  box  regulators,  376. 

Order  of  drop  of  stamps,  428. 

Ore  deposits,  238. 
dressing,  418. 

Handling  of,  443. 

Orifice,  Equivalent,  367. 
Oscillating  bars,  432. 

Outbursts  of  gas,  352,  360. 

Outside  surveys,  67. 

Overcasts,  393. 

Overhand  stoping,  304,  317. 
Overshot  wheels,  158. 

Oxygen,  348. 


Packing  for  Pumps,  159. 

Pack  walls,  283. 

Paint,  59. 

Pamely’s  formula  for  shaft  pillars,  286. 
Panel  system,  283. 

Parallel  circuits,  206. 

Parallelograms,  28. 

Parallelopiped,  33. 

Peele,  Robert,  194. 

Percentage,  20. 

Percussion  drills,  242.  . 

Period  of  winding  on  a cylindrical 
drum,  To  find,  397. 

Permitted  explosives,  329. 

Petroleum,  Fuel  value  of  167. 

Prospecting  for,  249 
Pick  machines,  336. 

Pillar  timber,  268. 
and  chamber,  280. 
and  stall,  281,  292. 
drawing,  289. 

Pillars,  285.  , , 

Weight  on,  at  different  depths,  28/. 
Wooden,  105. 

Pins,  43. 

Pipes,  Flow  through,  147, 150. 

Friction  in,  151. 

Pressure  of  water  in,  132. 
Thickness  of,  133. 
used  for  compressed-air  haulage, 
Table  of,  406. 

Piston  speed  of  pumps,  161. 


632 


INDEX. 


Pitch  at  which  anthracite  will  run, 
Table  of,  443. 
distance,  51. 

Pitching  work  surveys,  68. 

Pittsburg  method  of  mining,  295. 
Placer  deposits,  Prospecting  for,  240. 

mining,  278. 

Plane  trigonometry,  34. 

Planes,  Engine,  399. 

Gravity,  398. 

Plates,  metal,  Weight  of.  112. 

Platform  bars,  431. 

Plats,  Timbering  of,  272. 

Plenum  system  of  ventilation,  386. 
Plotting,  49. 

by  coordinates,  51. 

Plow-steel  rope,  120. 

Plugs,  186. 

Plumb-bob,  44. 

Plumbing  of  shafts,  69. 

Pneumatic  method  of  shaft  sinking 
260. 

stamps,  430. 

Pockets  of  gas,  352. 

Poetsch-Sooy smith  process  (freezing 
method),  260. 

Polaris  observation,  46. 

Polygons,  30. 

Post  and  breast  cap,  268. 

Potential  factor  of  a mine,  367. 

Pound  calorie,  168. 

Power,  Electrical,  204. 
for  hoisting,  395. 
in  mine  ventilation,  367. 
of  air-currents,  363. 
of  a hoisting  engine,  To  find,  396. 
of  an  explosive,  334. 
of  waterfall,  157. 
pumps,  162. 

required  for  inclined  roads,  402. 
stamps,  431. 

Water,  156. 

Practical  examples  in  the  solution  of 
triangles,  35. 

splitting  of  air-currents,  373. 
Precious  stones,  Prospecting  for,  241. 
Preliminary  work,  257. 

Preparation'  of  anthracite,  Diagram 
of,  442. 

of  coal  and  ore,  418. 

Preservation  of  timber,  265. 

Pressure.  Absolute,  345.  / 

as  affecting  explosive  conditions, 
361. 

developed  by  explosives,  334. 
for  box  regulators,  376. 
gauge,  185. 

of  anthracite  coal  against  walls, 
445. 

of  bituminous  coal  against  walls, 
444. 

of  gases,  345. 

of  liquids  on  surfaces,  130. 
of  occluded  gases,  352. 
of  steam  at  different  tempera- 
tures, 188. 

of  water  in  pipes,  132. 
on  heading,  130. 


Pressure  of  water  on  plane  surface, 
132. 

Prices  per  ton  of  coal  at  mines, Table, 
327. 

Primary  splits,  374. 

Prism,  33. 

Prismoidal  formula,  34. 

Problem  in  compressed-air  haulage, 
404. 

Problems  in  geometrical  construc- 
j tion,  25. 

in  haulage,  399. 

I in  hoisting,  396. 

j Progression,  Arithmetical,  20. 

| Geometrical,  21. 

Properties  of  copper  wire,  208. 

of  materials,  107. 

Proportion,  or  Pule  of  Three,  18. 
Proportional  division  of  the  air-cur- 
rent, 375. 

Props,  Undersetting  of,  276,  277. 

Wooden,  105. 

Prospecting,  235. 
for  bitumen,  249. 
for  natural  gas,  249. 
for  petroleum,  249. 

Magnetic,  248. 

Prussian  measures  of  length,  3. 
Pulley,  94. 

Pulleys  and  belting,  193. 

Pulverizers,  423. 

Pump  machinery,  158. 
memoranda,  163. 
packing,  159. 
valves,  162. 

Pumps,  158. 

Air-lift,  164. 

Centrifugal,  164. 

Cornish,  158. 

Electrical,  162. 
for  acid  waters,  165. 

, Power,  162. 

Simple  and  duplex,  158. 

Sinking,  165. 

Vacuum,  164. 

Push  button,  234. 

Pyramid,  33. 

Quadrant,  34. 

Quantity  of  air  required  by  State 
Laws,  363. 

for  dilution  of  mine  gases,  363. 
for  ventilation,  362. 
to  produce  necessary  velocity 
at  face,  363. 

Radial  Roller  Mills,  426. 

Radii  of  curves,  79. 

Rail  bending  for  mine  roads,  412. 

elevation  for  mine  roads,  412. 
Railroad  curves,  78. 

Rails  for  mine  roads,  411. 

per  mile  of  track,  117. 

Raises,  316. 

j Rapid  firing  of  boilers,  187. 

method  of  splicing  a wire  rope, 
127. 

I Rate  of  diffusion,  346. 


INDEX. 


633 


Rating  of  compressors,  195. 

Ratio  of  steam  and  water  cylinders  in 
pump,  160. 

Reaumur  to  Fahrenheit,  366. 
Reciprocals,  545.  . 

Recoil  of  an  explosion,  361. 

Reduction  of  inches  to  decimals  of  a 
foot,  2. 

Regular  polygon,  30. 

Regulation  of  motors  for  speed,  222. 
Regulators,  375.  , 

Relation  of  power,  pressure,  and  ve- 
locity, 364. 

Relative  volume  of  gases,  343. 
Relighting  stations,  359. 

Removal  of  sulphur  from  coal,  441. 
Repair  of  boiler  coverings,  187. 
Repairs  to  boilers,  180. 

Reporting  on  mineral  lands,  252. 
Requirements  of  law  as  to  splitting, 
373. 

Reservoirs,  154. 

Resistance,  Electric,  203. 

Estimation  of  (electric) , 209. 
in  electric  lines,  206. 
of  soils  to  erosion,  143. 

Mine,  364. 

Return-call  system,  232. 

Revolving  screen  mesh  for  anthracite, 

Reynoldsville  method  of  mining,  295. 
Right-angled  V notch,  137 . 

Rise  workings,  Ventilation  of,  382. 
Rivers,  Flow  of  water  in,  145. 

Roads,  Haulage  on  inclined,  398. 
Level,  398. 

Mine,  410. 

Rock-chute  mining,  310. 
drills,  263. 

Handling  of,  443. 

Roller  mills,  426. 

Rollers,  412.  . 

Rolling  friction,  Coefficient  of,  398. 
Roll-jaw  crushers,  420. 

Rolls,  421. 

Amount  crushed  by,  424. 
Crushing,  423. 

Speeds  of,  424. 

Teeth  of,  422. 

Roof  pressure,  280. 

Control  of,  284. 

Room-and-pillar,  280. 
modifications  of,  291. 
openings,  281. 
pillars,  286. 

Rooming  with  filling,  319. 

Rope  haulage,  122,  400. 

Ropes,  118. 

fastenings,  126. 

Flat,  394. 

Manila.  120, 126. 

Rotary  crushers,  420,  422. 

Roughness,  Coefficient  of,  144. 

Rule  of  Three,  18.  . 

Rules  for  engine  drivers,  191. 
Running  of  coal,  312. 

Russian  measures  of  length,  3. 


Safe  Loads  for  Cast-Iron  Columns,  106. 

Safe  loads  for  I beams,  104. 

Safety  catches,  398. 
explosives,  329. 
lamp  oils,  356. 
lamps,  355,  356. 

lamps,  Locks  for,  358.  • 

lamps,  Illuminating  power  of,  3o9. 
valves,  185.  . 

Sampling  available  mineral,  251. 

of  coal,  173.  • 

Scaife  trough  washer,  437. 

Scale,  Removal  of,  from  boilers,  181. 
Scalp  wounds,  451. 

Schiele  ventilator,  388. 

Schmidt’s  law  of  faults,  239. 

Screens,  431,  432. 

Screw,  93.  „ , , 

Diameter  and  number  of,  113. 

Seam  blasting,  331. 

Seasons,  Influence  of,  382. 

Secant,  35,  454. 

Secondary  splits,  374. 

Sederholm,  E.  T.,  125. 

Semianthracite  coal,  169. 
Semibituminous  coal',  169. 
Series-circuits,  205. 

parallel  method  of  regulation,  222- 
wound  dynamos,  219. 

Settling  boxes,  435. 

particles,  Law  of,  439. 

Shaft  bottoms,  Steel,  276. 
bottom  tracks,  416. 
pillars,  285. 

Sn?irainage  for,  263. 
sinking,  Ventilation,  263. 
timbering,  270. 

Shafting,  Frictional  resistance  of,  96. 

Strength  of,  110. 

Shafts,  259.  # ^ . 

Calculation  of  depth  of,  340. 

Form  of,  259. 

Methods  of  sinking,  259. 

Size  of,  259, 

Surface  tracks  at,  417. 

Table  of  depths  of,  etc.,  261. 
Shaking  screens,  432. 

Shanty,  268. 

Shearing  machines,  337. 

Sheaves  for  wire  rope,  1221. 
Sheet-metal  gauges,  122k. 

Shoes  for  stamps,  429. 

Short  horn,  285. 

Shots  in  close  workings,  361. 
Shunt-wound  dynamos,  219. 

Side  notes,  60,  61. 

•Signal  for  haulage  roads,  235. 
Signaling,  Electric,  229-235. 

Silver  coins,  10. 

Similar  airways,  372. 

Simple  bell  circuit,  230. 

Sine,  34,  453. 

Sines,  Natural,  Table  ot,  453. 
Single-chute  battery,  309. 
entry,  284. 

phase  alternators,  225.  . 

wire  method  of  slope  surveying, 74 


634 


INDEX. 


Sinking  a shaft,  259. 

Cost  of,  263. 
engines,  263. 
head-frames,  262. 
pumps,  165. 

Slope,  263. 

Speed  of,  263. 

Siphons,  149. 

Size  of  engine  for  engine-plane  haul- 
age, 399. 

of  hoisting  engine,  To  find,  396. 
of  mesh  for  screens,  433. 
of  opening  for  door  regulator,  377. 
of  opening  in  box  regulator,  376. 
of  pillars,  285. 
of  timber,  267, 

Sizes  of  anthracite,  percentages  of 
each,  323,  326. 
coal,  173,  434. 

Sizing  apparatus,  431. 

Slack,  167. 

Slicing  method,  319. 

Slightly  inclined  deposits,  318. 

Slope  bottoms,  413. 
level,  44. 
sinking,  263. 
surveying,  73. 
tracks,  413.  * 

Surface  tracks  at,  417. 

Small  percentages  of  gas,  356. 

seams,  mining  of,  313. 

Soft  coal,  169. 

Soils,  Resistance  of,  to  erosion,  143. 
Solar  attachment,  47. 

Sole,  268. 

Space  required  to  store  coins,  11. 
Special  forms  of  supports,  272. 
mining  methods,  322. 
work,  77. 

Specific  gravity,  107. 
of  coal,  171. 
of  gases,  344. 

of  various  substances,  Table 
of,  108, 109. 
volume,  341. 

Speed  of  crushing  rolls,  426. 
of  drilling,  244. 
of  haulage,  408. 
of  revolving  screens,  434. 
of  rolls,  423. 
of  sinking,  263. 
of  stamps,  429. 

of  water  through  pump  passages, 
160. 

regulation  of  motors,  222. 

Sphere,  33. 

Spikes,  Railroad,  117. 

Sizes,  etc.,  114. 

Spiling,  270. 

Spillways,  155. 

Spitzkasten,  435. 

Spitzlutten,  435. 

Splices  per  mile  of  track,  117. 

Splicing  a wire  rope,  127. 

Splint  coal,  170. 

Splitting  formulas,  378. 

of  air-currents,  373. 

Spontaneous  combustion,  291. 


Sprags,  270. 

Square  feet  to  acres,  4. 
root,  19,  545. 
roots,  Table  of,  545. 
sets,  270. 
set  system,  321. 
work,  318. 

Squares,  Table  of,  545. 

Squibbing,  330. 

Stack,  Furnace,  385. 

Stadia  measurements,  81. 

table,  86. 

Stamps,  427. 
heads,  429. 

Pneumatic,  430. 

Power,  431. 

Speed  of,  429. 

Steam,  431. 

Standard  steel  buckets,  Weights  and 
capacities  of,  446. 

Starting  strain  on  hoisting  rope,  126. 
Stationary  screen  jigs,  437. 
screens,  431. 

Stations,  Distinguishing,  59. 
Establishment  of,  57. 

Kinds  of,  57. 

Marking,  58. 

Relighting,  359. 

Timbering  of,  272. 

Steam,  175. 
engine,  190. 
pipe  coverings,  183. 
pressure  at  different  tempera- 
tures, 188. 
shovel  mines,  278. 
stamps,  431. 

Steaming  coals,  171. 

Steel  beams,  103. 

shaft  bottoms,  276. 
supports,  272. 
tape,  43. 

Stems  for  stamps,  429. 

Stinkdamp,  350. 

Stone  dams,  155. 

Stope  books,  62. 

Stoping,  316. 

Overhand,  304. 
with  filling,  319. 

Stoppings,  393. 

Storage,  Coal,  291. 

Stowing,  283. 

Stream  horsepower,  157. 

Strength  of  anthracite,  289. 
of  electric  current,  203. 
of  materials,  102. 
of  metals,  115. 
of  roof,  280. 
of  shafting,  110. 
of  wire  ropes,  119. 

Stress  in  hoisting  ropes,  1221. 

Strike  from  bore-hole  records,  250. 
Stulls,  268. 

Stuttles,  270. 

Suction,  162. 

in  jigging,  440. 

Sulphureted  hydrogen,  350. 

Sulphur  in  coal,  171, 174. 

Removal  of,  from  coal,  441. 


INDEX. 


635 


Sump,  264. 

Supplement  of  angle,  34. 

Surface  tracks  for  shafts  and  slopes, 
417. 

Surveying,  38. 

drill  holes,  243. 
methods,  67. 

Underground,  56,  67. 

Susquehanna  Coal  Co.  (friction  of 
mine  cars),  98. 

Swedish  measures  of  length,  4. 
Switches,  413. 

Symbols,  Chemical,  341. 

Synchronous  motors,  226. 

Systems  of  working  coal,  280. 


Table,  Coal  Dealers’  Computing,  452. 
Tables  of  Barrier  Pillars,  288. 
batteries,  231. 

circles,  545.  . 

circumferences  and  areas  of  cir- 
cles, ^ to  100,  561. 
combustibles,  166. 
elements,  342. 
hydraulic,  135-154. 
logarithms  of  numbers,  473. 
logarithms  of  trigonometric  func- 
tions, 492. 
mine  gases,  349. 
natural  sines  and  cosines,  453. 
natural  tangents  and  cotangents, 
464. 

rail  elevations,  412. 
reciprocals,  545. 

squares,  cubes,  square  roots,  cube 
roots,  circumferences  and  areas, 
545-560. 

Stadia,  88. 

strength  of  materials,  102-106. 
traverse  (latitudes  and  depar- 
tures), 537. 

well-known  shafts,  261. 

( For  tables  not  enumerated  above  see  the 
various  subjects.) 

Tail-rope  haulage,  400. 

Tamping,  331. 

Tangent,  35,  453. 

Tangents,  Natural,  Table  of,  464. 
Tappets  for  stamps,  429. 

Teeth  for  rolls,  422. 

Telephones  in  mines,  233. 

Telpherage,  278. 

Temperature,  Absolute,  344,  345. 

Measurement  of,  366. 

Tension  on  hauling  rope,  Calculation 
of,  401. 

Tertiary  splits,  374. 

Tesla,  Cal.,  method  of  mining,  300. 
Test  of  mine-car  frictions,  98. 

Testing  for  gas  by  lamp  flame,  354. 

lamps,  355. 

Tests,  Boiler,  188. 

Fan,  392. 

of  compressive  strength  of  an- 
thracite, 290. 

Thawing  dynamite,  329. 

Theory  of  air  compression,  194. 
jigging,  439. 


Theory  of  stadia  measurements,  81. 
Thermal  unit,  168. 

Thermometer  readings,  Conversion 
of,  366. 

Thermometers,  366. 

Thickness  of  boiler  iron,  187. 
pipe,  133. 

Thin  seams,  Mining,  313.  ♦ 

Three-phase  alternators,  226. 

Thurston,  table  of  lubricants,  102. 

Ties  for  mine  roads,  410. 

Timber,  Crushing  load  of,  105. 
Gangway,  268. 
joints,  267. 

Level,  268. 
measure,  12. 

Placing  of,  266. 

Preservation  of,  265. 

Size  of,  267. 

Timbering,  265. 

Forms  of,  267. 
longwall  face,  284. 

Tools  for  sinking,  263. 

Torque,  220. 

T't’ppIt  iron  117 

Tracks  for  shaft  bottoms,  416. 

Mine,  410. 

Tractive  efforts  of  compressed-air 
locomotives,  404. 

Train  of  gears,  92. 

Transformers.  228. 

Transit,  40. 

adjustment,  41. 
notes,  60. 
surveying,  45. 

Transmission  of  air  in  pipes,  196, 198. 
Electric,  210. 

pressure  through  water,  132. 

Rope,  120,  122, 

Transpiration  of  gases,  346,  348. 
Transporting  a wounded  person, 
450. 

Transverse  rooming  with  filling, 
319. 

Trapeziums,  30.  k 

Trapezoids,  30. 

Traverse  tables,  537. 

Traversing  a survey,  51. 

Treatment  of  injured  persons,  449. 

persons  overcome  by  gas,  451. 
Tremain  stamp,  431. 

Trestles,  274. 

Triangles,  28,  35. 

Trigonometric  leveling,  56. 
Trigonometry,  34. 

Triple  entry,  284. 

Trommels,  433. 

Trough  washer,  437. 

Troy  weight,  1. 

True  north  from  Polaris,  46. 

with  the  Burt  solar,  48. 

T-square  method  of  plumbing  shafts, 
73. 

Tunnels,  265. 

. Flow  of  water  through,  147. 
Turbines,  158. 

Turnouts,  413. 

Two-phase  alternators,  226. 


636 


INDEX. 


Undercasts,  393. 

Undercutting,  283. 

Underground  prospecting,  239. 
supports,  267. 
surveying,  56,  67. 

Underhand  stoping,  316. 

Undersetting  of  props,  267,  276,  277. 
Undershot  wheels,  157. 

Unequal  splits  of  air.  374. 

Units  of  electricity,  203. 

of  resistance,  Electric,  203. 
of  work,  Electric,  205. 

Unloading  coal,  Cost  of,  447. 

Useful  horsepower  during  winding, 
To  find,  397. 

Use  of  compass,  39. 

Vacuum  Pumps,  164. 

V acuum  system  of  ventilation,  386. 
Value  of  a'fuel,  166. 

Values  of  explosives,  335. 

Valves,  Pump,  162. 

Safety,  185. 

Variation,  Barometric,  339. 

of  ventilation  elements,  372. 

To  turn  off  the,  39. 

Velocity,  Coefficient  of  (water),  135. 
of  air-current,  364. 
of  a water  jet,  135. 
of  water  through  pump  passages, 
±60. 

Ventilating  currents,  Measurements 
of,  364. 

Ventilation  elements,  363. 

elements,  Variation  of,  372. 
formulas,  370. 
in  shaft  sinking,  263. 
methods  and  appliances,  381. 
of  Mines,  337. 

of  rise  and  dip  workings,  382. 
Ventilators,  Mechanical,  385. 
Verniers,  Reading,  39. 

Versed  sine,  35. 

Vertical  angle,  51. 

curves  on  slopes,  416. 
distances,  50,  87,  537. 
distances,  stadia  table,  87. 

V Notch,  137. 

Volatile  combustible  matter  of  coal, 
171,  174. 

Volume  and  absolute  pressure,  345. 
and  absolute  temperature,  Rela- 
tion of,  345. 

Atomic,  341. 

Measures  of,  5. 

Specific,  341. 

Waddle  Ventilator,  387. 

Wall  plates,  270. 

Wardle’s  formula  for  shaft  pillars,  2S5. 
Washers,  Ore  and  coal,  436. 

Weight  of,  116. 

Waste  gates,  146. 
ways,  155. 

Water,  Battery,  430. 
buckets,  164. 

column  corresponding  to  any 
mercury  column,  340. 


Water  elevators,  164. 

flow  through  orifices,  135. 
gauge.  186,  365. 

Gauging,  136. 
level,  186. 
memoranda,  163. 
power,  156. 

raised  by  single-acting  lift  pump. 
162. 

weight  of,  107, 130. 

Waterproof  push  button,  234. 
Waterwheels,  157. 

See  Wheels. 

Watt-hour,  205. 

Weather-proof  wire,  212. 

Wedge,  93. 

Weight,  Apothecaries’,  1. 

Atomic,  344. 

Avoirdupois,  2. 

Metric,  2. 

Troy,  1. 

Weight  of  atmosphere,  337. 

boltheads,  nuts,  and  washers,  116. 

bolts,  116. 

castings,  111. 

chains,  130. 

coal,  170. 

flat  wrought  iron,  115. 
gases,  344. 
iron  pipe,  113. 
materials,  102. 

plates  of  steel,  wrought  iron,  etc., 
112. 

standard  steel  buckets,  446. 
water,  107,  130. 
wire  ropes.  119. 

■wrought  iron,  114. 

Weight  on  pillars  at  different  depths, 
Table  of,  287. 

Weights  and  measures,  7. 

Weir  discharge,  140. 

Weirs,  138. 

Well  drilling.  Cost  of.  242. 

West  Virginia  method  of  mining. 
296. 

West  Vulcan  telephone  system,  234. 
Wheel  and  axle,  92. 

Wheels,  Water,  157. 

Breast,  157. 

Impulse,  158. 

Overshot,  158. 

Turbines,  158. 

Undershot,  157. 

Whitedamp,  349. 

Whiting  system  of  hoisting,  395. 
Williams’  'method  of  mining,  312. 
Wing  dams,  156. 

Winslow,  Arthur,  81. 

Winzes,  316. 

Wire  gauge  122k,  207. 

nails,  114. 

Wire  rope,  118. 

calculations,  124. 
fastenings.  126. 
flattened-strand  rope,  122. 
glossary,  Z22h. 

Inspection  of,  124b. 

Life  of,  1221. 


INDEX 


637 


Wire  rope  lubrication,  124b. 

size  of  drums  for,  1221. 
splicing,  127. 

suspension  cableways,  122b. 
tramways,  122c. 
transmission  of  power  by, 122d. 


Wear  of,  124b. 

Weight  and  strength  of,  119. 
Wiring,  Bell,  230. 

Electric,  207. 

Wolf  lamp,  358. 

Wood,  Crushing  load  of,  105. 


Wood  fuel,  Value  of,  166. 

screws,  113. 

Wooden  beams,  102. 

Constants  for,  103. 
dams,  154. 

Working  load  for  wire  rope,  120. 

Methods  of,  277. 

Wrought  iron.  Fl^t,  115. 

Wyoming  region,  Costs  of  mining  m 
325. 

Zinc,  Weight  of,  111. 


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Practical  Promotion 
For  Mine  Employes 


The  use  of  labor-saving  machinery  and  the  State  mine-exam- 
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Metallurgist 
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The  I.  C.  S.  Courses  in  Coal  Mining  have  been  remarkably  suc- 
cessful in  enabling  coal  miners  to  secure  the  knowledge  of  their 
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Arithmetic 
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Logarithms 

Geometry  and  Trigonometry 
Geometrical  Drawing 
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Properties  of  Gases 
Mine  Gases 
Mine  Ventilation 
Geology  of  Coal 
Examination  of  Coal  Properties 
Rock  Boring 
Rock  Drilling 
Explosives  and  Blasting 
Drifts,  Slopes,  and  Shafts 
Methods  of  Working 
Mechanics 
Fuels 

Steam  and  Steam  Boilers 
Steam  Engines 
Air  Compression 
Elements  of  Electricity  and 

Magnetism 

Direct-Current  Dynamos  and 

Motors 

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Alternating  - Current  Machin- 
ery 

Operation  of  Dynamo-Electric 
Machinery 

Transmission,  Lighting,  and 
Signaling 

Coal-Cutting  Machinery 

Trackwork 

Timbering 

Timber  Trees 

Hoisting 

Haulage 

Hydromechanics 
Mine  Drainage 
Mine  Pumps 

Surface  Arrangements  at  Bitu- 
minous Mines 

Surface  Arrangements  at  An- 
thracite Mines 
Preparation  of  Anthracite 
Coal  Washing 
Principles  of  Coking 
Coking  in  the  Beehive  Oven 
By-Product  Coking 
First  Aid  to  the  Injured 


2 


Advancement 
For  Metal  Miners 


As  in  coal  mining,  the  man  who  wishes  to  rise  in  the  metal- 
mining profession  must  secure  a knowledge  of  the  theory  and 
science  of  modern  metal  mining.  A large  amount  of  money 
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many  ways  the  most  valuable  source  of  knowledge  on  mining 
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Arithmetic 

Formulas 

Geometry  and  Trigonometry 
Logarithms  (Optional) 
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Fuels 

Mine  Surveying 
Metal-Mine  Surveying 
Mineral-Land  Surveying 
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Air  Compression 
Elements  of  Electricity  and 
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Direct-Current  Dynamos  and 
Motors 

Alternating-Current  Machinery 
Operation  of  Dynamo-Electric 
Machinery 

Transmission,  Lighting,  and 
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Hydromechanics 
Mine  Pumps 
Hoisting 


Haulage 
Mine  Drainage 
Rock  Boring 
Rock  Drilling 
Explosives  and  Blasting 
Timber  Trees 
Gas  and  Oil  Engines 
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Engines 

Ore  Dressing  and  Milling 
Theoretical  Chemistry 
Practical  Chemistry 
Elementary  Inorganic  Chemis- 
' try 

Blowpiping 

Mineralogy 

Geology 

Prospecting 

Assaying 

Placer  Mining 

Surface  Arrangements  at  Ore 
Mines 

Preliminary  Operations 
Ore  Mining 

Supporting  Excavations 


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Training 


Mechanical  Engineering 
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and  there  is  no  reason  why  they  should  not  be  of  the  same 
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